Abstract

Topological photonics provides a novel route for designing and realizing optical devices with unprecedented functionalities. Topological edge states, which are supported at the boundary of two photonic systems with different band topologies, enable robust light transport immune to structural imperfections and/or sharp bends in waveguides. Furthermore, the topological edge states are expected to revolutionize cavity-based optical devices such as lasers. Optical devices with built-in topological protection with a small footprint are fascinating as on-chip optical devices for low-loss and functional photonic integrated circuits. Semiconductor photonic crystals are promising platforms enabling the miniaturization of topological optical devices. Herein, we review the recent realizations of semiconductor topological photonic crystals. In particular, we discuss topological waveguides in valley photonic crystals, which have received increasing attention because of their simple realization. In addition, we provide recent demonstrations of topological nanocavities, which are another key component of topological nanophotonics. Progress in semiconductor topological photonic crystals will propel the use of topological photonic devices in various applications as well as deepen the understanding of topological photonic phenomena at the wavelength scale.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Topological photonics [17], which has been receiving significant attention, offers a new approach for controlling light waves based on the concept of band topology. Photonic states with topological origin can equip optical devices with novel functionalities that cannot be realized by conventional approaches. Haldane and Raghu theoretically demonstrated that a photonic crystal (PhC) with broken time reversal symmetry can exhibit photonic analogue of the quantum Hall effect [8,9]. Photonic chiral edge states appearing at the perimeter of such a PhC can transport light unidirectionally without backscattering even in the presence of structural imperfections and sharp bends. Following the first demonstration of robust waveguiding using a photonic chiral edge state in the microwave regime [10], topologically protected wave propagation utilizing topological edge states in photonic quantum Hall, photonic quantum spin Hall, and photonic quantum valley Hall systems has been observed not only in microwaves [1120] but also in optical and near-infrared ranges. [2124]. Robust single mode lasing from topological edge states in microcavity arrays has been demonstrated [2528].

The capability of guiding light robustly and other intriguing functionalities enabled by topological protection are highly attractive for photonic integrated circuit technology. Currently, photonic integrated circuits are crucial in a wide range of photonic applications including data communication, signal processing, sensing, and quantum photonics [29]. For further progress, it is expected to miniaturize photonic devices while maintaining or even improving their performances. Conventional photonic devices are often sensitive to local structural perturbations, which will become more prominent when the devices are miniaturized further. Hence, topological photonics may address the demand for high-performance photonic circuits densely integrating various optical components.

In this context, semiconductor PhC slabs are promising platforms. The large refractive index of a semiconductor enables a large in-plane photonic bandgap at near-infrared wavelengths while confining light within the semiconductor layer by total internal reflection. Low-loss PhC waveguides [30,31], slow-light devices [3234], and nanocavities with high quality factors (Q) [35] have been developed. PhC waveguides and nanocavities can confine photons strongly, enhancing light-matter interactions dramatically. The enhanced light-matter interactions enable various nanophotonic devices, including low-power photonic processing components [36], nanolasers [3739], and quantum photonic devices [4043]. Harnessing topological states of light in semiconductor PhCs could allow diverse nanophotonic devices with novel functionalities to be realized.

Herein, we review the recent progress in semiconductor topological PhCs primary operating in the near-infrared regime, focusing on the introduction of experimental realizations. First, we discuss topological waveguides in semiconductor PhCs in Section 2. Topological waveguides can be realized using an edge state hosted in photonic analogues of quantum Hall, quantum spin Hall, and quantum valley Hall systems. Among them, we mainly discuss topological waveguides in the valley quantum Hall system, which have recently begun to attract attention because of their ease of realization. The waveguides in the first two systems will be discussed in detail in other review papers in this special issue. Section 3 is dedicated to reviewing topological nanocavities, which include topological nanobeam cavities and nanocavities based on corner states. Finally, we briefly discuss other related topics and provide the prospects in Section 4. This paper will not comprehensively explain the theory of topological photonics itself, the progress in topological photonics in other platforms, and emerging fields such as active and nonlinear topological photonics. Many excellent review papers have been published regarding topological photonics [17]. Review articles focusing on active [44] and nonlinear topological photonics [45] are available as well. Readers can refer to these review papers.

2. Topological waveguides in semiconductor PhCs and their applications

We discuss semiconductor topological PhC waveguides formed by connecting two two-dimensional (2D) PhCs possessing different band topologies side by side. The boundary between the two PhCs can support one-dimensional (1D) topological edge states, which are exploited as a waveguide mode. The properties of the edge states depend on the topological phase of the bulk PhCs: the photonic quantum Hall, quantum spin Hall, and quantum valley Hall phases. In this section, we introduce the features of the edge state in each phase and the corresponding experiments in sequence.

2.1 Topological PhC waveguide in photonic quantum Hall system

Chiral edge states hosted in photonic quantum Hall systems differ significantly from conventional waveguide modes. The chiral edge states can travel only in one direction along the boundary of two PhCs forming a waveguide with no backscattering, even in the presence of structural imperfections [8,9]. To obtain chiral edge states, the time-reversal symmetry of the system should be broken. The strong gyromagnetic effect of vanadium-doped calcium-iron-garnet enabled the realization of chiral edge state in a microwave PhC [10]. However, in the optical domain, only a weak magneto-optical effect is available, making the realization of chiral edges states challenging. Bahari et al. adopted a hybrid approach to break the time-reversal symmetry of a semiconductor PhC [46]. They bonded a semiconductor PhC slab with InGaAsP quantum wells on an yttrium iron garnet film, which is known as one of the best magneto-optical materials at near-infrared wavelengths. Figure 1(a) shows a traveling-wave cavity constructed by surrounding a topological PhC by a trivial PhC. An external magnetic field perpendicular to the plane opens a topological bandgap with a 42-pm width at a wavelength of 1.55 µm in the topological PhC, resulting in the appearance of a chiral edge state at the boundary between two PhCs. Despite the small bandgap, nonreciprocal lasing showing a unidirectional output was demonstrated at room temperature [46]. However, a narrow topological bandgap due to the weak magneto-optical effect hinders the further studies. In fact, one-way propagations in passive devices have not yet been demonstrated.

 

Fig. 1. Semiconductor-based topological PhCs with (a) broken and (b) with preserved time-reversal symmetry, corresponding to photonic quantum Hall and photonic quantum spin Hall systems, respectively. (a) Adapted from [46] with permission from AAAS. Copyright 2017. (b) Adapted from [51] with permission from AAAS. Copyright 2018.

Download Full Size | PPT Slide | PDF

2.2 Topological PhC waveguides in the photonic quantum spin Hall system

Helical edge states in the photonic quantum spin Hall phase can be realized while preserving the time reversal symmetry. Two edge states propagating along opposite directions coexist at the same boundary. They have opposite binary degrees of freedom, that is, opposite photonic pseudospin. The propagation direction of edge states depends on the pseudospin, resulting in robust unidirectional waveguiding by the edge states unless the pseudospin flips.

Helical edge states have been demonstrated in a semiconductor ring-resonator array [22,23,28]. The photonic pseudospins in the system are represented by degenerate whispering gallery modes circulating in opposite directions in each ring resonator. Introducing couplings with a complex phase between two adjacent ring resonators is required to make the system topological. Photonic quantum spin Hall systems can be realized using bianisotropic metamaterials [12,14,47,48]. However, these metamaterials need sophisticated structures in subwavelength scale, which are difficult to be realized for the optical domain.

Wu and Hu [49] proposed another approach for emulating the quantum spin-Hall phase by exploiting the crystalline symmetry of PhCs. Although they discussed a PhC structure consisting of dielectric rods in air, the scheme can be directly applied to semiconductor PhCs because it requires neither a magneto-optical material nor a metamaterial. One year later from the proposal, Barik et al. reported a design of the topological PhC in a semiconductor slab [50]. They arrayed triangular-shaped air holes in a semiconductor slab as shown in Fig. 1(b). In Fig. 1(b), the blue region corresponds to the PhC having a topological bandgap, whereas the PhC in the yellow region has a trivial bandgap. Therefore, the boundary between two PhCs can host helical edge states. A quantum optical interface utilizing the spin-momentum locking of helical edge states was demonstrated [51]. Circularly polarized photons emitted from a single InAs quantum dot (QD) coupled predominantly with one of the counterpropagating edge states, depending on the handedness of photon polarization. In addition, topological protection on the edge states allowed the robust single-photon routing against sharp bends, which indicates that topological waveguides are attractive platforms for chiral quantum optics [52]. Chiral light-matter interactions can be observed in topological ring resonators utilizing helical edge states as well [53,54].

Note that the topological edge states created by this scheme are inherently leaky because the edge states are above the light line. Optical modes above the light line cannot be confined within a PhC slab and will eventually be radiated out through coupling with the free-space modes. This radiation loss limits the propagation length of the edge states [51,55]. Meanwhile, this feature allows the edge state to be observed directly by measuring the radiation from the waveguide [56,57]. The leaky nature elucidates the surface emitting laser using helical edge states [58]. Interestingly, owing to the spin-momentum locking feature of the edge state and the gain saturation, one of helical modes becomes dominant in the lasing process, resulting in vortex laser emission. A surface emitting laser without using an edge state, topological bulk laser, has been also reported [59]. The band edge states of the topological and trivial PhCs have different symmetries, inducing the light reflection at the boundary between two PhCs. This band-inversion-induced reflection is the optical feedback mechanism in the topological bulk laser.

2.3 Topological PhC waveguides in the photonic quantum valley hall system

The other structure garnering significant attention recently is valley PhCs (VPhCs), which are photonic analogues of the quantum valley Hall system. VPhCs can be realized by breaking the spatial inversion symmetry of PhCs originally possessing photonic Dirac cones in their band structures. VPhCs can host topological edge states, referred to as valley kink states. The valley kink states are in below the light line, allowing guiding light without radiation loss in principle.

2.3.1 Valley PhCs

Triangular and honeycomb lattices are the famous basic structures of VPhCs. They have symmetry-protected photonic Dirac cones at the K and K’ points in the Brillouin zone. The photonic valley phase emerges when the degeneracies at the Dirac cones are lifted by breaking spatial inversion symmetry of the lattices. VPhC was originally discussed in a triangular-lattice PhC made of silicon posts [60]. Immediately after the proposal, robust wave propagation utilizing valley kink states has been demonstrated in microwave PhCs [1720] and in an array of optical waveguides [24]. It is noteworthy that the effect of reduced symmetry in triangular and honeycomb lattices has been investigated previously, aiming to open a complete 2D photonic bandgap [6163]. Triangular-shaped air holes arranged in a triangular lattice reduce the crystal symmetry and lift the Dirac degeneracy for the TM mode at the K points, resulting in a complete gap. The complete gap was experimentally confirmed in a silicon PhC slab [62].

Herein, we explain some of the fundamental features of VPhC using a honeycomb-PhC with air holes as an example. Figure 2(a) shows the unit cell of a honeycomb lattice with equilateral triangular air holes located at sublattices A and B as well as the corresponding first Brillouin zone. When the holes at sublattices A and B are of the same size, the PhC has photonic Dirac cones for the TE mode at the K and K’ points (see dashed black curves in Fig. 2(c)), which are protected by time-reversal and spatial inversion symmetries of the original lattice. For structures with different hole sizes at A and B (see Fig. 2(b)), owing to the broken spatial inversion symmetry, the degeneracies at the Dirac points are lifted and a photonic bandgap is opened (see the red curves in Fig. 2(c))), resulting in the emergence of photonic valley Hall phase. The Berry curvature becomes finite at around the K and K’ points and with opposite signs. Interchanging the hole sizes at the sites A and B flips the signs of the Berry curvature at the K and K’ points. This means that the two VPhCs shown in Fig. 1(b) possess different band topologies. The topological invariant characterizing the band topology of a VPhC is known as the valley Chern number [60], which is defined as the integral of the Berry curvature only within half of the Brillouin zone, not over the entire Brillouin zone as for the Chern number characterizing the photonic quantum Hall phase. The sign of valley Chern number reflects the sign of the Berry curvature at the valley of interested. The difference in valley Chern number gives the number of edge states at the K(K’) valley. The valley Chern number is quantized to 1/2 or −1/2 provided that the difference between the hole sizes at the sites A and B is small. Hence, according to the bulk-edge correspondence [64], an interface can host one topological edge state at the most at each valley.

 

Fig. 2. (a) Unit cell of a honeycomb PhC with equilateral triangular air holes and corresponding first Brillouin zone. (b) unit cells of VPhCs with opposite Berry curvatures. (c) TE-mode photonic band structures for the structure shown in (a) (black dashed curves) and for the structures shown in (b) (red curves). Band structures were calculated by two-dimensional plane-wave expansion method using a semiconductor refractive index of 3.4. Note that the two structures in (b) have the same band structure.

Download Full Size | PPT Slide | PDF

Figure 3(a) illustrates zigzag and bearded interfaces, which can support valley kink states. The red and blue curves in Fig. 3(b) show typical dispersion curves for the kink states in the zigzag and bearded interfaces, respectively. Note that the dispersions change when the larger holes face each other at the interface. Both interfaces can support an edge state below the light line (dashed line in Fig. 3(b)), which is in a stark contrast to the helical edge states in topological PhCs based on crystalline symmetry. Although the dispersions are symmetric with respect to the zone center (kx = 0) because of the time-reversal symmetry, backscattering at sharp corners and certain types of defects is well suppressed provide that the inter-valley scattering is negligible [60]. Thus, a VPhC waveguide is expected to function as a compact and low-loss waveguide in integrated photonic circuits.

 

Fig. 3. (a) Zigzag and bearded interfaces. (b) Projected band diagram for interfaces with LL= 1.3a/$\sqrt {3}$ and LS=0.9a/$\sqrt {3}$, where a is the period. Red and blue curves are dispersion curves for edge states at zigzag and bearded interfaces, respectively. Shaded regions show bulk modes. Dashed lines represent light line. Optical modes above the light line couple with radiation modes. Band diagram was calculated using two-dimensional plane-wave expansion method. Refractive index of 3.4 was used for the calculations.

Download Full Size | PPT Slide | PDF

The dispersion of the kink state of a bearded interface shows the band degeneracy at the zone boundary. This degeneracy is protected by glide plane symmetry with respect to the boundary of two VPhCs [6567]. Around the degeneracy point, the dispersion tends to be flat, giving a large group index. This feature was employed to design a single-mode slow-light waveguide in a silicon VPhC [68]. Robust light propagation through sharp corners in a slow-light VPhC waveguide with large group indices of ∼60 was demonstrated using two-dimensional finite-difference time-domain calculations. Another theoretical study suggests that the valley-protected slow light is more robust than trivial waveguides against the disorder-induced backscattering provided that the disorder level is small [69].

2.3.2 Silicon-based VPhC waveguides

Since silicon photonics is a technology underpinning the recent development of photonic integrated circuits [29], the realization of topological nanophotonic devices in silicon platforms is of great importance. Figure 4(a) shows a silicon VPhC with a trapezoidal-shape zigzag interface [70]. The VPhC was designed such that the edge state can guide light at telecommunication wavelengths and was patterned in a 270-nm-thick silicon membrane suspended in air. The transmittance along the interface was almost the same as that through a straight interface, indicating that the back reflection at the sharp turns was suppressed owing to the topological protection [70]. Furthermore, the optical tuning of the transmission of a silicon VPhC waveguide was demonstrated [71]. Free carriers excited in the VPhC by photopumping induced a change in the complex refractive index of silicon, resulting in a shift in transmission spectrum and reduced transmission by ∼85%.

 

Fig. 4. Silicon VPhCs: (a) VPhC waveguide formed in a silicon membrane. (b) SOI VPhC waveguide. (c) topological photon router composed of a microdisk and two VPhC waveguides. (d) Si-based VPhC cavity and (e) beam splitter. (a): Adapted from [70] with permission from Springer Nature: Nature Nanotechnology, Copyright (2019). (b) and (c): Adapted from [73] under a Creative Commons Attribution 4.0 International license. (d) and (e): Adapted from [75] with permission, Copyright (2019).

Download Full Size | PPT Slide | PDF

Silicon-on-insulator (SOI) is a widely used platform in silicon photonics. Collins et al. fabricated a VPhC structure on an SOI platform and confirmed the gap opening induced by spatial inversion symmetry breaking [72]. The first demonstration of robust light propagation in an SOI VPhC waveguide was reported in [73] (Fig. 4(b)). The structural asymmetry with respect to the center of the Si slab layer, in principle, induces a finite TE/TM coupling. However, the coupling is weak enough to preserve the topologically protected light transport at the interface. The spin-momentum locking effect of valley kink states enables the selective excitation of valley kink states of two different interfaces. Figure 4(c) shows a device realizing the selective excitation [73]. A subwavelength micro-disk coupled with two silicon waveguides was located close to the entrance of a VPhC having two bearded interfaces along the K and K’ directions. When light is introduced from silicon waveguides, a phase vortex is excited in the microdisk. The direction of the phase winding depends on the direction from which the light is introduced [74]. The phase vortex can excite the edge state selectively. In fact, in the experiment, either of the edge states along the K or K’ direction was excited with high selectivity depending on the input direction, whereas almost no selectivity was observed in a control experiment using two silicon waveguides instead of VPhC waveguides.

Moreover, resonators and beam splitters in SOI VPhCs have been demonstrated [75]. The topological protection at sharp corners allows the construction of a tortuous cavity, as shown in Fig. 4(d), while maintaining relatively high Q factors. A loaded Q at the telecom band of 1.6 × 104, corresponding to the intrinsic Q of 2 × 104, was experimentally obtained. Figure 4(e) shows a valley-dependent beam splitter. The incident light propagating along the K’ direction excited only the kink states propagating along the K’ direction after the splitting. This result indicates that the beam splitter functions based on the conservation of valley pseudospin. In the demonstration, topological refraction [20] was utilized for efficient coupling between the VPhC waveguide and silicon waveguides at the input and output ports. The coupling efficiency between the VPhC waveguide and the silicon waveguide was estimated to be at least 40%. The development of efficient couplers between a topological waveguide and a conventional waveguide will be more important for the use of topological nanophotonic devices in integrated photonic circuits [70,76].

Although robust light propagation has been demonstrated in recent experiments discussed above, the direct quantification of topological protection has not been reported. A recent experiment using a phase-sensitive near-field microscope technique quantitatively demonstrated the effectiveness of topological protection [77]. In the experiment, the light field propagating in a silicon VPhC waveguide with sharp turns was mapped in the momentum space, enabling the extent of backscattering in the waveguide to be estimated. The results show that VPhC waveguides utilizing valley kink states were about 100 times more robust against backscattering compared with trivial W1 PhC waveguides. This is encouraging when considering the application of topological waveguides in integrated photonics.

2.3.3 VPhC waveguides using III–V semiconductors

PhCs fabricated using IIIV semiconductors with high-quality light emitters and optical gain materials are attractive for active/quantum topological nanophotonics. The first demonstration of a VPhC with light emitters was a GaAs VPhC slab embedding high-density InAs QDs [78]. Figure 5(a) (top) shows a scanning electron microscopy (SEM) image of a GaAs VPhC with a Z-shaped zigzag interface. The QDs around the input grating located on the upper left were optically excited at low temperature. Subsequently, the emission from the output grating at the bottom right was measured. Although the QD ensemble showed a broad emission from 920 to 1,250 nm, in the spectrum measured above the output grating, strong emission was observed only in the range from 1,020 to 1,120 nm, which corresponded to the wavelength range of the edge state. The PL image captured for the transmission wavelength range is shown in Fig. 5(a) (bottom). In addition to clear emission from the output grating, no significant scattering at the corners was observed. These results indicate that the light emitted from the QDs was efficiently guided along the interface, even in the presence of sharp turns in the topological waveguide.

 

Fig. 5. III-V VPhCs with light emitter: (a) SEM image of GaAs VPhC embedding QD light emitters as internal light sources (top) and PL image (bottom). (b) SEM image of VPhC laser with quantum well gain (top), emission spectra at different pumping power (middle), and emission patterns measured at pumping powers indicated in middle panel (bottom). (a): Adapted from [78]. Copyright (2019) The Japan Society of Applied Physics. (b): Adapted with permission from [79] © The Optical Society.

Download Full Size | PPT Slide | PDF

Topological lasers with a small footprint are key for future applications. Noh et al. recently realized a valley PhC laser at a telecommunication wavelength [79]. The authors fabricated a triangular-shaped ring resonator comprised of a zigzag interface between two topologically distinct VPhCs in a III-V membrane containing InGaAsP quantum wells (Fig. 5(b) (top)). The valley edge state below the light line forms high-Q resonant modes that extends throughout the ring cavity. By optimizing the structure such that the difference between the highest and the second-highest Q of these modes is maximized, the authors successfully demonstrated single-mode lasing at 1.55 µm (Fig. 5(b) (middle)). Figure 5(b) (bottom) shows the emission patterns at different pumping powers. Below the threshold, emission was observed over a broad area corresponding to the pump beam size. Above the threshold, strong emission was observed mainly from the vertices of the triangular cavity. The robustness of the lasing against defects is an issue to be investigated in future research.

Valley kink states are also attractive as photonic states available for chiral quantum photonics [52]. Chiral interactions between a single quantum emitter and valley kink states have been investigated using a triangular-shaped ring resonator like Fig. 5(b) (top) [80]. Owing to the suppressed backscattering at the sharp corners of the interface, the cavity hosted two counterpropagating cavity modes preserving the spin-momentum locking property. Photon routing with directionality as high as ∼90% was demonstrated via the chiral interaction between single QDs and the cavity modes [80]. A high directionality of emission from a single QD embedded in a topological ring cavity formed by a bearded interface has been also reported [81]. As shown in Fig. 3(b), two branches of interface modes appeared in a bearded interface. Cavity modes originating from the band at lower frequencies had high Q factors up to 125,000 (in simulation), whereas modes from the band at higher frequencies had smaller Q factors and their fields tended to localize at the corners. This result is consistent with the argument that only the modes belonging to the band at low frequency possesses topological protection when the small holes face each other at the interface [68].

2.3.4 Semiconductor VPhCs for terahertz (THz) waves

The applications of semiconductor VPhCs are not limited to the near-infrared range. The robust transport of THz waves through sharp corners has been observed in a VPhC THz chip fabricated using a high-resistivity 190-µm-thick Si membrane [82]. The error-free real-time transmission of an uncompressed 4K high-definition video through the VPhC chip was demonstrated, indicating the potential of valley kink states as excellent information carriers for on-chip THz communication. Zeng et al. realized a topological THz quantum cascade laser, which is the first electrically driven VPhC laser. The authors formed a triangular ring cavity utilizing a valley kink state in a wafer containing multiple quantum wells, providing optical gain in the THz range via quantum cascade process and realizing multi-mode lasing [83]. In contrast to a laser using trivial guiding modes, the laser emission wavelengths in the topological cavity are insensitive to defects around the cavity. Furthermore, the lasing wavelengths are fixed along the perimeter of the ring cavity. These results show that the wave localization at the corners and defects is sufficiently suppressed due to the topological protection of the valley kink state forming the cavity modes.

3. Topological nanocavity in semiconductor PhC systems

Nanocavities are another key component of integrated photonics. The topological concept can offer a different approach from conventional ones for designing PhC nanocavities. For example, a single-mode optical cavity can be designed deterministically because the presence and number of topological edge states are predictable by knowing the band topologies of two PhCs in contact. In contrast to topological ring cavities utilizing 1D topological edge states, a topological nanocavity has a mode volume close to the diffraction limit, resulting in a significant enhancement in its light-matter interaction. This enhanced interaction will enable the realization of efficient lasers, nonlinear optical devices, and sensors using topological nanocavities. In addition, coupling between topological nanocavities and topological waveguides may offer a new opportunity for exploring intriguing functionalities combining the topological features for both. In this section, we discuss two types of topological nanocavities: nanocavities based on a 0D topological state hosted in a 1D system and nanocavities based on a higher-order topological state appearing at a corner in a 2D PhC system.

3.1 Topological nanocavity in 1D PhC systems

Topological edge states in a 1D system are spatially localized at the edge of the system or at the boundary between two systems with different band topologies, resulting in a state functioning as a standing-wave optical cavity. A representative model of a topological 1D system is the Su-Schrieffer-Heeger (SSH) model initially introduced to describe the electron transport in polyacetylene molecules [84]. 1D arrays of optical waveguides or microcavities have been employed to implement a photonic SSH chain [2527,85,86]. Lasers using the edge states in microcavity-based photonic SSH chains have been demonstrated [2527]. Constructing such an SSH chain using PhC nanocavities is expected to yield a localized state with much a smaller mode volume. Han et al. realized a nanophotonic SSH chain with an array of L3 PhC nanocavities in a 230-nm-thick InP slab containing InGaAs quantum wells [87]. The coupling between adjacent nanocavities was controlled by changing the distance between two cavities (Fig. 6(a)). Topological-edge-state lasing was confirmed based on the emission wavelength and of the near-field distribution of the lasing mode. The robustness of the topological-edge-state lasing was also investigated experimentally.

 

Fig. 6. Topological nanocavities based on edge states in 1D systems. (a) SSH chain comprising L3 nanocavities (top) and emission spectra (bottom) for edge mode lasing (red) and for bulk mode lasing (blue). (b) Schematic of topological nanocavity formed in PhC nanobeam. Blue and red regions have Zak phases of π and 0, respectively. (c) SEM image of topological nanobeam cavity and calculated field distribution of in-gap localized mode. (d) Emission spectra below and above the laser threshold. (a) Adapted from [87] under a Creative Commons Attribution 4.0 International license. (b-d) Adapted from [88] under a Creative Commons Attribution 4.0 International license.

Download Full Size | PPT Slide | PDF

PhC nanobeams are another platform that can support a topological localized state. A topological nanocavity in a GaAs PhC nanobeam and its lasing oscillation have been reported [88]. Figure 6(b) schematically shows the topological nanocavity. The nanocavity is formed at the interface between two topologically distinct PhC nanobeams. The unit cells on both sides of the interface contain two air holes of different sizes. In each cell, one hole is located at the center and the other at the edge. The band topology in 1D systems can be characterized by the Zak phase. Since the unit cells have inversion symmetry, the Zak phase of each photonic band in the system is either as 0 or π [89]. The Zak phase of the first band for the blue region in Fig. 6(a) having a larger hole at the edge is π while the Zak phase for the red unit cell is 0. The nontrivial nature of the band can be recognized by a change in symmetry of the field distribution across the Brillouin zone [44,88]. The presence of a single in-gap mode at the interface between two nanobeam PhCs is guaranteed if the two PhCs have different quantized Zak phases [90]. This unique feature differentiates the topological nanocavity from conventional defect-based PhC nanocavities, in which the single-mode character is not guaranteed in general. Figure 6(c) shows an SEM image of a GaAs topological nanobeam cavity containing InAs QDs as the gain media along with a calculated mode distribution of the in-gap topological mode. Experimentally, the edge mode was identified as a sharp peak in µ-PL spectra measured at a cryogenic temperature. The cavity mode was observed as a single in-gap mode even when the photonic bandgap became narrow as the size difference between the two holes decreased. Lasing oscillation under quasi-CW optical pumping was realized when the pumping power increased (Fig. 6(d)). The experimental Q factor of the mode was 9,600. A spontaneous emission coupling factor of 0.03 for the laser was reported. This large coupling factor is a consequence of the enhanced light-matter interactions in the high Q nanocavity.

Topological physics is also applied to design a high-Q nanocavity in a line-defect PhC waveguide. An effective quasi-periodic bichromatic potential for light can be created by introducing additional air holes in a W1 waveguide with a period of a’, which differs from the period a for the surrounding bulk PhC, along the waveguide axis (Fig. 7(a) and (b)). The system is described by the Aubry-André-Harper model. An extremely high Q factor exceeding 109 with a mode volume of 1.6 (λ/n)3 was designed in a PhC waveguide with such an effective bichromatic potential [91]. An experimental Q of ∼106, which was limited by the scattering loss caused by fabrication imperfections, was obtained in a silicon PhC slab at 1,564 nm (Fig. 7(c)) [92]. A recent theoretical study [93] showed the nontrivial topology of the optical spectrum in a structure with bichiromatic potential and demonstrated the formation of a localized mode at the edge of the potential, which corresponds to a one-way edge state appear in the two dimensional momentum space including one synthetic dimension, i.e., β =a’/a.

 

Fig. 7. Nanocavity formed in effective bichromatic potential in a PhC waveguide. (a) Schematic of the structure. (b) SEM image of a nanocavity with a bichiromatic potential. (c) Measured spectrum indicating the presence of a high Q cavity. Adapted from [92] under a Creative Commons Attribution 4.0 International license.

Download Full Size | PPT Slide | PDF

3.2 Topological nanocavity based on corner states

Another approach for constructing a topological nanocavity is to utilize a topological corner state appearing as a higher-order topological state in a 2D system. The conventional bulk-edge correspondence [64] indicates that an n-dimensional topological system can host (n−1)-dimensional edge states at the boundary. By contrast, the higher-order topological phase recently discovered in condensed matter systems can support topological edge states with more than one dimension lower than that of the system [94,95]. Hence, the higher-order topological state in a 2D system becomes a corner state that is a localized state at the corner of a topological structure. Such a localized state of photons can be utilized as a nanocavity mode. The corner state formed in a 2D platform may facilitate coupling with topological waveguides, enabling the development of novel photonic circuits using topological photonic components.

The corner states originally discussed in condensed matter physics are induced by non zero bulk quadrupole polarization. The photonic counterpart has been realized in microwaves using a gigahertz-frequency reconfigurable microwave circuit [96] and in optical frequencies using a microring cavity array [97]. The unit-cell plaquette consists of a square with four resonators. A synthetic π flux threading each plaquette is introduced by rendering one of the couplings between adjacent resonators negative while keeping the others positive, resulting in the formation of quadrupole corner states. However, no simple mechanism exists for introducing negative coupling in the PhC platform. Recently, a 2D PhC exhibiting the quadrupole topology owing to the glide symmetry has been proposed, and quadrupole corner states were observed in the microwave regime [98]. Since such a quadrupole corner state can be supported only in a photonic bandgap between higher-order photonic bands, a careful design to increase the Q factor will be necessitated for nanocavity applications.

A bulk insulator without bulk quadrupole polarization can host another type of corner state. B. -Y Xie et al. considered a square-lattice PhC with dielectric rods and theoretically demonstrated the appearance of topological corner states with no negative coupling [99]. The corner states appear in the bandgap between the first and second photonic bands and are originated from non-zero bulk dipole polarization instead of non-zero bulk quadrupole polarization.

The first experimental observation of the corner state in the optical regime using a PhC platform was reported in a GaAs PhC slab as depicted schematically in Fig. 8(a) [100]. The unit cells for the topological and trivial lattices are indicated by red and blue squares in Fig. 8(b), respectively. Each contains two square-shaped air holes with sides of different lengths, d1 and d2. One is located at the center, whereas the other at the corner of the unit cell as shown in Fig. 8(b). When d1 = d2, the first and second bands degenerate along the X-M line in the first Brillouin zone and no photonic bandgap appears. Breaking the size symmetry between two holes creates a photonic bandgap between the first and second bands for the TE mode. Figure 8(c) shows the band structure calculated using 2D plane wave expansion method for the trivial and topological PhCs with (d1,d2) = (0.7a, 0.1a), where a is the period. Because the unit cells can be exchanged with each other by shifting one of them by half a period along the x- and y- directions, the trivial and topological PhCs have the same band structure. However, their band topologies characterized by the 2D Zak phase [99,101] are different. The 2D Zak phase ($\theta_{x}^{zak}, \theta_{x}^{zak}$) associated with the first band is (0, 0) for the trivial PhC and ($\pi, \pi$) for the topological PhCs. This is reflected in the field distributions at the band edges. Figure 8(d) shows the magnetic field (Hz) distributions at the X point for the first and second bands in the trivial and topological PhCs. The distributions in the first and second bands for the trivial PhC are symmetric and antisymmetric with respect to the centerline along the y direction, respectively. Meanwhile, each distribution for the topological PhC shows the opposite symmetry. This band inversion is also confirmed at the M point. The same topological transition can be induced by changing the hole position instead of the hole size [102].

 

Fig. 8. PhC nanocavity based on a topological corner state. (a) Schematic of a corner structure constructed using topological and trivial PhCs with square lattice along with a calculated field distribution of a corner mode. (b) Definitions of unit cells for topological and trivial PhCs. Corresponding Brillouin zone is also shown. (c) Photonic band structure for the PhCs with (d1,d2)=(0.7a, 0.1a). (d) Field distributions at X point for the first two bands in trivial (upper) and topological (lower) PhCs. (e) SEM image of a GaAs nanocavity based on a corner state. (f) µ-PL spectrum measured at cryogenic temperature. The peak around 1075 nm is originated form the corner state. Adapted with permission from [100] © The Optical Society.

Download Full Size | PPT Slide | PDF

When a 90° corner is formed by the topological and trivial PhCs, an in-gap localized state at the corner emerges. 3D FDTD simulations indicated that the mode possesses a Q factor over 10,000 and a small mode volume of ∼0.4(λ/n)3. A typical field distribution of the corner mode is shown in Fig. 8(a). The simple 2D-SSH model including only the nearest-neighbor couplings predicts a corner state embedded in a bulk band. Long-range interactions are essential to isolate the corner state from the bulk modes in frequency and to localize the corner state spatially [102]. Long-range interactions in photonic systems also induce a new class of topological corner states, which have been observed in a photonic kagome lattice [103].

The authors of [100] fabricated the structure in a 180-nm-thick GaAs slab, embedding five layers of InAs QDs as internal light sources for characterizing the nanocavity. An SEM image of the structure is shown in Fig. 8(e). Because of fabrication limitations, d1 was set to zero. In µ-PL measurements, a sharp peak was observed at a wavelength of 1,079 nm, which corresponds the corner state (Fig. 8(f)). Specially resolved PL measurements confirmed that the emission was highly localized at the corner. The observed Q factor was ∼2,500 [100]. Independent observations of the corner states in PhCs with dielectric rods have been reported in the microwave regime [104,105]. Photonic corner states realized with no negative coupling have been also observed in optical-waveguide arrays [106,107].

Nanocavity lasers based on the corner state have been demonstrated at cryogenic temperatures [108] and room temperature [102]. The authors of [102] patterned a square-shaped topological PhC surrounded by a trivial PhC into a 230-nm-thick membrane with InGaAsP quantum wells. By optically pumping the area of a corner, lasing oscillation was observed at room temperature (Fig. 9(a)). The spontaneous emission coupling factor of the laser was ∼0.06. A topological nanocavity in a VPhC platform was also experimentally demonstrated (Fig. 9(b)) [109]. A large difference between the hole sizes at the sites A and B indicated in Fig. 3(a) induces a frequency gap between the bulk modes and the valley kink state. Consequently, a state spatially localized at three corners, which the authors termed as the “triad mode”, is formed within the frequency gap. The nanocavity formed in an InGaAsP slab with quantum wells emitting at 1.5 µm exhibited lasing oscillation at room temperature with pulsed optical pumping. The far-field pattern from an isolated corner shows a doughnut shape (Fig. 9(b), right bottom), suggesting the laser beam has an optical singularity [109].

 

Fig. 9. Topological nanocavity lasers based on corner states. (a) SEM images of nanocavity laser based on a corner state in a square lattice (top). Emission spectra from a corner pumped with different pump powers (bottom). (b) SEM image of topological nanocavity laser in a VPhC (top left). Emission pattern of the triad mode (top right). Far field patters (bottom) measured through apertures show in the middle. (a) Adapted from [102] with permission. Copyright (2020) American Chemical Society. (b): Adapted from [109] under a Creative Commons Attribution 4.0 International license.

Download Full Size | PPT Slide | PDF

4. Summary

In this paper, we reviewed the recent progress in semiconductor topological PhCs, focusing on waveguides and nanocavities harnessing topological edge states. We also discussed their applications to lasers and quantum photonics. Table 1 summarizes semiconductor-based topological PhC waveguides and nanocavities we discussed.

Tables Icon

Table 1. Topological waveguides and nanocavities realized in semiconductor-based PhCs

Topological waveguides and nanocavities in semiconductor PhC platform will be fundamental elements for various topological nanophotonic devices, potentially advancing integrated photonics technology. Besides, semiconductor topological PhCs can provide fascinating platforms for exploring the new realms of topological photonics such as nonlinear topological photonics [45,110112] and non-Hermitian topological photonics [113116] on-chip. The progress in these fields could realize novel nanophotonic devices including robust signal processing devices, compact optical switches, and sensors with high sensitivity. Utilizing additional dimensions would be one of the future directions of the field of semiconductor topological PhCs. The introduction of synthetic dimensions in the PhC platform is worth investigating as it may enable the realization of nonreciprocal light propagation without a magneto-optical material [117119]. Compact and high-performance optical isolators are highly demanded in the current integrated photonic circuit technology. The realization of semiconductor topological three-dimensional (3D) PhCs at the optical domain is one of the future challenges. Novel nanophotonic applications leveraging topological physics of gapped and gapless photonic phases in 3D systems [120123] are expected to be discovered. Furthermore, topological 3D PhCs with optical gain would provide a playground for 3D non-Hermitian topological physics.

Semiconductor topological PhCs will gather further attention as a platform of topological nanophotonics. We envision that further advance in semiconductor topological PhCs will open a new frontier of nanophotonics and will pave the way to integrated topological photonics.

Funding

Ministry of Education, Culture, Sports, Science and Technology (17H06138, JP15H05700, JP15H05868); Core Research for Evolutional Science and Technology (JPMJCR19T1); Nippon Sheet Glass Foundation for Materials Science and Engineering; Asahi Glass Foundation.

Acknowledgements

The authors thank T. Yamaguchi, H. Yoshimi, F. Liu, K. Wakabayashi, H. Hatsugai, T. Ozawa, S. Takahashi, T. Baba, K. Kobayashi, and K. Ikeda for fruitful discussions regarding some of the topics discussed herein.

Disclosures

The authors declare no conflicts of interest.

References

1. L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014). [CrossRef]  

2. A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11(12), 763–773 (2017). [CrossRef]  

3. Y. Wu, C. Li, X. Hu, Y. Ao, Y. Zhao, and Q. Gong, “Applications of topological photonics in integrated photonic devices,” Adv. Opt. Mater. 5(18), 1700357 (2017). [CrossRef]  

4. B.-Y. Xie, H.-F. Wang, X.-Y. Zhu, M.-H. Lu, Z. D. Wang, and Y.-F. Chen, “Photonics meets topology,” Opt. Express 26(19), 24531 (2018). [CrossRef]  

5. T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019). [CrossRef]  

6. M. S. Rider, S. J. Palmer, S. R. Pocock, X. Xiao, P. A. Huidobro, and V. Giannini, “A perspective on topological nanophotonics: Current status and future challenges,” J. Appl. Phys. 125(12), 120901 (2019). [CrossRef]  

7. M. Kim, Z. Jacob, and J. Rho, “Recent advances in 2D, 3D and higher-order topological photonics,” Light: Sci. Appl. 9(1), 130 (2020). [CrossRef]  

8. F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013905 (2008). [CrossRef]  

9. S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008). [CrossRef]  

10. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009). [CrossRef]  

11. Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106(9), 093903 (2011). [CrossRef]  

12. W. -Jie Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5(1), 5782 (2014). [CrossRef]  

13. S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015). [CrossRef]  

14. X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, “Robust reconfigurable electromagnetic pathways within a photonic topological insulator,” Nat. Mater. 15(5), 542–548 (2016). [CrossRef]  

15. A. P. Slobozhanyuk, A. B. Khanikaev, D. S. Filonov, D. A. Smirnova, A. E. Miroshnichenko, and Y. S. Kivshar, “Experimental demonstration of topological effects in bianisotropic metamaterials,” Sci. Rep. 6(1), 22270 (2016). [CrossRef]  

16. S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey, “Crystalline metamaterials for topological properties at subwavelength scales,” Nat. Commun. 8(1), 16023 (2017). [CrossRef]  

17. X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017). [CrossRef]  

18. X.-D. Chen, F.-L. Zhao, M. Chen, and J.-W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017). [CrossRef]  

19. Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96(20), 201402 (2017). [CrossRef]  

20. F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018). [CrossRef]  

21. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013). [CrossRef]  

22. M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013). [CrossRef]  

23. S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113(8), 087403 (2014). [CrossRef]  

24. J. Noh, S. Huang, K. P. Chen, and M. C. Rechtsman, “Observation of photonic topological valley Hall edge states,” Phys. Rev. Lett. 120(6), 063902 (2018). [CrossRef]  

25. P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017). [CrossRef]  

26. M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018). [CrossRef]  

27. H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, “Topological hybrid silicon microlasers,” Nat. Commun. 9(1), 981 (2018). [CrossRef]  

28. M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018). [CrossRef]  

29. J. Wang and Y. Long, “On-chip silicon photonic signaling and processing: a review,” Sci. Bull. 63(19), 1267–1310 (2018). [CrossRef]  

30. S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11(22), 2927 (2003). [CrossRef]  

31. E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005). [CrossRef]  

32. X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001). [CrossRef]  

33. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001). [CrossRef]  

34. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]  

35. T. Asano and S. Noda, “Photonic crystal devices in silicon photonics,” Proc. IEEE 106(12), 2183–2195 (2018). [CrossRef]  

36. M. Notomi, K. Nozaki, A. Shinya, S. Matsuo, and E. Kuramochi, “Toward fJ/bit optical communication in a chip,” Opt. Commun. 314, 3–17 (2014). [CrossRef]  

37. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999). [CrossRef]  

38. K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013). [CrossRef]  

39. Y Ota, M Kakuda, K Watanabe, S Iwamoto, and Y Arakawa, “Thresholdless quantum dot nanolaser,” Opt. Express 25(17), 19981 (2017). [CrossRef]  

40. I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 (2008). [CrossRef]  

41. H. Kim, R. Bose, T. C. Shen, G. S. Solomon, and E. Waks, “A quantum logic gate between a solid-state quantum bit and a photon,” Nat. Photonics 7(5), 373–377 (2013). [CrossRef]  

42. R. S. Daveau, K. C. Balram, T. Pregnolato, J. Liu, E. H. Lee, J. D. Song, V. Verma, R. Mirin, S. W. Nam, L. Midolo, S. Stobbe, K. Srinivasan, and P. Lodahl, “Efficient fiber-coupled single-photon source based on quantum dots in a photonic-crystal waveguide,” Optica 4(2), 178 (2017). [CrossRef]  

43. R. Katsumi, Y. Ota, M. Kakuda, S. Iwamoto, and Y. Arakawa, “Transfer-printed single-photon sources coupled to wire waveguides,” Optica 5(6), 691 (2018). [CrossRef]  

44. Y. Ota, K. Takaka, T. Ozawa, A. Amo, Z. Jia, B. Kante, M. Notomi, Y. Arakawa, and S. Iwamoto, “Active Topological Photonics,” Nanophotonics 9(3), 547–567 (2020). [CrossRef]  

45. D. Smirnova, D. Leykam, Y. Chong, and Y. Kivshar, “Nonlinear topological photonics,” Appl. Phys. Rev. 7(2), 021306 (2020). [CrossRef]  

46. B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, “Nonreciprocal lasing in topological cavities of arbitrary geometries,” Science 358(6363), 636–640 (2017). [CrossRef]  

47. A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013). [CrossRef]  

48. A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019). [CrossRef]  

49. H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015). [CrossRef]  

50. S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016). [CrossRef]  

51. S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum interface,” Science 359(6376), 666–668 (2018). [CrossRef]  

52. P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017). [CrossRef]  

53. Y. Yang and Z. H. Hang, “Topological whispering gallery modes in two-dimensional photonic crystal cavities,” Opt. Express 26(16), 21235–21241 (2018). [CrossRef]  

54. M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020). [CrossRef]  

55. E. Sauer, J. P. Vasco, and S. Hughes, “Theory of intrinsic propagation losses in topological edge states of planar photonic crystals,” Phys. Rev. Res. 2(4), 043109 (2020). [CrossRef]  

56. M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018). [CrossRef]  

57. N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, “Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing,” Sci. Adv. 6(10), eaaw4137 (2020). [CrossRef]  

58. Z.-Q. Yang, Z.-K. Shao, H.-Z. Chen, X.-R. Mao, and R.-M. Ma, “Spin-momentum-locked edge mode for topological vortex lasing,” Phys. Rev. Lett. 125(1), 013903 (2020). [CrossRef]  

59. Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020). [CrossRef]  

60. T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016). [CrossRef]  

61. T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two-dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004). [CrossRef]  

62. S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87(6), 061107 (2005). [CrossRef]  

63. F. Wen, S. David, X. Checoury, M. El Kurdi, and P. Boucaud, “Two-dimensional photonic crystals with large complete photonic band gaps in both TE and TM polarizations,” Opt. Express 16(16), 12278–12289 (2008). [CrossRef]  

64. Y. Hatsugai, “Chern number and edge states in the integer quantum Hall effect,” Phys. Rev. Lett. 71(22), 3697–3700 (1993). [CrossRef]  

65. A. Mock, L. Lu, and J. O’Brien, “Space group theory and Fourier space analysis of two-dimensional photonic crystal waveguides,” Phys. Rev. B 81(15), 155115 (2010). [CrossRef]  

66. A. Mock and J. D. O’Brien, “Strategies for reducing the out-of-plane radiation in photonic crystal heterostructure microcavities for continuous wave laser applications,” J. Lightwave Technol. 28(7), 1042–1050 (2010). [CrossRef]  

67. S. Mahmoodian, K. Prindal-Nielsen, I. Söllner, S. Stobbe, and P. Lodahl, “Engineering chiral light–matter interaction in photonic crystal waveguides with slow light,” Opt. Mater. Express 7(1), 43 (2017). [CrossRef]  

68. H. Yoshimi, T. Yamaguchi, Y. Ota, Y. Arakawa, and S. Iwamoto, “Slow light waveguides in topological valley photonic crystal,” Opt. Lett. 45(9), 2648 (2020). [CrossRef]  

69. G. Arregui, J. Gomis-Bresco, C. M. Sotomayor-Torres, and P. D. Garcia, “Quantifying the robustness of topological slow light,” arXiv:2007.15606 (2020).

70. M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, “Robust topologically protected transport in photonic crystals at telecommunication wavelengths,” Nat. Nanotechnol. 14(1), 31–34 (2019). [CrossRef]  

71. M. I. Shalaev, W. Walasik, and N. M. Litchinitser, “Optically tunable topological photonic crystal,” Optica 6(7), 839 (2019). [CrossRef]  

72. M. J. Collins, F. Zhang, R. Bojko, L. Chrostowski, and M. C. Rechtsman, “Integrated optical Dirac physics via inversion symmetry breaking,” Phys. Rev. A 94(6), 063827 (2016). [CrossRef]  

73. X.-T. He, E.-T. Liang, J.-J. Yuan, H.-Y. Qiu, X.-D. Chen, F.-L. Zhao, and J.-W. Dong, “A silicon-on-insulator slab for topological valley transport,” Nat. Commun. 10(1), 872 (2019). [CrossRef]  

74. F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photonics 1(9), 762–767 (2014). [CrossRef]  

75. J. Ma, X. Xi, and X. Sun, “Topological photonic integrated circuits based on valley kink states,” Laser Photonics Rev. 13(12), 1900087 (2019). [CrossRef]  

76. H. Kagami, T. Amemiya, S. Okada, N. Nishiyama, and X. Hu, “Topological converter for high-efficiency coupling between Si wire waveguide and topological waveguide,” Opt. Express 28(22), 33619 (2020). [CrossRef]  

77. S. Arora, T. Bauer, R. Barczyk, E. Verhagen, and L. Kuipers, “Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths,” Light: Sci. Appl. 10, 9 (2021) [CrossRef]  .

78. T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” Appl. Phys. Express 12(6), 062005 (2019). [CrossRef]  

79. W. Noh, H. Nasari, H.-M. Kim, Q. Le-Van, Z. Jia, C.-H. Huang, and B. Kante, “Experimental demonstration of single-mode topologial valley-Hall lasing at telecommuniction wavelength controlled by the degree of asymmetry,” Opt. Lett. 45(15), 4108 (2020). [CrossRef]  

80. S. Barik, A. Karasahin, S. Mittal, E. Waks, and M. Hafezi, “Chiral quantum optics using a topological resonator,” Phys. Rev. B 101(20), 205303 (2020). [CrossRef]  

81. M. J. Mehrabad, A. P. Foster, R. Dost, A. M. Fox, M. S. Skolnick, and L. R. Wilson, “Chiral topological photonics with an embedded quantum emitter,” Optica 7(12), 1690 (2020). [CrossRef]  

82. Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020). [CrossRef]  

83. Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020). [CrossRef]  

84. W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979). [CrossRef]  

85. N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Che, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett. 34(11), 1633 (2009). [CrossRef]  

86. A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, “Topological optical waveguiding in silicon and the transition between topological and trivial defect states,” Phys. Rev. Lett. 116(16), 163901 (2016). [CrossRef]  

87. C Han, M. Lee, S. Callard, C. Seassal, and H. Jeon, “Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array,” Light: Sci. Appl. 8(1), 40 (2019). [CrossRef]  

88. Y. Ota, R. Katsumi, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Topological photonic crystal nanocavity laser,” Commun. Phys. 1(1), 86 (2018). [CrossRef]  

89. J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989). [CrossRef]  

90. M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014). [CrossRef]  

91. F. Alpeggiani, L. C. Andreani, and D. Gerace, “Effective bichromatic potential for ultra-high Q-factor photonic crystal slab cavities,” Appl. Phys. Lett. 107(26), 261110 (2015). [CrossRef]  

92. A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017). [CrossRef]  

93. F. Alpeggiani and L. Kuipers, “Topological edge states in bichromatic photonic crystals,” Optica 6(1), 96 (2019). [CrossRef]  

94. W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Quantized electric multipole insulators,” Science 357(6346), 61–66 (2017). [CrossRef]  

95. W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators,” Phys. Rev. B 96(24), 245115 (2017). [CrossRef]  

96. C. W. Peterson, W. A. Benalcazar, T. L. Hughes, and G. Bahl, “A quantized microwave quadrupole insulator with topologically protected corner states,” Nature 555(7696), 346–350 (2018). [CrossRef]  

97. S. Mittal, V. V. Orre, G. Zhu, M. A. Gorlach, A. Poddubny, and M. Hafezi, “Photonic quadrupole topological phases,” Nat. Photonics 13(10), 692–696 (2019). [CrossRef]  

98. X. Zhou, Z.-K. Lin, W. Lu, Y. Lai, B. Hou, and J.-H. Jiang, “Twisted quadrupole topological photonic crystals,” Laser Photonics Rev. 14(8), 2000010 (2020). [CrossRef]  

99. B. -Y Xie, H.-F. Wang, H. -X Wang, X.-Y Zhu, J.-H. Jiang, M.-H. Lu, and Y. -F. Chen, “Second-order photonic topological insulator with corner states,” Phys. Rev. B 98(20), 205147 (2018). [CrossRef]  

100. Y. Ota, F. Liu, R. Katsumi, K. Watanabe, K. Wakabayashi, Y. Arakawa, and S. Iwamoto, “Photonic crystal nanocavity based on topological corner state,” Optica 6(6), 786 (2019). [CrossRef]  

101. F. Liu, H.-Y. Deng, and K. Wakabayashi, “Topological photonic crystals with zero Berry curvature,” Phys. Rev. B 97(3), 035442 (2018). [CrossRef]  

102. C. Han, M. Kang, and H. Jeon, “Lasing at multidimensional topological states in a two-dimensional photonic crystal structure,” ACS Photonics 7(8), 2027–2036 (2020). [CrossRef]  

103. M. Li, D. Zhirihin, M. Gorlach, X. Ni, Dmitry Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, “Higher-order topological states in photonic kagome crystals with long-range interactions,” Nat. Photonics 14(2), 89–94 (2020). [CrossRef]  

104. B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019). [CrossRef]  

105. X.-D. Chen, W.-M. Deng, F.-L. Shi, F.-L Zhao, M. Chen, and J. -W. Dong, “Direct observation of corner states in second-order topological photonic crystal slabs,” Phys. Rev. Lett. 122(23), 233902 (2019). [CrossRef]  

106. J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, “Topological protection of photonic mid-gap defect modes,” Nat. Photonics 12(7), 408–415 (2018). [CrossRef]  

107. A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” Nat. Photonics 13(10), 697–700 (2019). [CrossRef]  

108. W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020). [CrossRef]  

109. D. Smirnova, A. Tripathi, S. Kruk, M.-S. Hwang, H.-R. Kim, H.-G. Park, and Y. Kivshar, “Room-temperature lasing from nanophotonic topological cavities,” Light: Sci. Appl. 9(1), 127 (2020). [CrossRef]  

110. S. Mittal, E. A. Goldschmidt, and M. Hafezi, “A topological source of quantum light,” Nature 561(7724), 502–506 (2018). [CrossRef]  

111. S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019). [CrossRef]  

112. D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan, D.-Y. Choi, and Y. Kivshar, “Third-harmonic generation in photonic topological metasurfaces,” Phys. Rev. Lett. 123(10), 103901 (2019). [CrossRef]  

113. B. Midya, H. Zhao, and L. Feng, “Non-Hermitian photonics promises exceptional topology of light,” Nat. Commun. 9(1), 2674 (2018). [CrossRef]  

114. R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulide, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14(1), 11–19 (2018). [CrossRef]  

115. Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, “Parity–time symmetry and exceptional points in photonics,” Nat. Mater. 18(8), 783–798 (2019). [CrossRef]  

116. K. Takata and M. Notomi, “Photonic topological insulating phase induced solely by gain and loss,” Phys. Rev. Lett. 121(21), 213902 (2018). [CrossRef]  

117. T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics,” Phys. Rev. A 93(4), 043827 (2016). [CrossRef]  

118. L. Yuan, Q. Lin, M. Xiao, and S. Fan, “Synthetic dimension in photonics,” Optica 5(11), 1396 (2018). [CrossRef]  

119. L. Yuan, Y. Shi, and S. Fan, “Photonic gauge potential in a system with a synthetic frequency dimension,” Opt. Lett. 41(4), 741 (2016). [CrossRef]  

120. L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015). [CrossRef]  

121. J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13(6), 611–617 (2017). [CrossRef]  

122. B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018). [CrossRef]  

123. Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
    [Crossref]
  2. A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11(12), 763–773 (2017).
    [Crossref]
  3. Y. Wu, C. Li, X. Hu, Y. Ao, Y. Zhao, and Q. Gong, “Applications of topological photonics in integrated photonic devices,” Adv. Opt. Mater. 5(18), 1700357 (2017).
    [Crossref]
  4. B.-Y. Xie, H.-F. Wang, X.-Y. Zhu, M.-H. Lu, Z. D. Wang, and Y.-F. Chen, “Photonics meets topology,” Opt. Express 26(19), 24531 (2018).
    [Crossref]
  5. T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
    [Crossref]
  6. M. S. Rider, S. J. Palmer, S. R. Pocock, X. Xiao, P. A. Huidobro, and V. Giannini, “A perspective on topological nanophotonics: Current status and future challenges,” J. Appl. Phys. 125(12), 120901 (2019).
    [Crossref]
  7. M. Kim, Z. Jacob, and J. Rho, “Recent advances in 2D, 3D and higher-order topological photonics,” Light: Sci. Appl. 9(1), 130 (2020).
    [Crossref]
  8. F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013905 (2008).
    [Crossref]
  9. S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
    [Crossref]
  10. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
    [Crossref]
  11. Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106(9), 093903 (2011).
    [Crossref]
  12. W. -Jie Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5(1), 5782 (2014).
    [Crossref]
  13. S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
    [Crossref]
  14. X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, “Robust reconfigurable electromagnetic pathways within a photonic topological insulator,” Nat. Mater. 15(5), 542–548 (2016).
    [Crossref]
  15. A. P. Slobozhanyuk, A. B. Khanikaev, D. S. Filonov, D. A. Smirnova, A. E. Miroshnichenko, and Y. S. Kivshar, “Experimental demonstration of topological effects in bianisotropic metamaterials,” Sci. Rep. 6(1), 22270 (2016).
    [Crossref]
  16. S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey, “Crystalline metamaterials for topological properties at subwavelength scales,” Nat. Commun. 8(1), 16023 (2017).
    [Crossref]
  17. X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
    [Crossref]
  18. X.-D. Chen, F.-L. Zhao, M. Chen, and J.-W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
    [Crossref]
  19. Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96(20), 201402 (2017).
    [Crossref]
  20. F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018).
    [Crossref]
  21. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
    [Crossref]
  22. M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
    [Crossref]
  23. S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113(8), 087403 (2014).
    [Crossref]
  24. J. Noh, S. Huang, K. P. Chen, and M. C. Rechtsman, “Observation of photonic topological valley Hall edge states,” Phys. Rev. Lett. 120(6), 063902 (2018).
    [Crossref]
  25. P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017).
    [Crossref]
  26. M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
    [Crossref]
  27. H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, “Topological hybrid silicon microlasers,” Nat. Commun. 9(1), 981 (2018).
    [Crossref]
  28. M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
    [Crossref]
  29. J. Wang and Y. Long, “On-chip silicon photonic signaling and processing: a review,” Sci. Bull. 63(19), 1267–1310 (2018).
    [Crossref]
  30. S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11(22), 2927 (2003).
    [Crossref]
  31. E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
    [Crossref]
  32. X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
    [Crossref]
  33. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
    [Crossref]
  34. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
    [Crossref]
  35. T. Asano and S. Noda, “Photonic crystal devices in silicon photonics,” Proc. IEEE 106(12), 2183–2195 (2018).
    [Crossref]
  36. M. Notomi, K. Nozaki, A. Shinya, S. Matsuo, and E. Kuramochi, “Toward fJ/bit optical communication in a chip,” Opt. Commun. 314, 3–17 (2014).
    [Crossref]
  37. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
    [Crossref]
  38. K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
    [Crossref]
  39. Y Ota, M Kakuda, K Watanabe, S Iwamoto, and Y Arakawa, “Thresholdless quantum dot nanolaser,” Opt. Express 25(17), 19981 (2017).
    [Crossref]
  40. I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 (2008).
    [Crossref]
  41. H. Kim, R. Bose, T. C. Shen, G. S. Solomon, and E. Waks, “A quantum logic gate between a solid-state quantum bit and a photon,” Nat. Photonics 7(5), 373–377 (2013).
    [Crossref]
  42. R. S. Daveau, K. C. Balram, T. Pregnolato, J. Liu, E. H. Lee, J. D. Song, V. Verma, R. Mirin, S. W. Nam, L. Midolo, S. Stobbe, K. Srinivasan, and P. Lodahl, “Efficient fiber-coupled single-photon source based on quantum dots in a photonic-crystal waveguide,” Optica 4(2), 178 (2017).
    [Crossref]
  43. R. Katsumi, Y. Ota, M. Kakuda, S. Iwamoto, and Y. Arakawa, “Transfer-printed single-photon sources coupled to wire waveguides,” Optica 5(6), 691 (2018).
    [Crossref]
  44. Y. Ota, K. Takaka, T. Ozawa, A. Amo, Z. Jia, B. Kante, M. Notomi, Y. Arakawa, and S. Iwamoto, “Active Topological Photonics,” Nanophotonics 9(3), 547–567 (2020).
    [Crossref]
  45. D. Smirnova, D. Leykam, Y. Chong, and Y. Kivshar, “Nonlinear topological photonics,” Appl. Phys. Rev. 7(2), 021306 (2020).
    [Crossref]
  46. B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, “Nonreciprocal lasing in topological cavities of arbitrary geometries,” Science 358(6363), 636–640 (2017).
    [Crossref]
  47. A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
    [Crossref]
  48. A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019).
    [Crossref]
  49. H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
    [Crossref]
  50. S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
    [Crossref]
  51. S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum interface,” Science 359(6376), 666–668 (2018).
    [Crossref]
  52. P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
    [Crossref]
  53. Y. Yang and Z. H. Hang, “Topological whispering gallery modes in two-dimensional photonic crystal cavities,” Opt. Express 26(16), 21235–21241 (2018).
    [Crossref]
  54. M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020).
    [Crossref]
  55. E. Sauer, J. P. Vasco, and S. Hughes, “Theory of intrinsic propagation losses in topological edge states of planar photonic crystals,” Phys. Rev. Res. 2(4), 043109 (2020).
    [Crossref]
  56. M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
    [Crossref]
  57. N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, “Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing,” Sci. Adv. 6(10), eaaw4137 (2020).
    [Crossref]
  58. Z.-Q. Yang, Z.-K. Shao, H.-Z. Chen, X.-R. Mao, and R.-M. Ma, “Spin-momentum-locked edge mode for topological vortex lasing,” Phys. Rev. Lett. 125(1), 013903 (2020).
    [Crossref]
  59. Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020).
    [Crossref]
  60. T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
    [Crossref]
  61. T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two-dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
    [Crossref]
  62. S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87(6), 061107 (2005).
    [Crossref]
  63. F. Wen, S. David, X. Checoury, M. El Kurdi, and P. Boucaud, “Two-dimensional photonic crystals with large complete photonic band gaps in both TE and TM polarizations,” Opt. Express 16(16), 12278–12289 (2008).
    [Crossref]
  64. Y. Hatsugai, “Chern number and edge states in the integer quantum Hall effect,” Phys. Rev. Lett. 71(22), 3697–3700 (1993).
    [Crossref]
  65. A. Mock, L. Lu, and J. O’Brien, “Space group theory and Fourier space analysis of two-dimensional photonic crystal waveguides,” Phys. Rev. B 81(15), 155115 (2010).
    [Crossref]
  66. A. Mock and J. D. O’Brien, “Strategies for reducing the out-of-plane radiation in photonic crystal heterostructure microcavities for continuous wave laser applications,” J. Lightwave Technol. 28(7), 1042–1050 (2010).
    [Crossref]
  67. S. Mahmoodian, K. Prindal-Nielsen, I. Söllner, S. Stobbe, and P. Lodahl, “Engineering chiral light–matter interaction in photonic crystal waveguides with slow light,” Opt. Mater. Express 7(1), 43 (2017).
    [Crossref]
  68. H. Yoshimi, T. Yamaguchi, Y. Ota, Y. Arakawa, and S. Iwamoto, “Slow light waveguides in topological valley photonic crystal,” Opt. Lett. 45(9), 2648 (2020).
    [Crossref]
  69. G. Arregui, J. Gomis-Bresco, C. M. Sotomayor-Torres, and P. D. Garcia, “Quantifying the robustness of topological slow light,” arXiv:2007.15606 (2020).
  70. M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, “Robust topologically protected transport in photonic crystals at telecommunication wavelengths,” Nat. Nanotechnol. 14(1), 31–34 (2019).
    [Crossref]
  71. M. I. Shalaev, W. Walasik, and N. M. Litchinitser, “Optically tunable topological photonic crystal,” Optica 6(7), 839 (2019).
    [Crossref]
  72. M. J. Collins, F. Zhang, R. Bojko, L. Chrostowski, and M. C. Rechtsman, “Integrated optical Dirac physics via inversion symmetry breaking,” Phys. Rev. A 94(6), 063827 (2016).
    [Crossref]
  73. X.-T. He, E.-T. Liang, J.-J. Yuan, H.-Y. Qiu, X.-D. Chen, F.-L. Zhao, and J.-W. Dong, “A silicon-on-insulator slab for topological valley transport,” Nat. Commun. 10(1), 872 (2019).
    [Crossref]
  74. F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photonics 1(9), 762–767 (2014).
    [Crossref]
  75. J. Ma, X. Xi, and X. Sun, “Topological photonic integrated circuits based on valley kink states,” Laser Photonics Rev. 13(12), 1900087 (2019).
    [Crossref]
  76. H. Kagami, T. Amemiya, S. Okada, N. Nishiyama, and X. Hu, “Topological converter for high-efficiency coupling between Si wire waveguide and topological waveguide,” Opt. Express 28(22), 33619 (2020).
    [Crossref]
  77. S. Arora, T. Bauer, R. Barczyk, E. Verhagen, and L. Kuipers, “Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths,” Light: Sci. Appl. 10, 9 (2021) .
    [Crossref]
  78. T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” Appl. Phys. Express 12(6), 062005 (2019).
    [Crossref]
  79. W. Noh, H. Nasari, H.-M. Kim, Q. Le-Van, Z. Jia, C.-H. Huang, and B. Kante, “Experimental demonstration of single-mode topologial valley-Hall lasing at telecommuniction wavelength controlled by the degree of asymmetry,” Opt. Lett. 45(15), 4108 (2020).
    [Crossref]
  80. S. Barik, A. Karasahin, S. Mittal, E. Waks, and M. Hafezi, “Chiral quantum optics using a topological resonator,” Phys. Rev. B 101(20), 205303 (2020).
    [Crossref]
  81. M. J. Mehrabad, A. P. Foster, R. Dost, A. M. Fox, M. S. Skolnick, and L. R. Wilson, “Chiral topological photonics with an embedded quantum emitter,” Optica 7(12), 1690 (2020).
    [Crossref]
  82. Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020).
    [Crossref]
  83. Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
    [Crossref]
  84. W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979).
    [Crossref]
  85. N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Che, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett.34(11), 1633 (2009).
    [Crossref]
  86. A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, “Topological optical waveguiding in silicon and the transition between topological and trivial defect states,” Phys. Rev. Lett. 116(16), 163901 (2016).
    [Crossref]
  87. C Han, M. Lee, S. Callard, C. Seassal, and H. Jeon, “Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array,” Light: Sci. Appl. 8(1), 40 (2019).
    [Crossref]
  88. Y. Ota, R. Katsumi, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Topological photonic crystal nanocavity laser,” Commun. Phys. 1(1), 86 (2018).
    [Crossref]
  89. J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989).
    [Crossref]
  90. M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
    [Crossref]
  91. F. Alpeggiani, L. C. Andreani, and D. Gerace, “Effective bichromatic potential for ultra-high Q-factor photonic crystal slab cavities,” Appl. Phys. Lett. 107(26), 261110 (2015).
    [Crossref]
  92. A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017).
    [Crossref]
  93. F. Alpeggiani and L. Kuipers, “Topological edge states in bichromatic photonic crystals,” Optica 6(1), 96 (2019).
    [Crossref]
  94. W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Quantized electric multipole insulators,” Science 357(6346), 61–66 (2017).
    [Crossref]
  95. W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators,” Phys. Rev. B 96(24), 245115 (2017).
    [Crossref]
  96. C. W. Peterson, W. A. Benalcazar, T. L. Hughes, and G. Bahl, “A quantized microwave quadrupole insulator with topologically protected corner states,” Nature 555(7696), 346–350 (2018).
    [Crossref]
  97. S. Mittal, V. V. Orre, G. Zhu, M. A. Gorlach, A. Poddubny, and M. Hafezi, “Photonic quadrupole topological phases,” Nat. Photonics 13(10), 692–696 (2019).
    [Crossref]
  98. X. Zhou, Z.-K. Lin, W. Lu, Y. Lai, B. Hou, and J.-H. Jiang, “Twisted quadrupole topological photonic crystals,” Laser Photonics Rev. 14(8), 2000010 (2020).
    [Crossref]
  99. B. -Y Xie, H.-F. Wang, H. -X Wang, X.-Y Zhu, J.-H. Jiang, M.-H. Lu, and Y. -F. Chen, “Second-order photonic topological insulator with corner states,” Phys. Rev. B 98(20), 205147 (2018).
    [Crossref]
  100. Y. Ota, F. Liu, R. Katsumi, K. Watanabe, K. Wakabayashi, Y. Arakawa, and S. Iwamoto, “Photonic crystal nanocavity based on topological corner state,” Optica 6(6), 786 (2019).
    [Crossref]
  101. F. Liu, H.-Y. Deng, and K. Wakabayashi, “Topological photonic crystals with zero Berry curvature,” Phys. Rev. B 97(3), 035442 (2018).
    [Crossref]
  102. C. Han, M. Kang, and H. Jeon, “Lasing at multidimensional topological states in a two-dimensional photonic crystal structure,” ACS Photonics 7(8), 2027–2036 (2020).
    [Crossref]
  103. M. Li, D. Zhirihin, M. Gorlach, X. Ni, Dmitry Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, “Higher-order topological states in photonic kagome crystals with long-range interactions,” Nat. Photonics 14(2), 89–94 (2020).
    [Crossref]
  104. B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019).
    [Crossref]
  105. X.-D. Chen, W.-M. Deng, F.-L. Shi, F.-L Zhao, M. Chen, and J. -W. Dong, “Direct observation of corner states in second-order topological photonic crystal slabs,” Phys. Rev. Lett. 122(23), 233902 (2019).
    [Crossref]
  106. J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, “Topological protection of photonic mid-gap defect modes,” Nat. Photonics 12(7), 408–415 (2018).
    [Crossref]
  107. A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” Nat. Photonics 13(10), 697–700 (2019).
    [Crossref]
  108. W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
    [Crossref]
  109. D. Smirnova, A. Tripathi, S. Kruk, M.-S. Hwang, H.-R. Kim, H.-G. Park, and Y. Kivshar, “Room-temperature lasing from nanophotonic topological cavities,” Light: Sci. Appl. 9(1), 127 (2020).
    [Crossref]
  110. S. Mittal, E. A. Goldschmidt, and M. Hafezi, “A topological source of quantum light,” Nature 561(7724), 502–506 (2018).
    [Crossref]
  111. S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019).
    [Crossref]
  112. D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan, D.-Y. Choi, and Y. Kivshar, “Third-harmonic generation in photonic topological metasurfaces,” Phys. Rev. Lett. 123(10), 103901 (2019).
    [Crossref]
  113. B. Midya, H. Zhao, and L. Feng, “Non-Hermitian photonics promises exceptional topology of light,” Nat. Commun. 9(1), 2674 (2018).
    [Crossref]
  114. R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulide, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14(1), 11–19 (2018).
    [Crossref]
  115. Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, “Parity–time symmetry and exceptional points in photonics,” Nat. Mater. 18(8), 783–798 (2019).
    [Crossref]
  116. K. Takata and M. Notomi, “Photonic topological insulating phase induced solely by gain and loss,” Phys. Rev. Lett. 121(21), 213902 (2018).
    [Crossref]
  117. T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics,” Phys. Rev. A 93(4), 043827 (2016).
    [Crossref]
  118. L. Yuan, Q. Lin, M. Xiao, and S. Fan, “Synthetic dimension in photonics,” Optica 5(11), 1396 (2018).
    [Crossref]
  119. L. Yuan, Y. Shi, and S. Fan, “Photonic gauge potential in a system with a synthetic frequency dimension,” Opt. Lett. 41(4), 741 (2016).
    [Crossref]
  120. L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
    [Crossref]
  121. J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13(6), 611–617 (2017).
    [Crossref]
  122. B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
    [Crossref]
  123. Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
    [Crossref]

2021 (1)

S. Arora, T. Bauer, R. Barczyk, E. Verhagen, and L. Kuipers, “Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths,” Light: Sci. Appl. 10, 9 (2021) .
[Crossref]

2020 (20)

H. Kagami, T. Amemiya, S. Okada, N. Nishiyama, and X. Hu, “Topological converter for high-efficiency coupling between Si wire waveguide and topological waveguide,” Opt. Express 28(22), 33619 (2020).
[Crossref]

W. Noh, H. Nasari, H.-M. Kim, Q. Le-Van, Z. Jia, C.-H. Huang, and B. Kante, “Experimental demonstration of single-mode topologial valley-Hall lasing at telecommuniction wavelength controlled by the degree of asymmetry,” Opt. Lett. 45(15), 4108 (2020).
[Crossref]

S. Barik, A. Karasahin, S. Mittal, E. Waks, and M. Hafezi, “Chiral quantum optics using a topological resonator,” Phys. Rev. B 101(20), 205303 (2020).
[Crossref]

M. J. Mehrabad, A. P. Foster, R. Dost, A. M. Fox, M. S. Skolnick, and L. R. Wilson, “Chiral topological photonics with an embedded quantum emitter,” Optica 7(12), 1690 (2020).
[Crossref]

Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020).
[Crossref]

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

X. Zhou, Z.-K. Lin, W. Lu, Y. Lai, B. Hou, and J.-H. Jiang, “Twisted quadrupole topological photonic crystals,” Laser Photonics Rev. 14(8), 2000010 (2020).
[Crossref]

C. Han, M. Kang, and H. Jeon, “Lasing at multidimensional topological states in a two-dimensional photonic crystal structure,” ACS Photonics 7(8), 2027–2036 (2020).
[Crossref]

M. Li, D. Zhirihin, M. Gorlach, X. Ni, Dmitry Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, “Higher-order topological states in photonic kagome crystals with long-range interactions,” Nat. Photonics 14(2), 89–94 (2020).
[Crossref]

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

D. Smirnova, A. Tripathi, S. Kruk, M.-S. Hwang, H.-R. Kim, H.-G. Park, and Y. Kivshar, “Room-temperature lasing from nanophotonic topological cavities,” Light: Sci. Appl. 9(1), 127 (2020).
[Crossref]

M. Kim, Z. Jacob, and J. Rho, “Recent advances in 2D, 3D and higher-order topological photonics,” Light: Sci. Appl. 9(1), 130 (2020).
[Crossref]

Y. Ota, K. Takaka, T. Ozawa, A. Amo, Z. Jia, B. Kante, M. Notomi, Y. Arakawa, and S. Iwamoto, “Active Topological Photonics,” Nanophotonics 9(3), 547–567 (2020).
[Crossref]

D. Smirnova, D. Leykam, Y. Chong, and Y. Kivshar, “Nonlinear topological photonics,” Appl. Phys. Rev. 7(2), 021306 (2020).
[Crossref]

N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, “Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing,” Sci. Adv. 6(10), eaaw4137 (2020).
[Crossref]

Z.-Q. Yang, Z.-K. Shao, H.-Z. Chen, X.-R. Mao, and R.-M. Ma, “Spin-momentum-locked edge mode for topological vortex lasing,” Phys. Rev. Lett. 125(1), 013903 (2020).
[Crossref]

Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020).
[Crossref]

M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020).
[Crossref]

E. Sauer, J. P. Vasco, and S. Hughes, “Theory of intrinsic propagation losses in topological edge states of planar photonic crystals,” Phys. Rev. Res. 2(4), 043109 (2020).
[Crossref]

H. Yoshimi, T. Yamaguchi, Y. Ota, Y. Arakawa, and S. Iwamoto, “Slow light waveguides in topological valley photonic crystal,” Opt. Lett. 45(9), 2648 (2020).
[Crossref]

2019 (19)

M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, “Robust topologically protected transport in photonic crystals at telecommunication wavelengths,” Nat. Nanotechnol. 14(1), 31–34 (2019).
[Crossref]

M. I. Shalaev, W. Walasik, and N. M. Litchinitser, “Optically tunable topological photonic crystal,” Optica 6(7), 839 (2019).
[Crossref]

A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019).
[Crossref]

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

M. S. Rider, S. J. Palmer, S. R. Pocock, X. Xiao, P. A. Huidobro, and V. Giannini, “A perspective on topological nanophotonics: Current status and future challenges,” J. Appl. Phys. 125(12), 120901 (2019).
[Crossref]

Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, “Parity–time symmetry and exceptional points in photonics,” Nat. Mater. 18(8), 783–798 (2019).
[Crossref]

A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” Nat. Photonics 13(10), 697–700 (2019).
[Crossref]

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019).
[Crossref]

X.-D. Chen, W.-M. Deng, F.-L. Shi, F.-L Zhao, M. Chen, and J. -W. Dong, “Direct observation of corner states in second-order topological photonic crystal slabs,” Phys. Rev. Lett. 122(23), 233902 (2019).
[Crossref]

S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019).
[Crossref]

D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan, D.-Y. Choi, and Y. Kivshar, “Third-harmonic generation in photonic topological metasurfaces,” Phys. Rev. Lett. 123(10), 103901 (2019).
[Crossref]

Y. Ota, F. Liu, R. Katsumi, K. Watanabe, K. Wakabayashi, Y. Arakawa, and S. Iwamoto, “Photonic crystal nanocavity based on topological corner state,” Optica 6(6), 786 (2019).
[Crossref]

F. Alpeggiani and L. Kuipers, “Topological edge states in bichromatic photonic crystals,” Optica 6(1), 96 (2019).
[Crossref]

S. Mittal, V. V. Orre, G. Zhu, M. A. Gorlach, A. Poddubny, and M. Hafezi, “Photonic quadrupole topological phases,” Nat. Photonics 13(10), 692–696 (2019).
[Crossref]

J. Ma, X. Xi, and X. Sun, “Topological photonic integrated circuits based on valley kink states,” Laser Photonics Rev. 13(12), 1900087 (2019).
[Crossref]

X.-T. He, E.-T. Liang, J.-J. Yuan, H.-Y. Qiu, X.-D. Chen, F.-L. Zhao, and J.-W. Dong, “A silicon-on-insulator slab for topological valley transport,” Nat. Commun. 10(1), 872 (2019).
[Crossref]

T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” Appl. Phys. Express 12(6), 062005 (2019).
[Crossref]

C Han, M. Lee, S. Callard, C. Seassal, and H. Jeon, “Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array,” Light: Sci. Appl. 8(1), 40 (2019).
[Crossref]

2018 (23)

Y. Ota, R. Katsumi, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Topological photonic crystal nanocavity laser,” Commun. Phys. 1(1), 86 (2018).
[Crossref]

C. W. Peterson, W. A. Benalcazar, T. L. Hughes, and G. Bahl, “A quantized microwave quadrupole insulator with topologically protected corner states,” Nature 555(7696), 346–350 (2018).
[Crossref]

F. Liu, H.-Y. Deng, and K. Wakabayashi, “Topological photonic crystals with zero Berry curvature,” Phys. Rev. B 97(3), 035442 (2018).
[Crossref]

B. -Y Xie, H.-F. Wang, H. -X Wang, X.-Y Zhu, J.-H. Jiang, M.-H. Lu, and Y. -F. Chen, “Second-order photonic topological insulator with corner states,” Phys. Rev. B 98(20), 205147 (2018).
[Crossref]

B. Midya, H. Zhao, and L. Feng, “Non-Hermitian photonics promises exceptional topology of light,” Nat. Commun. 9(1), 2674 (2018).
[Crossref]

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulide, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14(1), 11–19 (2018).
[Crossref]

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, “Topological protection of photonic mid-gap defect modes,” Nat. Photonics 12(7), 408–415 (2018).
[Crossref]

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

L. Yuan, Q. Lin, M. Xiao, and S. Fan, “Synthetic dimension in photonics,” Optica 5(11), 1396 (2018).
[Crossref]

K. Takata and M. Notomi, “Photonic topological insulating phase induced solely by gain and loss,” Phys. Rev. Lett. 121(21), 213902 (2018).
[Crossref]

S. Mittal, E. A. Goldschmidt, and M. Hafezi, “A topological source of quantum light,” Nature 561(7724), 502–506 (2018).
[Crossref]

B.-Y. Xie, H.-F. Wang, X.-Y. Zhu, M.-H. Lu, Z. D. Wang, and Y.-F. Chen, “Photonics meets topology,” Opt. Express 26(19), 24531 (2018).
[Crossref]

F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018).
[Crossref]

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
[Crossref]

H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, “Topological hybrid silicon microlasers,” Nat. Commun. 9(1), 981 (2018).
[Crossref]

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref]

J. Wang and Y. Long, “On-chip silicon photonic signaling and processing: a review,” Sci. Bull. 63(19), 1267–1310 (2018).
[Crossref]

J. Noh, S. Huang, K. P. Chen, and M. C. Rechtsman, “Observation of photonic topological valley Hall edge states,” Phys. Rev. Lett. 120(6), 063902 (2018).
[Crossref]

T. Asano and S. Noda, “Photonic crystal devices in silicon photonics,” Proc. IEEE 106(12), 2183–2195 (2018).
[Crossref]

R. Katsumi, Y. Ota, M. Kakuda, S. Iwamoto, and Y. Arakawa, “Transfer-printed single-photon sources coupled to wire waveguides,” Optica 5(6), 691 (2018).
[Crossref]

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum interface,” Science 359(6376), 666–668 (2018).
[Crossref]

Y. Yang and Z. H. Hang, “Topological whispering gallery modes in two-dimensional photonic crystal cavities,” Opt. Express 26(16), 21235–21241 (2018).
[Crossref]

M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
[Crossref]

2017 (16)

S. Mahmoodian, K. Prindal-Nielsen, I. Söllner, S. Stobbe, and P. Lodahl, “Engineering chiral light–matter interaction in photonic crystal waveguides with slow light,” Opt. Mater. Express 7(1), 43 (2017).
[Crossref]

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

R. S. Daveau, K. C. Balram, T. Pregnolato, J. Liu, E. H. Lee, J. D. Song, V. Verma, R. Mirin, S. W. Nam, L. Midolo, S. Stobbe, K. Srinivasan, and P. Lodahl, “Efficient fiber-coupled single-photon source based on quantum dots in a photonic-crystal waveguide,” Optica 4(2), 178 (2017).
[Crossref]

B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, “Nonreciprocal lasing in topological cavities of arbitrary geometries,” Science 358(6363), 636–640 (2017).
[Crossref]

Y Ota, M Kakuda, K Watanabe, S Iwamoto, and Y Arakawa, “Thresholdless quantum dot nanolaser,” Opt. Express 25(17), 19981 (2017).
[Crossref]

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017).
[Crossref]

A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11(12), 763–773 (2017).
[Crossref]

Y. Wu, C. Li, X. Hu, Y. Ao, Y. Zhao, and Q. Gong, “Applications of topological photonics in integrated photonic devices,” Adv. Opt. Mater. 5(18), 1700357 (2017).
[Crossref]

S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey, “Crystalline metamaterials for topological properties at subwavelength scales,” Nat. Commun. 8(1), 16023 (2017).
[Crossref]

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref]

X.-D. Chen, F.-L. Zhao, M. Chen, and J.-W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
[Crossref]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96(20), 201402 (2017).
[Crossref]

J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13(6), 611–617 (2017).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Quantized electric multipole insulators,” Science 357(6346), 61–66 (2017).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators,” Phys. Rev. B 96(24), 245115 (2017).
[Crossref]

A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017).
[Crossref]

2016 (8)

A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, “Topological optical waveguiding in silicon and the transition between topological and trivial defect states,” Phys. Rev. Lett. 116(16), 163901 (2016).
[Crossref]

L. Yuan, Y. Shi, and S. Fan, “Photonic gauge potential in a system with a synthetic frequency dimension,” Opt. Lett. 41(4), 741 (2016).
[Crossref]

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics,” Phys. Rev. A 93(4), 043827 (2016).
[Crossref]

X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, “Robust reconfigurable electromagnetic pathways within a photonic topological insulator,” Nat. Mater. 15(5), 542–548 (2016).
[Crossref]

A. P. Slobozhanyuk, A. B. Khanikaev, D. S. Filonov, D. A. Smirnova, A. E. Miroshnichenko, and Y. S. Kivshar, “Experimental demonstration of topological effects in bianisotropic metamaterials,” Sci. Rep. 6(1), 22270 (2016).
[Crossref]

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

M. J. Collins, F. Zhang, R. Bojko, L. Chrostowski, and M. C. Rechtsman, “Integrated optical Dirac physics via inversion symmetry breaking,” Phys. Rev. A 94(6), 063827 (2016).
[Crossref]

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

2015 (4)

H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
[Crossref]

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref]

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref]

F. Alpeggiani, L. C. Andreani, and D. Gerace, “Effective bichromatic potential for ultra-high Q-factor photonic crystal slab cavities,” Appl. Phys. Lett. 107(26), 261110 (2015).
[Crossref]

2014 (6)

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photonics 1(9), 762–767 (2014).
[Crossref]

W. -Jie Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5(1), 5782 (2014).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

M. Notomi, K. Nozaki, A. Shinya, S. Matsuo, and E. Kuramochi, “Toward fJ/bit optical communication in a chip,” Opt. Commun. 314, 3–17 (2014).
[Crossref]

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113(8), 087403 (2014).
[Crossref]

2013 (5)

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
[Crossref]

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

H. Kim, R. Bose, T. C. Shen, G. S. Solomon, and E. Waks, “A quantum logic gate between a solid-state quantum bit and a photon,” Nat. Photonics 7(5), 373–377 (2013).
[Crossref]

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

2011 (1)

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106(9), 093903 (2011).
[Crossref]

2010 (2)

A. Mock, L. Lu, and J. O’Brien, “Space group theory and Fourier space analysis of two-dimensional photonic crystal waveguides,” Phys. Rev. B 81(15), 155115 (2010).
[Crossref]

A. Mock and J. D. O’Brien, “Strategies for reducing the out-of-plane radiation in photonic crystal heterostructure microcavities for continuous wave laser applications,” J. Lightwave Technol. 28(7), 1042–1050 (2010).
[Crossref]

2009 (1)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref]

2008 (5)

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[Crossref]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[Crossref]

F. Wen, S. David, X. Checoury, M. El Kurdi, and P. Boucaud, “Two-dimensional photonic crystals with large complete photonic band gaps in both TE and TM polarizations,” Opt. Express 16(16), 12278–12289 (2008).
[Crossref]

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 (2008).
[Crossref]

2005 (2)

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87(6), 061107 (2005).
[Crossref]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[Crossref]

2004 (1)

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two-dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[Crossref]

2003 (1)

2001 (2)

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[Crossref]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref]

1999 (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref]

1993 (1)

Y. Hatsugai, “Chern number and edge states in the integer quantum Hall effect,” Phys. Rev. Lett. 71(22), 3697–3700 (1993).
[Crossref]

1989 (1)

J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989).
[Crossref]

1979 (1)

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979).
[Crossref]

Alcubilla, R.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two-dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[Crossref]

Alpeggiani, F.

N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, “Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing,” Sci. Adv. 6(10), eaaw4137 (2020).
[Crossref]

F. Alpeggiani and L. Kuipers, “Topological edge states in bichromatic photonic crystals,” Optica 6(1), 96 (2019).
[Crossref]

A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017).
[Crossref]

F. Alpeggiani, L. C. Andreani, and D. Gerace, “Effective bichromatic potential for ultra-high Q-factor photonic crystal slab cavities,” Appl. Phys. Lett. 107(26), 261110 (2015).
[Crossref]

Alù, A.

M. Li, D. Zhirihin, M. Gorlach, X. Ni, Dmitry Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, “Higher-order topological states in photonic kagome crystals with long-range interactions,” Nat. Photonics 14(2), 89–94 (2020).
[Crossref]

A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019).
[Crossref]

M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
[Crossref]

Amemiya, T.

Amo, A.

Y. Ota, K. Takaka, T. Ozawa, A. Amo, Z. Jia, B. Kante, M. Notomi, Y. Arakawa, and S. Iwamoto, “Active Topological Photonics,” Nanophotonics 9(3), 547–567 (2020).
[Crossref]

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017).
[Crossref]

Andler, G.

A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” Nat. Photonics 13(10), 697–700 (2019).
[Crossref]

Andonegui, I.

A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, “Topological optical waveguiding in silicon and the transition between topological and trivial defect states,” Phys. Rev. Lett. 116(16), 163901 (2016).
[Crossref]

Andreani, L. C.

A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017).
[Crossref]

F. Alpeggiani, L. C. Andreani, and D. Gerace, “Effective bichromatic potential for ultra-high Q-factor photonic crystal slab cavities,” Appl. Phys. Lett. 107(26), 261110 (2015).
[Crossref]

Ao, Y.

Y. Wu, C. Li, X. Hu, Y. Ao, Y. Zhao, and Q. Gong, “Applications of topological photonics in integrated photonic devices,” Adv. Opt. Mater. 5(18), 1700357 (2017).
[Crossref]

Arakawa, Y

T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” Appl. Phys. Express 12(6), 062005 (2019).
[Crossref]

Y Ota, M Kakuda, K Watanabe, S Iwamoto, and Y Arakawa, “Thresholdless quantum dot nanolaser,” Opt. Express 25(17), 19981 (2017).
[Crossref]

Arakawa, Y.

Arora, S.

S. Arora, T. Bauer, R. Barczyk, E. Verhagen, and L. Kuipers, “Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths,” Light: Sci. Appl. 10, 9 (2021) .
[Crossref]

Arregui, G.

G. Arregui, J. Gomis-Bresco, C. M. Sotomayor-Torres, and P. D. Garcia, “Quantifying the robustness of topological slow light,” arXiv:2007.15606 (2020).

Asano, T.

T. Asano and S. Noda, “Photonic crystal devices in silicon photonics,” Proc. IEEE 106(12), 2183–2195 (2018).
[Crossref]

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87(6), 061107 (2005).
[Crossref]

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[Crossref]

Bahari, B.

B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, “Nonreciprocal lasing in topological cavities of arbitrary geometries,” Science 358(6363), 636–640 (2017).
[Crossref]

Bahl, G.

C. W. Peterson, W. A. Benalcazar, T. L. Hughes, and G. Bahl, “A quantized microwave quadrupole insulator with topologically protected corner states,” Nature 555(7696), 346–350 (2018).
[Crossref]

Balram, K. C.

Bandres, M. A.

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
[Crossref]

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref]

Barber-Sanz, I.

F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photonics 1(9), 762–767 (2014).
[Crossref]

Barczyk, R.

S. Arora, T. Bauer, R. Barczyk, E. Verhagen, and L. Kuipers, “Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths,” Light: Sci. Appl. 10, 9 (2021) .
[Crossref]

Barik, S.

S. Barik, A. Karasahin, S. Mittal, E. Waks, and M. Hafezi, “Chiral quantum optics using a topological resonator,” Phys. Rev. B 101(20), 205303 (2020).
[Crossref]

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum interface,” Science 359(6376), 666–668 (2018).
[Crossref]

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

Barr, L. E.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Bauer, T.

S. Arora, T. Bauer, R. Barczyk, E. Verhagen, and L. Kuipers, “Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths,” Light: Sci. Appl. 10, 9 (2021) .
[Crossref]

Belov, P. A.

A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019).
[Crossref]

M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
[Crossref]

Benalcazar, W. A.

C. W. Peterson, W. A. Benalcazar, T. L. Hughes, and G. Bahl, “A quantized microwave quadrupole insulator with topologically protected corner states,” Nature 555(7696), 346–350 (2018).
[Crossref]

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, “Topological protection of photonic mid-gap defect modes,” Nat. Photonics 12(7), 408–415 (2018).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Quantized electric multipole insulators,” Science 357(6346), 61–66 (2017).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators,” Phys. Rev. B 96(24), 245115 (2017).
[Crossref]

Bergholtz, E. J.

A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” Nat. Photonics 13(10), 697–700 (2019).
[Crossref]

Bernevig, B. A.

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators,” Phys. Rev. B 96(24), 245115 (2017).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Quantized electric multipole insulators,” Science 357(6346), 61–66 (2017).
[Crossref]

Berthelot, T.

S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey, “Crystalline metamaterials for topological properties at subwavelength scales,” Nat. Commun. 8(1), 16023 (2017).
[Crossref]

Blanco-Redondo, A.

A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, “Topological optical waveguiding in silicon and the transition between topological and trivial defect states,” Phys. Rev. Lett. 116(16), 163901 (2016).
[Crossref]

Bloch, J.

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017).
[Crossref]

Bojko, R.

M. J. Collins, F. Zhang, R. Bojko, L. Chrostowski, and M. C. Rechtsman, “Integrated optical Dirac physics via inversion symmetry breaking,” Phys. Rev. A 94(6), 063827 (2016).
[Crossref]

Bose, R.

H. Kim, R. Bose, T. C. Shen, G. S. Solomon, and E. Waks, “A quantum logic gate between a solid-state quantum bit and a photon,” Nat. Photonics 7(5), 373–377 (2013).
[Crossref]

Boucaud, P.

Bourennane, M.

A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” Nat. Photonics 13(10), 697–700 (2019).
[Crossref]

Bryant, G.

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Che, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett.34(11), 1633 (2009).
[Crossref]

Cai, T.

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum interface,” Science 359(6376), 666–668 (2018).
[Crossref]

Callard, S.

C Han, M. Lee, S. Callard, C. Seassal, and H. Jeon, “Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array,” Light: Sci. Appl. 8(1), 40 (2019).
[Crossref]

Carusotto, I.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics,” Phys. Rev. A 93(4), 043827 (2016).
[Crossref]

Cassagne, D.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[Crossref]

Chan, C. T.

W. -Jie Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5(1), 5782 (2014).
[Crossref]

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106(9), 093903 (2011).
[Crossref]

Chattopadhyay, U.

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

Che, Z.

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Che, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett.34(11), 1633 (2009).
[Crossref]

Checoury, X.

Chen, H.

Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020).
[Crossref]

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

Chen, H.-Z.

Z.-Q. Yang, Z.-K. Shao, H.-Z. Chen, X.-R. Mao, and R.-M. Ma, “Spin-momentum-locked edge mode for topological vortex lasing,” Phys. Rev. Lett. 125(1), 013903 (2020).
[Crossref]

Chen, J.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Chen, K. P.

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, “Topological protection of photonic mid-gap defect modes,” Nat. Photonics 12(7), 408–415 (2018).
[Crossref]

J. Noh, S. Huang, K. P. Chen, and M. C. Rechtsman, “Observation of photonic topological valley Hall edge states,” Phys. Rev. Lett. 120(6), 063902 (2018).
[Crossref]

J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13(6), 611–617 (2017).
[Crossref]

Chen, M.

X.-D. Chen, W.-M. Deng, F.-L. Shi, F.-L Zhao, M. Chen, and J. -W. Dong, “Direct observation of corner states in second-order topological photonic crystal slabs,” Phys. Rev. Lett. 122(23), 233902 (2019).
[Crossref]

X.-D. Chen, F.-L. Zhao, M. Chen, and J.-W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
[Crossref]

Chen, X.-D.

X.-T. He, E.-T. Liang, J.-J. Yuan, H.-Y. Qiu, X.-D. Chen, F.-L. Zhao, and J.-W. Dong, “A silicon-on-insulator slab for topological valley transport,” Nat. Commun. 10(1), 872 (2019).
[Crossref]

X.-D. Chen, W.-M. Deng, F.-L. Shi, F.-L Zhao, M. Chen, and J. -W. Dong, “Direct observation of corner states in second-order topological photonic crystal slabs,” Phys. Rev. Lett. 122(23), 233902 (2019).
[Crossref]

X.-D. Chen, F.-L. Zhao, M. Chen, and J.-W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
[Crossref]

W. -Jie Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5(1), 5782 (2014).
[Crossref]

Chen, Y. -F.

B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019).
[Crossref]

B. -Y Xie, H.-F. Wang, H. -X Wang, X.-Y Zhu, J.-H. Jiang, M.-H. Lu, and Y. -F. Chen, “Second-order photonic topological insulator with corner states,” Phys. Rev. B 98(20), 205147 (2018).
[Crossref]

Chen, Y.-F.

Cheng, X.

X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, “Robust reconfigurable electromagnetic pathways within a photonic topological insulator,” Nat. Mater. 15(5), 542–548 (2016).
[Crossref]

Choi, D.-Y.

D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan, D.-Y. Choi, and Y. Kivshar, “Third-harmonic generation in photonic topological metasurfaces,” Phys. Rev. Lett. 123(10), 103901 (2019).
[Crossref]

Chong, Y

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

Chong, Y.

D. Smirnova, D. Leykam, Y. Chong, and Y. Kivshar, “Nonlinear topological photonics,” Appl. Phys. Rev. 7(2), 021306 (2020).
[Crossref]

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018).
[Crossref]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref]

Chong, Y. D.

J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13(6), 611–617 (2017).
[Crossref]

Christodoulide, D. N.

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulide, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14(1), 11–19 (2018).
[Crossref]

Christodoulides, D. N.

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref]

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
[Crossref]

Chrostowski, L.

M. J. Collins, F. Zhang, R. Bojko, L. Chrostowski, and M. C. Rechtsman, “Integrated optical Dirac physics via inversion symmetry breaking,” Phys. Rev. A 94(6), 063827 (2016).
[Crossref]

Clarke, E.

M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020).
[Crossref]

Collins, M. J.

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, “Topological protection of photonic mid-gap defect modes,” Nat. Photonics 12(7), 408–415 (2018).
[Crossref]

M. J. Collins, F. Zhang, R. Bojko, L. Chrostowski, and M. C. Rechtsman, “Integrated optical Dirac physics via inversion symmetry breaking,” Phys. Rev. A 94(6), 063827 (2016).
[Crossref]

A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, “Topological optical waveguiding in silicon and the transition between topological and trivial defect states,” Phys. Rev. Lett. 116(16), 163901 (2016).
[Crossref]

Dang, J.

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref]

Daveau, R. S.

David, S.

Davies, A. G.

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

DeGottardi, W.

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum interface,” Science 359(6376), 666–668 (2018).
[Crossref]

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

Deng, H.-Y.

F. Liu, H.-Y. Deng, and K. Wakabayashi, “Topological photonic crystals with zero Berry curvature,” Phys. Rev. B 97(3), 035442 (2018).
[Crossref]

Deng, W.-M.

X.-D. Chen, W.-M. Deng, F.-L. Shi, F.-L Zhao, M. Chen, and J. -W. Dong, “Direct observation of corner states in second-order topological photonic crystal slabs,” Phys. Rev. Lett. 122(23), 233902 (2019).
[Crossref]

Dong, J.

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96(20), 201402 (2017).
[Crossref]

Dong, J. -W.

X.-D. Chen, W.-M. Deng, F.-L. Shi, F.-L Zhao, M. Chen, and J. -W. Dong, “Direct observation of corner states in second-order topological photonic crystal slabs,” Phys. Rev. Lett. 122(23), 233902 (2019).
[Crossref]

Dong, J.-W.

X.-T. He, E.-T. Liang, J.-J. Yuan, H.-Y. Qiu, X.-D. Chen, F.-L. Zhao, and J.-W. Dong, “A silicon-on-insulator slab for topological valley transport,” Nat. Commun. 10(1), 872 (2019).
[Crossref]

X.-D. Chen, F.-L. Zhao, M. Chen, and J.-W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
[Crossref]

W. -Jie Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5(1), 5782 (2014).
[Crossref]

Dost, R.

M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020).
[Crossref]

M. J. Mehrabad, A. P. Foster, R. Dost, A. M. Fox, M. S. Skolnick, and L. R. Wilson, “Chiral topological photonics with an embedded quantum emitter,” Optica 7(12), 1690 (2020).
[Crossref]

Dreisow, F.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref]

Eggleton, B. J.

A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, “Topological optical waveguiding in silicon and the transition between topological and trivial defect states,” Phys. Rev. Lett. 116(16), 163901 (2016).
[Crossref]

El Amili, A.

B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, “Nonreciprocal lasing in topological cavities of arbitrary geometries,” Science 358(6363), 636–640 (2017).
[Crossref]

El Hassan, A.

A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” Nat. Photonics 13(10), 697–700 (2019).
[Crossref]

El Kurdi, M.

El-Ganainy, R.

H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, “Topological hybrid silicon microlasers,” Nat. Commun. 9(1), 981 (2018).
[Crossref]

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulide, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14(1), 11–19 (2018).
[Crossref]

Englund, D.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 (2008).
[Crossref]

Faez, S.

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113(8), 087403 (2014).
[Crossref]

Fainman, Y.

B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, “Nonreciprocal lasing in topological cavities of arbitrary geometries,” Science 358(6363), 636–640 (2017).
[Crossref]

Fan, J.

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113(8), 087403 (2014).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
[Crossref]

Fan, S.

Fang, C.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Faraon, A.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 (2008).
[Crossref]

Farrer, I.

M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020).
[Crossref]

Feng, L.

H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, “Topological hybrid silicon microlasers,” Nat. Commun. 9(1), 981 (2018).
[Crossref]

B. Midya, H. Zhao, and L. Feng, “Non-Hermitian photonics promises exceptional topology of light,” Nat. Commun. 9(1), 2674 (2018).
[Crossref]

Filonov, D. S.

A. P. Slobozhanyuk, A. B. Khanikaev, D. S. Filonov, D. A. Smirnova, A. E. Miroshnichenko, and Y. S. Kivshar, “Experimental demonstration of topological effects in bianisotropic metamaterials,” Sci. Rep. 6(1), 22270 (2016).
[Crossref]

Filonov, Dmitry

M. Li, D. Zhirihin, M. Gorlach, X. Ni, Dmitry Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, “Higher-order topological states in photonic kagome crystals with long-range interactions,” Nat. Photonics 14(2), 89–94 (2020).
[Crossref]

Fink, M.

S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey, “Crystalline metamaterials for topological properties at subwavelength scales,” Nat. Commun. 8(1), 16023 (2017).
[Crossref]

Fleury, R.

S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey, “Crystalline metamaterials for topological properties at subwavelength scales,” Nat. Commun. 8(1), 16023 (2017).
[Crossref]

Flower, C.

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum interface,” Science 359(6376), 666–668 (2018).
[Crossref]

Foster, A. P.

M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020).
[Crossref]

M. J. Mehrabad, A. P. Foster, R. Dost, A. M. Fox, M. S. Skolnick, and L. R. Wilson, “Chiral topological photonics with an embedded quantum emitter,” Optica 7(12), 1690 (2020).
[Crossref]

Fox, A. M.

Fromherz, T.

A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017).
[Crossref]

Fu, L.

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref]

Fujita, M.

Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020).
[Crossref]

Fushman, I.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 (2008).
[Crossref]

Galli, M.

A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017).
[Crossref]

Galopin, E.

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017).
[Crossref]

Gao, F.

F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018).
[Crossref]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96(20), 201402 (2017).
[Crossref]

Gao, W.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Gao, Z.

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96(20), 201402 (2017).
[Crossref]

Garcia, P. D.

G. Arregui, J. Gomis-Bresco, C. M. Sotomayor-Torres, and P. D. Garcia, “Quantifying the robustness of topological slow light,” arXiv:2007.15606 (2020).

Genack, A. Z.

X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, “Robust reconfigurable electromagnetic pathways within a photonic topological insulator,” Nat. Mater. 15(5), 542–548 (2016).
[Crossref]

Gerace, D.

A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017).
[Crossref]

F. Alpeggiani, L. C. Andreani, and D. Gerace, “Effective bichromatic potential for ultra-high Q-factor photonic crystal slab cavities,” Appl. Phys. Lett. 107(26), 261110 (2015).
[Crossref]

Giannini, V.

M. S. Rider, S. J. Palmer, S. R. Pocock, X. Xiao, P. A. Huidobro, and V. Giannini, “A perspective on topological nanophotonics: Current status and future challenges,” J. Appl. Phys. 125(12), 120901 (2019).
[Crossref]

Goblot, V.

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017).
[Crossref]

Goldman, N.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics,” Phys. Rev. A 93(4), 043827 (2016).
[Crossref]

Goldschmidt, E. A.

S. Mittal, E. A. Goldschmidt, and M. Hafezi, “A topological source of quantum light,” Nature 561(7724), 502–506 (2018).
[Crossref]

Gomis-Bresco, J.

G. Arregui, J. Gomis-Bresco, C. M. Sotomayor-Torres, and P. D. Garcia, “Quantifying the robustness of topological slow light,” arXiv:2007.15606 (2020).

Gong, Q.

Y. Wu, C. Li, X. Hu, Y. Ao, Y. Zhao, and Q. Gong, “Applications of topological photonics in integrated photonic devices,” Adv. Opt. Mater. 5(18), 1700357 (2017).
[Crossref]

Gorlach, M.

M. Li, D. Zhirihin, M. Gorlach, X. Ni, Dmitry Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, “Higher-order topological states in photonic kagome crystals with long-range interactions,” Nat. Photonics 14(2), 89–94 (2020).
[Crossref]

Gorlach, M. A.

S. Mittal, V. V. Orre, G. Zhu, M. A. Gorlach, A. Poddubny, and M. Hafezi, “Photonic quadrupole topological phases,” Nat. Photonics 13(10), 692–696 (2019).
[Crossref]

M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
[Crossref]

Grillet, C.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[Crossref]

Griol, A.

F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photonics 1(9), 762–767 (2014).
[Crossref]

Guo, Q.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Hafezi, M.

S. Barik, A. Karasahin, S. Mittal, E. Waks, and M. Hafezi, “Chiral quantum optics using a topological resonator,” Phys. Rev. B 101(20), 205303 (2020).
[Crossref]

S. Mittal, V. V. Orre, G. Zhu, M. A. Gorlach, A. Poddubny, and M. Hafezi, “Photonic quadrupole topological phases,” Nat. Photonics 13(10), 692–696 (2019).
[Crossref]

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum interface,” Science 359(6376), 666–668 (2018).
[Crossref]

S. Mittal, E. A. Goldschmidt, and M. Hafezi, “A topological source of quantum light,” Nature 561(7724), 502–506 (2018).
[Crossref]

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113(8), 087403 (2014).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
[Crossref]

Haldane, F. D. M.

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[Crossref]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref]

Han, C

C Han, M. Lee, S. Callard, C. Seassal, and H. Jeon, “Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array,” Light: Sci. Appl. 8(1), 40 (2019).
[Crossref]

Han, C.

C. Han, M. Kang, and H. Jeon, “Lasing at multidimensional topological states in a two-dimensional photonic crystal structure,” ACS Photonics 7(8), 2027–2036 (2020).
[Crossref]

Han, D.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref]

Hang, Z. H.

Hao, H.

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

Harari, G.

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
[Crossref]

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref]

A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, “Topological optical waveguiding in silicon and the transition between topological and trivial defect states,” Phys. Rev. Lett. 116(16), 163901 (2016).
[Crossref]

Hasebe, K.

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

Hatsugai, Y.

Y. Hatsugai, “Chern number and edge states in the integer quantum Hall effect,” Phys. Rev. Lett. 71(22), 3697–3700 (1993).
[Crossref]

He, M.

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

He, X.-T.

X.-T. He, E.-T. Liang, J.-J. Yuan, H.-Y. Qiu, X.-D. Chen, F.-L. Zhao, and J.-W. Dong, “A silicon-on-insulator slab for topological valley transport,” Nat. Commun. 10(1), 872 (2019).
[Crossref]

Heeger, A. J.

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979).
[Crossref]

Heffernan, J.

M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020).
[Crossref]

Hibbins, A.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Hodaei, H.

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
[Crossref]

Hou, B.

X. Zhou, Z.-K. Lin, W. Lu, Y. Lai, B. Hou, and J.-H. Jiang, “Twisted quadrupole topological photonic crystals,” Laser Photonics Rev. 14(8), 2000010 (2020).
[Crossref]

Hromada, I.

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Che, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett.34(11), 1633 (2009).
[Crossref]

Hu, X.

Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020).
[Crossref]

H. Kagami, T. Amemiya, S. Okada, N. Nishiyama, and X. Hu, “Topological converter for high-efficiency coupling between Si wire waveguide and topological waveguide,” Opt. Express 28(22), 33619 (2020).
[Crossref]

Y. Wu, C. Li, X. Hu, Y. Ao, Y. Zhao, and Q. Gong, “Applications of topological photonics in integrated photonic devices,” Adv. Opt. Mater. 5(18), 1700357 (2017).
[Crossref]

H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
[Crossref]

Huang, C.-H.

Huang, S.

J. Noh, S. Huang, K. P. Chen, and M. C. Rechtsman, “Observation of photonic topological valley Hall edge states,” Phys. Rev. Lett. 120(6), 063902 (2018).
[Crossref]

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, “Topological protection of photonic mid-gap defect modes,” Nat. Photonics 12(7), 408–415 (2018).
[Crossref]

J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13(6), 611–617 (2017).
[Crossref]

Huang, Y.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref]

Hughes, S.

E. Sauer, J. P. Vasco, and S. Hughes, “Theory of intrinsic propagation losses in topological edge states of planar photonic crystals,” Phys. Rev. Res. 2(4), 043109 (2020).
[Crossref]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[Crossref]

Hughes, T. L.

C. W. Peterson, W. A. Benalcazar, T. L. Hughes, and G. Bahl, “A quantized microwave quadrupole insulator with topologically protected corner states,” Nature 555(7696), 346–350 (2018).
[Crossref]

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, “Topological protection of photonic mid-gap defect modes,” Nat. Photonics 12(7), 408–415 (2018).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Quantized electric multipole insulators,” Science 357(6346), 61–66 (2017).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators,” Phys. Rev. B 96(24), 245115 (2017).
[Crossref]

Huidobro, P. A.

M. S. Rider, S. J. Palmer, S. R. Pocock, X. Xiao, P. A. Huidobro, and V. Giannini, “A perspective on topological nanophotonics: Current status and future challenges,” J. Appl. Phys. 125(12), 120901 (2019).
[Crossref]

Hwang, M.-S.

D. Smirnova, A. Tripathi, S. Kruk, M.-S. Hwang, H.-R. Kim, H.-G. Park, and Y. Kivshar, “Room-temperature lasing from nanophotonic topological cavities,” Light: Sci. Appl. 9(1), 127 (2020).
[Crossref]

Igarashi, Y.

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref]

Ishida, S.

T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” Appl. Phys. Express 12(6), 062005 (2019).
[Crossref]

Iwamoto, S

Iwamoto, S.

Y. Ota, K. Takaka, T. Ozawa, A. Amo, Z. Jia, B. Kante, M. Notomi, Y. Arakawa, and S. Iwamoto, “Active Topological Photonics,” Nanophotonics 9(3), 547–567 (2020).
[Crossref]

H. Yoshimi, T. Yamaguchi, Y. Ota, Y. Arakawa, and S. Iwamoto, “Slow light waveguides in topological valley photonic crystal,” Opt. Lett. 45(9), 2648 (2020).
[Crossref]

T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” Appl. Phys. Express 12(6), 062005 (2019).
[Crossref]

Y. Ota, F. Liu, R. Katsumi, K. Watanabe, K. Wakabayashi, Y. Arakawa, and S. Iwamoto, “Photonic crystal nanocavity based on topological corner state,” Optica 6(6), 786 (2019).
[Crossref]

Y. Ota, R. Katsumi, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Topological photonic crystal nanocavity laser,” Commun. Phys. 1(1), 86 (2018).
[Crossref]

R. Katsumi, Y. Ota, M. Kakuda, S. Iwamoto, and Y. Arakawa, “Transfer-printed single-photon sources coupled to wire waveguides,” Optica 5(6), 691 (2018).
[Crossref]

Jacob, Z.

M. Kim, Z. Jacob, and J. Rho, “Recent advances in 2D, 3D and higher-order topological photonics,” Light: Sci. Appl. 9(1), 130 (2020).
[Crossref]

Jeon, H.

C. Han, M. Kang, and H. Jeon, “Lasing at multidimensional topological states in a two-dimensional photonic crystal structure,” ACS Photonics 7(8), 2027–2036 (2020).
[Crossref]

C Han, M. Lee, S. Callard, C. Seassal, and H. Jeon, “Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array,” Light: Sci. Appl. 8(1), 40 (2019).
[Crossref]

Jia, Z.

Jiang, J.-H.

X. Zhou, Z.-K. Lin, W. Lu, Y. Lai, B. Hou, and J.-H. Jiang, “Twisted quadrupole topological photonic crystals,” Laser Photonics Rev. 14(8), 2000010 (2020).
[Crossref]

B. -Y Xie, H.-F. Wang, H. -X Wang, X.-Y Zhu, J.-H. Jiang, M.-H. Lu, and Y. -F. Chen, “Second-order photonic topological insulator with corner states,” Phys. Rev. B 98(20), 205147 (2018).
[Crossref]

Jiang, S.-J.

W. -Jie Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5(1), 5782 (2014).
[Crossref]

-Jie Chen, W.

W. -Jie Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5(1), 5782 (2014).
[Crossref]

Jin, K.

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

Jin, Y.

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

Joannopoulos, J.

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref]

Joannopoulos, J. D.

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref]

Jouanin, C.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[Crossref]

Jouvaud, C.

X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, “Robust reconfigurable electromagnetic pathways within a photonic topological insulator,” Nat. Mater. 15(5), 542–548 (2016).
[Crossref]

Kagami, H.

Kakitsuka, T.

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

Kakuda, M

Kakuda, M.

Kang, M.

C. Han, M. Kang, and H. Jeon, “Lasing at multidimensional topological states in a two-dimensional photonic crystal structure,” ACS Photonics 7(8), 2027–2036 (2020).
[Crossref]

Kante, B.

Kanté, B.

B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, “Nonreciprocal lasing in topological cavities of arbitrary geometries,” Science 358(6363), 636–640 (2017).
[Crossref]

Karasahin, A.

S. Barik, A. Karasahin, S. Mittal, E. Waks, and M. Hafezi, “Chiral quantum optics using a topological resonator,” Phys. Rev. B 101(20), 205303 (2020).
[Crossref]

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum interface,” Science 359(6376), 666–668 (2018).
[Crossref]

Kargarian, M.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Katsumi, R.

T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” Appl. Phys. Express 12(6), 062005 (2019).
[Crossref]

Y. Ota, F. Liu, R. Katsumi, K. Watanabe, K. Wakabayashi, Y. Arakawa, and S. Iwamoto, “Photonic crystal nanocavity based on topological corner state,” Optica 6(6), 786 (2019).
[Crossref]

Y. Ota, R. Katsumi, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Topological photonic crystal nanocavity laser,” Commun. Phys. 1(1), 86 (2018).
[Crossref]

R. Katsumi, Y. Ota, M. Kakuda, S. Iwamoto, and Y. Arakawa, “Transfer-printed single-photon sources coupled to wire waveguides,” Optica 5(6), 691 (2018).
[Crossref]

Khajavikhan, M.

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref]

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
[Crossref]

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulide, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14(1), 11–19 (2018).
[Crossref]

Khanikaev, A. B.

M. Li, D. Zhirihin, M. Gorlach, X. Ni, Dmitry Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, “Higher-order topological states in photonic kagome crystals with long-range interactions,” Nat. Photonics 14(2), 89–94 (2020).
[Crossref]

A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019).
[Crossref]

M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
[Crossref]

A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11(12), 763–773 (2017).
[Crossref]

X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, “Robust reconfigurable electromagnetic pathways within a photonic topological insulator,” Nat. Mater. 15(5), 542–548 (2016).
[Crossref]

A. P. Slobozhanyuk, A. B. Khanikaev, D. S. Filonov, D. A. Smirnova, A. E. Miroshnichenko, and Y. S. Kivshar, “Experimental demonstration of topological effects in bianisotropic metamaterials,” Sci. Rep. 6(1), 22270 (2016).
[Crossref]

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Kim, H.

H. Kim, R. Bose, T. C. Shen, G. S. Solomon, and E. Waks, “A quantum logic gate between a solid-state quantum bit and a photon,” Nat. Photonics 7(5), 373–377 (2013).
[Crossref]

Kim, H.-M.

Kim, H.-R.

D. Smirnova, A. Tripathi, S. Kruk, M.-S. Hwang, H.-R. Kim, H.-G. Park, and Y. Kivshar, “Room-temperature lasing from nanophotonic topological cavities,” Light: Sci. Appl. 9(1), 127 (2020).
[Crossref]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref]

Kim, M.

M. Kim, Z. Jacob, and J. Rho, “Recent advances in 2D, 3D and higher-order topological photonics,” Light: Sci. Appl. 9(1), 130 (2020).
[Crossref]

Kitagawa, H.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87(6), 061107 (2005).
[Crossref]

Kivshar, Y.

D. Smirnova, D. Leykam, Y. Chong, and Y. Kivshar, “Nonlinear topological photonics,” Appl. Phys. Rev. 7(2), 021306 (2020).
[Crossref]

D. Smirnova, A. Tripathi, S. Kruk, M.-S. Hwang, H.-R. Kim, H.-G. Park, and Y. Kivshar, “Room-temperature lasing from nanophotonic topological cavities,” Light: Sci. Appl. 9(1), 127 (2020).
[Crossref]

D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan, D.-Y. Choi, and Y. Kivshar, “Third-harmonic generation in photonic topological metasurfaces,” Phys. Rev. Lett. 123(10), 103901 (2019).
[Crossref]

S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019).
[Crossref]

Kivshar, Y. S.

A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019).
[Crossref]

A. P. Slobozhanyuk, A. B. Khanikaev, D. S. Filonov, D. A. Smirnova, A. E. Miroshnichenko, and Y. S. Kivshar, “Experimental demonstration of topological effects in bianisotropic metamaterials,” Sci. Rep. 6(1), 22270 (2016).
[Crossref]

Kobayashi, W.

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

Korobkin, D.

M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
[Crossref]

Kravchenko, I.

S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019).
[Crossref]

Kruk, S.

D. Smirnova, A. Tripathi, S. Kruk, M.-S. Hwang, H.-R. Kim, H.-G. Park, and Y. Kivshar, “Room-temperature lasing from nanophotonic topological cavities,” Light: Sci. Appl. 9(1), 127 (2020).
[Crossref]

S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019).
[Crossref]

D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan, D.-Y. Choi, and Y. Kivshar, “Third-harmonic generation in photonic topological metasurfaces,” Phys. Rev. Lett. 123(10), 103901 (2019).
[Crossref]

Kuipers, L.

S. Arora, T. Bauer, R. Barczyk, E. Verhagen, and L. Kuipers, “Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths,” Light: Sci. Appl. 10, 9 (2021) .
[Crossref]

N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, “Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing,” Sci. Adv. 6(10), eaaw4137 (2020).
[Crossref]

F. Alpeggiani and L. Kuipers, “Topological edge states in bichromatic photonic crystals,” Optica 6(1), 96 (2019).
[Crossref]

Kunst, F. K.

A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” Nat. Photonics 13(10), 697–700 (2019).
[Crossref]

Kuramochi, E.

M. Notomi, K. Nozaki, A. Shinya, S. Matsuo, and E. Kuramochi, “Toward fJ/bit optical communication in a chip,” Opt. Commun. 314, 3–17 (2014).
[Crossref]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[Crossref]

Lai, K.

F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018).
[Crossref]

Lai, Y.

X. Zhou, Z.-K. Lin, W. Lu, Y. Lai, B. Hou, and J.-H. Jiang, “Twisted quadrupole topological photonic crystals,” Laser Photonics Rev. 14(8), 2000010 (2020).
[Crossref]

Le Gratiet, L.

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017).
[Crossref]

Le Vassor d’Yerville, M.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[Crossref]

Lee, E. H.

Lee, M.

C Han, M. Lee, S. Callard, C. Seassal, and H. Jeon, “Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array,” Light: Sci. Appl. 8(1), 40 (2019).
[Crossref]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref]

Lemaître, A.

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017).
[Crossref]

Lemoult, F.

S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey, “Crystalline metamaterials for topological properties at subwavelength scales,” Nat. Commun. 8(1), 16023 (2017).
[Crossref]

Lerosey, G.

S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey, “Crystalline metamaterials for topological properties at subwavelength scales,” Nat. Commun. 8(1), 16023 (2017).
[Crossref]

Letartre, X.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[Crossref]

Le-Van, Q.

Leykam, D.

D. Smirnova, D. Leykam, Y. Chong, and Y. Kivshar, “Nonlinear topological photonics,” Appl. Phys. Rev. 7(2), 021306 (2020).
[Crossref]

D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan, D.-Y. Choi, and Y. Kivshar, “Third-harmonic generation in photonic topological metasurfaces,” Phys. Rev. Lett. 123(10), 103901 (2019).
[Crossref]

J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13(6), 611–617 (2017).
[Crossref]

Li, C.

Y. Wu, C. Li, X. Hu, Y. Ao, Y. Zhao, and Q. Gong, “Applications of topological photonics in integrated photonic devices,” Adv. Opt. Mater. 5(18), 1700357 (2017).
[Crossref]

Li, J.

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

Li, L.

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

Li, M.

M. Li, D. Zhirihin, M. Gorlach, X. Ni, Dmitry Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, “Higher-order topological states in photonic kagome crystals with long-range interactions,” Nat. Photonics 14(2), 89–94 (2020).
[Crossref]

Liang, E.-T.

X.-T. He, E.-T. Liang, J.-J. Yuan, H.-Y. Qiu, X.-D. Chen, F.-L. Zhao, and J.-W. Dong, “A silicon-on-insulator slab for topological valley transport,” Nat. Commun. 10(1), 872 (2019).
[Crossref]

Lin, Q.

Lin, X.

F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018).
[Crossref]

Lin, Z.

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106(9), 093903 (2011).
[Crossref]

Lin, Z.-K.

X. Zhou, Z.-K. Lin, W. Lu, Y. Lai, B. Hou, and J.-H. Jiang, “Twisted quadrupole topological photonic crystals,” Laser Photonics Rev. 14(8), 2000010 (2020).
[Crossref]

Linfield, E. H.

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

Litchinitser, N. M.

M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, “Robust topologically protected transport in photonic crystals at telecommunication wavelengths,” Nat. Nanotechnol. 14(1), 31–34 (2019).
[Crossref]

M. I. Shalaev, W. Walasik, and N. M. Litchinitser, “Optically tunable topological photonic crystal,” Optica 6(7), 839 (2019).
[Crossref]

Liu, F.

Y. Ota, F. Liu, R. Katsumi, K. Watanabe, K. Wakabayashi, Y. Arakawa, and S. Iwamoto, “Photonic crystal nanocavity based on topological corner state,” Optica 6(6), 786 (2019).
[Crossref]

F. Liu, H.-Y. Deng, and K. Wakabayashi, “Topological photonic crystals with zero Berry curvature,” Phys. Rev. B 97(3), 035442 (2018).
[Crossref]

Liu, H.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Liu, J.

Liu, R.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Lodahl, P.

Long, Y.

J. Wang and Y. Long, “On-chip silicon photonic signaling and processing: a review,” Sci. Bull. 63(19), 1267–1310 (2018).
[Crossref]

Lu, L.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref]

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

A. Mock, L. Lu, and J. O’Brien, “Space group theory and Fourier space analysis of two-dimensional photonic crystal waveguides,” Phys. Rev. B 81(15), 155115 (2010).
[Crossref]

Lu, M.-H.

B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019).
[Crossref]

B. -Y Xie, H.-F. Wang, H. -X Wang, X.-Y Zhu, J.-H. Jiang, M.-H. Lu, and Y. -F. Chen, “Second-order photonic topological insulator with corner states,” Phys. Rev. B 98(20), 205147 (2018).
[Crossref]

B.-Y. Xie, H.-F. Wang, X.-Y. Zhu, M.-H. Lu, Z. D. Wang, and Y.-F. Chen, “Photonics meets topology,” Opt. Express 26(19), 24531 (2018).
[Crossref]

Lu, W.

X. Zhou, Z.-K. Lin, W. Lu, Y. Lai, B. Hou, and J.-H. Jiang, “Twisted quadrupole topological photonic crystals,” Laser Photonics Rev. 14(8), 2000010 (2020).
[Crossref]

Lumer, Y.

A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, “Topological optical waveguiding in silicon and the transition between topological and trivial defect states,” Phys. Rev. Lett. 116(16), 163901 (2016).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref]

Luther-Davies, B.

S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019).
[Crossref]

Ma, J.

J. Ma, X. Xi, and X. Sun, “Topological photonic integrated circuits based on valley kink states,” Laser Photonics Rev. 13(12), 1900087 (2019).
[Crossref]

Ma, R.

Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020).
[Crossref]

Ma, R.-M.

Z.-Q. Yang, Z.-K. Shao, H.-Z. Chen, X.-R. Mao, and R.-M. Ma, “Spin-momentum-locked edge mode for topological vortex lasing,” Phys. Rev. Lett. 125(1), 013903 (2020).
[Crossref]

Ma, T.

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

MacDonald, A. H.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Mahmoodian, S.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

S. Mahmoodian, K. Prindal-Nielsen, I. Söllner, S. Stobbe, and P. Lodahl, “Engineering chiral light–matter interaction in photonic crystal waveguides with slow light,” Opt. Mater. Express 7(1), 43 (2017).
[Crossref]

Makris, K. G.

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulide, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14(1), 11–19 (2018).
[Crossref]

Malkova, N.

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Che, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett.34(11), 1633 (2009).
[Crossref]

Malzard, S.

H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, “Topological hybrid silicon microlasers,” Nat. Commun. 9(1), 981 (2018).
[Crossref]

Mao, X.

Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020).
[Crossref]

Mao, X.-R.

Z.-Q. Yang, Z.-K. Shao, H.-Z. Chen, X.-R. Mao, and R.-M. Ma, “Spin-momentum-locked edge mode for topological vortex lasing,” Phys. Rev. Lett. 125(1), 013903 (2020).
[Crossref]

Marsal, L. F.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two-dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[Crossref]

Martínez, A.

F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photonics 1(9), 762–767 (2014).
[Crossref]

Matsuo, S.

M. Notomi, K. Nozaki, A. Shinya, S. Matsuo, and E. Kuramochi, “Toward fJ/bit optical communication in a chip,” Opt. Commun. 314, 3–17 (2014).
[Crossref]

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

McNab, S. J.

Mehrabad, M. J.

M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020).
[Crossref]

M. J. Mehrabad, A. P. Foster, R. Dost, A. M. Fox, M. S. Skolnick, and L. R. Wilson, “Chiral topological photonics with an embedded quantum emitter,” Optica 7(12), 1690 (2020).
[Crossref]

Melik-Gaykazyan, E.

D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan, D.-Y. Choi, and Y. Kivshar, “Third-harmonic generation in photonic topological metasurfaces,” Phys. Rev. Lett. 123(10), 103901 (2019).
[Crossref]

Meng, Y.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref]

Miao, P.

H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, “Topological hybrid silicon microlasers,” Nat. Commun. 9(1), 981 (2018).
[Crossref]

Midolo, L.

Midya, B.

B. Midya, H. Zhao, and L. Feng, “Non-Hermitian photonics promises exceptional topology of light,” Nat. Commun. 9(1), 2674 (2018).
[Crossref]

Migdall, A.

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113(8), 087403 (2014).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
[Crossref]

Mirin, R.

Miroshnichenko, A. E.

A. P. Slobozhanyuk, A. B. Khanikaev, D. S. Filonov, D. A. Smirnova, A. E. Miroshnichenko, and Y. S. Kivshar, “Experimental demonstration of topological effects in bianisotropic metamaterials,” Sci. Rep. 6(1), 22270 (2016).
[Crossref]

Mittal, S.

S. Barik, A. Karasahin, S. Mittal, E. Waks, and M. Hafezi, “Chiral quantum optics using a topological resonator,” Phys. Rev. B 101(20), 205303 (2020).
[Crossref]

S. Mittal, V. V. Orre, G. Zhu, M. A. Gorlach, A. Poddubny, and M. Hafezi, “Photonic quadrupole topological phases,” Nat. Photonics 13(10), 692–696 (2019).
[Crossref]

S. Mittal, E. A. Goldschmidt, and M. Hafezi, “A topological source of quantum light,” Nature 561(7724), 502–506 (2018).
[Crossref]

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113(8), 087403 (2014).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
[Crossref]

Miyake, H.

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum interface,” Science 359(6376), 666–668 (2018).
[Crossref]

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

Mock, A.

A. Mock and J. D. O’Brien, “Strategies for reducing the out-of-plane radiation in photonic crystal heterostructure microcavities for continuous wave laser applications,” J. Lightwave Technol. 28(7), 1042–1050 (2010).
[Crossref]

A. Mock, L. Lu, and J. O’Brien, “Space group theory and Fourier space analysis of two-dimensional photonic crystal waveguides,” Phys. Rev. B 81(15), 155115 (2010).
[Crossref]

Moll, N.

Moritz, A.

A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” Nat. Photonics 13(10), 697–700 (2019).
[Crossref]

Mousavi, S. H.

A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019).
[Crossref]

X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, “Robust reconfigurable electromagnetic pathways within a photonic topological insulator,” Nat. Mater. 15(5), 542–548 (2016).
[Crossref]

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Musslimani, Z. H.

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulide, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14(1), 11–19 (2018).
[Crossref]

Nagatsuma, T.

Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020).
[Crossref]

Nam, S. W.

Nasari, H.

Ndao, A.

B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, “Nonreciprocal lasing in topological cavities of arbitrary geometries,” Science 358(6363), 636–640 (2017).
[Crossref]

Ni, H.

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

Ni, X.

M. Li, D. Zhirihin, M. Gorlach, X. Ni, Dmitry Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, “Higher-order topological states in photonic kagome crystals with long-range interactions,” Nat. Photonics 14(2), 89–94 (2020).
[Crossref]

A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019).
[Crossref]

M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
[Crossref]

X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, “Robust reconfigurable electromagnetic pathways within a photonic topological insulator,” Nat. Mater. 15(5), 542–548 (2016).
[Crossref]

Nishiyama, N.

Niu, Z.

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

Noda, S.

T. Asano and S. Noda, “Photonic crystal devices in silicon photonics,” Proc. IEEE 106(12), 2183–2195 (2018).
[Crossref]

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87(6), 061107 (2005).
[Crossref]

Noh, J.

J. Noh, S. Huang, K. P. Chen, and M. C. Rechtsman, “Observation of photonic topological valley Hall edge states,” Phys. Rev. Lett. 120(6), 063902 (2018).
[Crossref]

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, “Topological protection of photonic mid-gap defect modes,” Nat. Photonics 12(7), 408–415 (2018).
[Crossref]

J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13(6), 611–617 (2017).
[Crossref]

Noh, W.

Nolte, S.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref]

Nori, F.

Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, “Parity–time symmetry and exceptional points in photonics,” Nat. Mater. 18(8), 783–798 (2019).
[Crossref]

Notomi, M.

Y. Ota, K. Takaka, T. Ozawa, A. Amo, Z. Jia, B. Kante, M. Notomi, Y. Arakawa, and S. Iwamoto, “Active Topological Photonics,” Nanophotonics 9(3), 547–567 (2020).
[Crossref]

K. Takata and M. Notomi, “Photonic topological insulating phase induced solely by gain and loss,” Phys. Rev. Lett. 121(21), 213902 (2018).
[Crossref]

M. Notomi, K. Nozaki, A. Shinya, S. Matsuo, and E. Kuramochi, “Toward fJ/bit optical communication in a chip,” Opt. Commun. 314, 3–17 (2014).
[Crossref]

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[Crossref]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref]

Nozaki, K.

M. Notomi, K. Nozaki, A. Shinya, S. Matsuo, and E. Kuramochi, “Toward fJ/bit optical communication in a chip,” Opt. Commun. 314, 3–17 (2014).
[Crossref]

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

O’Brien, J.

A. Mock, L. Lu, and J. O’Brien, “Space group theory and Fourier space analysis of two-dimensional photonic crystal waveguides,” Phys. Rev. B 81(15), 155115 (2010).
[Crossref]

O’Brien, J. D.

A. Mock and J. D. O’Brien, “Strategies for reducing the out-of-plane radiation in photonic crystal heterostructure microcavities for continuous wave laser applications,” J. Lightwave Technol. 28(7), 1042–1050 (2010).
[Crossref]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref]

Okada, S.

Orre, V. V.

S. Mittal, V. V. Orre, G. Zhu, M. A. Gorlach, A. Poddubny, and M. Hafezi, “Photonic quadrupole topological phases,” Nat. Photonics 13(10), 692–696 (2019).
[Crossref]

Osada, A.

T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” Appl. Phys. Express 12(6), 062005 (2019).
[Crossref]

Ota, Y

Ota, Y.

Y. Ota, K. Takaka, T. Ozawa, A. Amo, Z. Jia, B. Kante, M. Notomi, Y. Arakawa, and S. Iwamoto, “Active Topological Photonics,” Nanophotonics 9(3), 547–567 (2020).
[Crossref]

H. Yoshimi, T. Yamaguchi, Y. Ota, Y. Arakawa, and S. Iwamoto, “Slow light waveguides in topological valley photonic crystal,” Opt. Lett. 45(9), 2648 (2020).
[Crossref]

T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” Appl. Phys. Express 12(6), 062005 (2019).
[Crossref]

Y. Ota, F. Liu, R. Katsumi, K. Watanabe, K. Wakabayashi, Y. Arakawa, and S. Iwamoto, “Photonic crystal nanocavity based on topological corner state,” Optica 6(6), 786 (2019).
[Crossref]

Y. Ota, R. Katsumi, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Topological photonic crystal nanocavity laser,” Commun. Phys. 1(1), 86 (2018).
[Crossref]

R. Katsumi, Y. Ota, M. Kakuda, S. Iwamoto, and Y. Arakawa, “Transfer-printed single-photon sources coupled to wire waveguides,” Optica 5(6), 691 (2018).
[Crossref]

Ozawa, T.

Y. Ota, K. Takaka, T. Ozawa, A. Amo, Z. Jia, B. Kante, M. Notomi, Y. Arakawa, and S. Iwamoto, “Active Topological Photonics,” Nanophotonics 9(3), 547–567 (2020).
[Crossref]

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017).
[Crossref]

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics,” Phys. Rev. A 93(4), 043827 (2016).
[Crossref]

Özdemir, S. K.

Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, “Parity–time symmetry and exceptional points in photonics,” Nat. Mater. 18(8), 783–798 (2019).
[Crossref]

Painter, O.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref]

Pallarès, J.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two-dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[Crossref]

Palmer, S. J.

M. S. Rider, S. J. Palmer, S. R. Pocock, X. Xiao, P. A. Huidobro, and V. Giannini, “A perspective on topological nanophotonics: Current status and future challenges,” J. Appl. Phys. 125(12), 120901 (2019).
[Crossref]

Parappurath, N.

N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, “Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing,” Sci. Adv. 6(10), eaaw4137 (2020).
[Crossref]

Park, H.-G.

D. Smirnova, A. Tripathi, S. Kruk, M.-S. Hwang, H.-R. Kim, H.-G. Park, and Y. Kivshar, “Room-temperature lasing from nanophotonic topological cavities,” Light: Sci. Appl. 9(1), 127 (2020).
[Crossref]

Parto, M.

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
[Crossref]

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref]

Patil, P. K.

M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020).
[Crossref]

Peterson, C. W.

C. W. Peterson, W. A. Benalcazar, T. L. Hughes, and G. Bahl, “A quantized microwave quadrupole insulator with topologically protected corner states,” Nature 555(7696), 346–350 (2018).
[Crossref]

Petroff, P.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 (2008).
[Crossref]

Pichler, H.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

Pitchappa, P.

Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020).
[Crossref]

Plotnik, Y.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref]

Pocock, S. R.

M. S. Rider, S. J. Palmer, S. R. Pocock, X. Xiao, P. A. Huidobro, and V. Giannini, “A perspective on topological nanophotonics: Current status and future challenges,” J. Appl. Phys. 125(12), 120901 (2019).
[Crossref]

Poddubny, A.

S. Mittal, V. V. Orre, G. Zhu, M. A. Gorlach, A. Poddubny, and M. Hafezi, “Photonic quadrupole topological phases,” Nat. Photonics 13(10), 692–696 (2019).
[Crossref]

S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019).
[Crossref]

Podolsky, D.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref]

Poo, Y.

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106(9), 093903 (2011).
[Crossref]

Pregnolato, T.

Price, H. M.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics,” Phys. Rev. A 93(4), 043827 (2016).
[Crossref]

Prindal-Nielsen, K.

Puerto, D.

F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photonics 1(9), 762–767 (2014).
[Crossref]

Qiang, B.

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

Qiu, H.-Y.

X.-T. He, E.-T. Liang, J.-J. Yuan, H.-Y. Qiu, X.-D. Chen, F.-L. Zhao, and J.-W. Dong, “A silicon-on-insulator slab for topological valley transport,” Nat. Commun. 10(1), 872 (2019).
[Crossref]

Raghu, S.

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[Crossref]

Ramunno, L.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[Crossref]

Ran, L.

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref]

Rauschenbeutel, A.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

Rechtsman, M. C.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

J. Noh, S. Huang, K. P. Chen, and M. C. Rechtsman, “Observation of photonic topological valley Hall edge states,” Phys. Rev. Lett. 120(6), 063902 (2018).
[Crossref]

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
[Crossref]

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, “Topological protection of photonic mid-gap defect modes,” Nat. Photonics 12(7), 408–415 (2018).
[Crossref]

J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13(6), 611–617 (2017).
[Crossref]

M. J. Collins, F. Zhang, R. Bojko, L. Chrostowski, and M. C. Rechtsman, “Integrated optical Dirac physics via inversion symmetry breaking,” Phys. Rev. A 94(6), 063827 (2016).
[Crossref]

A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, “Topological optical waveguiding in silicon and the transition between topological and trivial defect states,” Phys. Rev. Lett. 116(16), 163901 (2016).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref]

Ren, J.

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
[Crossref]

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref]

Rho, J.

M. Kim, Z. Jacob, and J. Rho, “Recent advances in 2D, 3D and higher-order topological photonics,” Light: Sci. Appl. 9(1), 130 (2020).
[Crossref]

Rider, M. S.

M. S. Rider, S. J. Palmer, S. R. Pocock, X. Xiao, P. A. Huidobro, and V. Giannini, “A perspective on topological nanophotonics: Current status and future challenges,” J. Appl. Phys. 125(12), 120901 (2019).
[Crossref]

Rodríguez, A.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two-dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[Crossref]

Rodríguez-Fortuño, F. J.

F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photonics 1(9), 762–767 (2014).
[Crossref]

Rojo-Romeo, P.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[Crossref]

Rotter, S.

Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, “Parity–time symmetry and exceptional points in photonics,” Nat. Mater. 18(8), 783–798 (2019).
[Crossref]

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulide, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14(1), 11–19 (2018).
[Crossref]

Sagnes, I.

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017).
[Crossref]

Sato, T.

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

Sauer, E.

E. Sauer, J. P. Vasco, and S. Hughes, “Theory of intrinsic propagation losses in topological edge states of planar photonic crystals,” Phys. Rev. Res. 2(4), 043109 (2020).
[Crossref]

Schäffler, F.

A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017).
[Crossref]

Schatzl, M.

A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017).
[Crossref]

Scherer, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref]

Schneeweiss, P.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

Schomerus, H.

H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, “Topological hybrid silicon microlasers,” Nat. Commun. 9(1), 981 (2018).
[Crossref]

Schrieffer, J. R.

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979).
[Crossref]

Schuster, D.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Seassal, C.

C Han, M. Lee, S. Callard, C. Seassal, and H. Jeon, “Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array,” Light: Sci. Appl. 8(1), 40 (2019).
[Crossref]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[Crossref]

Segev, M.

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref]

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
[Crossref]

A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, “Topological optical waveguiding in silicon and the transition between topological and trivial defect states,” Phys. Rev. Lett. 116(16), 163901 (2016).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref]

Shalaev, M. I.

M. I. Shalaev, W. Walasik, and N. M. Litchinitser, “Optically tunable topological photonic crystal,” Optica 6(7), 839 (2019).
[Crossref]

M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, “Robust topologically protected transport in photonic crystals at telecommunication wavelengths,” Nat. Nanotechnol. 14(1), 31–34 (2019).
[Crossref]

Shao, Z.

Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020).
[Crossref]

Shao, Z.-K.

Z.-Q. Yang, Z.-K. Shao, H.-Z. Chen, X.-R. Mao, and R.-M. Ma, “Spin-momentum-locked edge mode for topological vortex lasing,” Phys. Rev. Lett. 125(1), 013903 (2020).
[Crossref]

Shchelokova, A. V.

A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019).
[Crossref]

Shen, T. C.

H. Kim, R. Bose, T. C. Shen, G. S. Solomon, and E. Waks, “A quantum logic gate between a solid-state quantum bit and a photon,” Nat. Photonics 7(5), 373–377 (2013).
[Crossref]

Shen, X.-P.

B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019).
[Crossref]

Shi, F.-L.

X.-D. Chen, W.-M. Deng, F.-L. Shi, F.-L Zhao, M. Chen, and J. -W. Dong, “Direct observation of corner states in second-order topological photonic crystal slabs,” Phys. Rev. Lett. 122(23), 233902 (2019).
[Crossref]

Shi, S.

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

Shi, Y.

Shinya, A.

M. Notomi, K. Nozaki, A. Shinya, S. Matsuo, and E. Kuramochi, “Toward fJ/bit optical communication in a chip,” Opt. Commun. 314, 3–17 (2014).
[Crossref]

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[Crossref]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref]

Shorokhov, A.

S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019).
[Crossref]

Shvets, G.

F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018).
[Crossref]

A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11(12), 763–773 (2017).
[Crossref]

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Simbula, A.

A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017).
[Crossref]

Simon, J.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Singh, R.

Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020).
[Crossref]

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

Skirlo, S. A.

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref]

Skolnick, M. S.

M. J. Mehrabad, A. P. Foster, R. Dost, A. M. Fox, M. S. Skolnick, and L. R. Wilson, “Chiral topological photonics with an embedded quantum emitter,” Optica 7(12), 1690 (2020).
[Crossref]

M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020).
[Crossref]

Slobozhanyuk, A.

M. Li, D. Zhirihin, M. Gorlach, X. Ni, Dmitry Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, “Higher-order topological states in photonic kagome crystals with long-range interactions,” Nat. Photonics 14(2), 89–94 (2020).
[Crossref]

A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019).
[Crossref]

S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019).
[Crossref]

Slobozhanyuk, A. P.

M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
[Crossref]

A. P. Slobozhanyuk, A. B. Khanikaev, D. S. Filonov, D. A. Smirnova, A. E. Miroshnichenko, and Y. S. Kivshar, “Experimental demonstration of topological effects in bianisotropic metamaterials,” Sci. Rep. 6(1), 22270 (2016).
[Crossref]

Smirnova, D.

D. Smirnova, D. Leykam, Y. Chong, and Y. Kivshar, “Nonlinear topological photonics,” Appl. Phys. Rev. 7(2), 021306 (2020).
[Crossref]

D. Smirnova, A. Tripathi, S. Kruk, M.-S. Hwang, H.-R. Kim, H.-G. Park, and Y. Kivshar, “Room-temperature lasing from nanophotonic topological cavities,” Light: Sci. Appl. 9(1), 127 (2020).
[Crossref]

S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019).
[Crossref]

D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan, D.-Y. Choi, and Y. Kivshar, “Third-harmonic generation in photonic topological metasurfaces,” Phys. Rev. Lett. 123(10), 103901 (2019).
[Crossref]

Smirnova, D. A.

A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019).
[Crossref]

M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
[Crossref]

A. P. Slobozhanyuk, A. B. Khanikaev, D. S. Filonov, D. A. Smirnova, A. E. Miroshnichenko, and Y. S. Kivshar, “Experimental demonstration of topological effects in bianisotropic metamaterials,” Sci. Rep. 6(1), 22270 (2016).
[Crossref]

Soljacic, M.

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref]

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref]

Söllner, I.

Solomon, G. S.

H. Kim, R. Bose, T. C. Shen, G. S. Solomon, and E. Waks, “A quantum logic gate between a solid-state quantum bit and a photon,” Nat. Photonics 7(5), 373–377 (2013).
[Crossref]

Song, J. D.

Sotomayor-Torres, C. M.

G. Arregui, J. Gomis-Bresco, C. M. Sotomayor-Torres, and P. D. Garcia, “Quantifying the robustness of topological slow light,” arXiv:2007.15606 (2020).

Srinivasan, K.

St-Jean, P.

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017).
[Crossref]

Stobbe, S.

Stoltz, N.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 (2008).
[Crossref]

Su, G.-X.

B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019).
[Crossref]

Su, H.

B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019).
[Crossref]

Su, W. P.

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979).
[Crossref]

Sun, X.

J. Ma, X. Xi, and X. Sun, “Topological photonic integrated circuits based on valley kink states,” Laser Photonics Rev. 13(12), 1900087 (2019).
[Crossref]

Szameit, A.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref]

Takaka, K.

Y. Ota, K. Takaka, T. Ozawa, A. Amo, Z. Jia, B. Kante, M. Notomi, Y. Arakawa, and S. Iwamoto, “Active Topological Photonics,” Nanophotonics 9(3), 547–567 (2020).
[Crossref]

Takata, K.

K. Takata and M. Notomi, “Photonic topological insulating phase induced solely by gain and loss,” Phys. Rev. Lett. 121(21), 213902 (2018).
[Crossref]

Takayama, S.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87(6), 061107 (2005).
[Crossref]

Takeda, K.

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

Tanaka, Y.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87(6), 061107 (2005).
[Crossref]

Taniyama, H.

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

Taylor, J.

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
[Crossref]

Taylor, J. M.

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113(8), 087403 (2014).
[Crossref]

Teimourpour, M. H.

H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, “Topological hybrid silicon microlasers,” Nat. Commun. 9(1), 981 (2018).
[Crossref]

Tian, J.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref]

Tremain, B.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Trifonov, T.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two-dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[Crossref]

Tripathi, A.

D. Smirnova, A. Tripathi, S. Kruk, M.-S. Hwang, H.-R. Kim, H.-G. Park, and Y. Kivshar, “Room-temperature lasing from nanophotonic topological cavities,” Light: Sci. Appl. 9(1), 127 (2020).
[Crossref]

Tse, W.-K.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Tsukernik, A.

M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, “Robust topologically protected transport in photonic crystals at telecommunication wavelengths,” Nat. Nanotechnol. 14(1), 31–34 (2019).
[Crossref]

Vallini, F.

B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, “Nonreciprocal lasing in topological cavities of arbitrary geometries,” Science 358(6363), 636–640 (2017).
[Crossref]

Vasco, J. P.

E. Sauer, J. P. Vasco, and S. Hughes, “Theory of intrinsic propagation losses in topological edge states of planar photonic crystals,” Phys. Rev. Res. 2(4), 043109 (2020).
[Crossref]

Verhagen, E.

S. Arora, T. Bauer, R. Barczyk, E. Verhagen, and L. Kuipers, “Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths,” Light: Sci. Appl. 10, 9 (2021) .
[Crossref]

N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, “Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing,” Sci. Adv. 6(10), eaaw4137 (2020).
[Crossref]

Verma, V.

Viktorovitch, P.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[Crossref]

Vlasov, Y. A.

Volz, J.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

Vuckovic, J.

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 (2008).
[Crossref]

Wakabayashi, K.

Y. Ota, F. Liu, R. Katsumi, K. Watanabe, K. Wakabayashi, Y. Arakawa, and S. Iwamoto, “Photonic crystal nanocavity based on topological corner state,” Optica 6(6), 786 (2019).
[Crossref]

F. Liu, H.-Y. Deng, and K. Wakabayashi, “Topological photonic crystals with zero Berry curvature,” Phys. Rev. B 97(3), 035442 (2018).
[Crossref]

Waks, E.

S. Barik, A. Karasahin, S. Mittal, E. Waks, and M. Hafezi, “Chiral quantum optics using a topological resonator,” Phys. Rev. B 101(20), 205303 (2020).
[Crossref]

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum interface,” Science 359(6376), 666–668 (2018).
[Crossref]

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

H. Kim, R. Bose, T. C. Shen, G. S. Solomon, and E. Waks, “A quantum logic gate between a solid-state quantum bit and a photon,” Nat. Photonics 7(5), 373–377 (2013).
[Crossref]

Walasik, W.

M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, “Robust topologically protected transport in photonic crystals at telecommunication wavelengths,” Nat. Nanotechnol. 14(1), 31–34 (2019).
[Crossref]

M. I. Shalaev, W. Walasik, and N. M. Litchinitser, “Optically tunable topological photonic crystal,” Optica 6(7), 839 (2019).
[Crossref]

Wang, C.

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

Wang, H. -X

B. -Y Xie, H.-F. Wang, H. -X Wang, X.-Y Zhu, J.-H. Jiang, M.-H. Lu, and Y. -F. Chen, “Second-order photonic topological insulator with corner states,” Phys. Rev. B 98(20), 205147 (2018).
[Crossref]

Wang, H.-F.

B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019).
[Crossref]

B. -Y Xie, H.-F. Wang, H. -X Wang, X.-Y Zhu, J.-H. Jiang, M.-H. Lu, and Y. -F. Chen, “Second-order photonic topological insulator with corner states,” Phys. Rev. B 98(20), 205147 (2018).
[Crossref]

B.-Y. Xie, H.-F. Wang, X.-Y. Zhu, M.-H. Lu, Z. D. Wang, and Y.-F. Chen, “Photonics meets topology,” Opt. Express 26(19), 24531 (2018).
[Crossref]

Wang, J.

J. Wang and Y. Long, “On-chip silicon photonic signaling and processing: a review,” Sci. Bull. 63(19), 1267–1310 (2018).
[Crossref]

Wang, L.

S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019).
[Crossref]

Wang, Q. J.

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

Wang, S.

Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020).
[Crossref]

Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020).
[Crossref]

Wang, X.

Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020).
[Crossref]

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Che, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett.34(11), 1633 (2009).
[Crossref]

Wang, Z.

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref]

Wang, Z. D.

Wang, Z.-L.

B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019).
[Crossref]

Watanabe, K

Watanabe, K.

Y. Ota, F. Liu, R. Katsumi, K. Watanabe, K. Wakabayashi, Y. Arakawa, and S. Iwamoto, “Photonic crystal nanocavity based on topological corner state,” Optica 6(6), 786 (2019).
[Crossref]

T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” Appl. Phys. Express 12(6), 062005 (2019).
[Crossref]

Y. Ota, R. Katsumi, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Topological photonic crystal nanocavity laser,” Commun. Phys. 1(1), 86 (2018).
[Crossref]

Watanabe, T.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[Crossref]

Webber, J.

Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020).
[Crossref]

Wen, F.

Wen, W.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref]

Wilson, L. R.

M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020).
[Crossref]

M. J. Mehrabad, A. P. Foster, R. Dost, A. M. Fox, M. S. Skolnick, and L. R. Wilson, “Chiral topological photonics with an embedded quantum emitter,” Optica 7(12), 1690 (2020).
[Crossref]

Wittek, S.

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
[Crossref]

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref]

Wu, H.

H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
[Crossref]

Wu, R.

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106(9), 093903 (2011).
[Crossref]

Wu, X.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref]

Wu, Y.

Y. Wu, C. Li, X. Hu, Y. Ao, Y. Zhao, and Q. Gong, “Applications of topological photonics in integrated photonic devices,” Adv. Opt. Mater. 5(18), 1700357 (2017).
[Crossref]

Xi, X.

J. Ma, X. Xi, and X. Sun, “Topological photonic integrated circuits based on valley kink states,” Laser Photonics Rev. 13(12), 1900087 (2019).
[Crossref]

Xiang, H.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref]

Xiang, Y.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Xiao, M.

L. Yuan, Q. Lin, M. Xiao, and S. Fan, “Synthetic dimension in photonics,” Optica 5(11), 1396 (2018).
[Crossref]

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

Xiao, S.

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

Xiao, X.

M. S. Rider, S. J. Palmer, S. R. Pocock, X. Xiao, P. A. Huidobro, and V. Giannini, “A perspective on topological nanophotonics: Current status and future challenges,” J. Appl. Phys. 125(12), 120901 (2019).
[Crossref]

Xie, B. -Y

B. -Y Xie, H.-F. Wang, H. -X Wang, X.-Y Zhu, J.-H. Jiang, M.-H. Lu, and Y. -F. Chen, “Second-order photonic topological insulator with corner states,” Phys. Rev. B 98(20), 205147 (2018).
[Crossref]

Xie, B.-Y.

B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019).
[Crossref]

B.-Y. Xie, H.-F. Wang, X.-Y. Zhu, M.-H. Lu, Z. D. Wang, and Y.-F. Chen, “Photonics meets topology,” Opt. Express 26(19), 24531 (2018).
[Crossref]

Xie, X.

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

Xu, X.

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

Xu, Y.

M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, “Robust topologically protected transport in photonic crystals at telecommunication wavelengths,” Nat. Nanotechnol. 14(1), 31–34 (2019).
[Crossref]

Xue, H.

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018).
[Crossref]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96(20), 201402 (2017).
[Crossref]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref]

Yamagami, Y.

Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020).
[Crossref]

Yamaguchi, T.

H. Yoshimi, T. Yamaguchi, Y. Ota, Y. Arakawa, and S. Iwamoto, “Slow light waveguides in topological valley photonic crystal,” Opt. Lett. 45(9), 2648 (2020).
[Crossref]

T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” Appl. Phys. Express 12(6), 062005 (2019).
[Crossref]

Yan, Q.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref]

Yang, B.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Yang, L.

Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, “Parity–time symmetry and exceptional points in photonics,” Nat. Mater. 18(8), 783–798 (2019).
[Crossref]

Yang, Y.

Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020).
[Crossref]

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

Y. Yang and Z. H. Hang, “Topological whispering gallery modes in two-dimensional photonic crystal cavities,” Opt. Express 26(16), 21235–21241 (2018).
[Crossref]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96(20), 201402 (2017).
[Crossref]

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106(9), 093903 (2011).
[Crossref]

Yang, Z.

Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020).
[Crossref]

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018).
[Crossref]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96(20), 201402 (2017).
[Crossref]

Yang, Z.-Q.

Z.-Q. Yang, Z.-K. Shao, H.-Z. Chen, X.-R. Mao, and R.-M. Ma, “Spin-momentum-locked edge mode for topological vortex lasing,” Phys. Rev. Lett. 125(1), 013903 (2020).
[Crossref]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref]

Ye, D.

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref]

Yoshimi, H.

Yu, X.

Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020).
[Crossref]

Yu, Y.

F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018).
[Crossref]

Yuan, J.-J.

X.-T. He, E.-T. Liang, J.-J. Yuan, H.-Y. Qiu, X.-D. Chen, F.-L. Zhao, and J.-W. Dong, “A silicon-on-insulator slab for topological valley transport,” Nat. Commun. 10(1), 872 (2019).
[Crossref]

Yuan, L.

Yves, S.

S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey, “Crystalline metamaterials for topological properties at subwavelength scales,” Nat. Commun. 8(1), 16023 (2017).
[Crossref]

Zagaglia, L.

A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017).
[Crossref]

Zak, J.

J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989).
[Crossref]

Zeng, Y.

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

Zeuner, J. M.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref]

Zhan, P.

B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019).
[Crossref]

Zhang, B

F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018).
[Crossref]

Zhang, B.

Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020).
[Crossref]

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96(20), 201402 (2017).
[Crossref]

Zhang, F.

M. J. Collins, F. Zhang, R. Bojko, L. Chrostowski, and M. C. Rechtsman, “Integrated optical Dirac physics via inversion symmetry breaking,” Phys. Rev. A 94(6), 063827 (2016).
[Crossref]

Zhang, L.

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

Zhang, S.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Zhang, W.

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

Zhang, X.

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

Zhang, Z. Q.

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

Zhao, F.-L

X.-D. Chen, W.-M. Deng, F.-L. Shi, F.-L Zhao, M. Chen, and J. -W. Dong, “Direct observation of corner states in second-order topological photonic crystal slabs,” Phys. Rev. Lett. 122(23), 233902 (2019).
[Crossref]

Zhao, F.-L.

X.-T. He, E.-T. Liang, J.-J. Yuan, H.-Y. Qiu, X.-D. Chen, F.-L. Zhao, and J.-W. Dong, “A silicon-on-insulator slab for topological valley transport,” Nat. Commun. 10(1), 872 (2019).
[Crossref]

X.-D. Chen, F.-L. Zhao, M. Chen, and J.-W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
[Crossref]

Zhao, H.

H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, “Topological hybrid silicon microlasers,” Nat. Commun. 9(1), 981 (2018).
[Crossref]

B. Midya, H. Zhao, and L. Feng, “Non-Hermitian photonics promises exceptional topology of light,” Nat. Commun. 9(1), 2674 (2018).
[Crossref]

Zhao, Y.

Y. Wu, C. Li, X. Hu, Y. Ao, Y. Zhao, and Q. Gong, “Applications of topological photonics in integrated photonic devices,” Adv. Opt. Mater. 5(18), 1700357 (2017).
[Crossref]

Zhirihin, D.

M. Li, D. Zhirihin, M. Gorlach, X. Ni, Dmitry Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, “Higher-order topological states in photonic kagome crystals with long-range interactions,” Nat. Photonics 14(2), 89–94 (2020).
[Crossref]

M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
[Crossref]

Zhou, L.

W. -Jie Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5(1), 5782 (2014).
[Crossref]

Zhou, X.

X. Zhou, Z.-K. Lin, W. Lu, Y. Lai, B. Hou, and J.-H. Jiang, “Twisted quadrupole topological photonic crystals,” Laser Photonics Rev. 14(8), 2000010 (2020).
[Crossref]

Zhu, B.

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

W. -Jie Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5(1), 5782 (2014).
[Crossref]

Zhu, G.

S. Mittal, V. V. Orre, G. Zhu, M. A. Gorlach, A. Poddubny, and M. Hafezi, “Photonic quadrupole topological phases,” Nat. Photonics 13(10), 692–696 (2019).
[Crossref]

Zhu, X.-Y

B. -Y Xie, H.-F. Wang, H. -X Wang, X.-Y Zhu, J.-H. Jiang, M.-H. Lu, and Y. -F. Chen, “Second-order photonic topological insulator with corner states,” Phys. Rev. B 98(20), 205147 (2018).
[Crossref]

Zhu, X.-Y.

Zilberberg, O.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics,” Phys. Rev. A 93(4), 043827 (2016).
[Crossref]

Zoller, P.

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

ACS Photonics (2)

F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photonics 1(9), 762–767 (2014).
[Crossref]

C. Han, M. Kang, and H. Jeon, “Lasing at multidimensional topological states in a two-dimensional photonic crystal structure,” ACS Photonics 7(8), 2027–2036 (2020).
[Crossref]

Adv. Opt. Mater. (1)

Y. Wu, C. Li, X. Hu, Y. Ao, Y. Zhao, and Q. Gong, “Applications of topological photonics in integrated photonic devices,” Adv. Opt. Mater. 5(18), 1700357 (2017).
[Crossref]

APL Photonics (1)

A. Simbula, M. Schatzl, L. Zagaglia, F. Alpeggiani, L. C. Andreani, F. Schäffler, T. Fromherz, M. Galli, and D. Gerace, “Realization of high-Q/V photonic crystal cavities defined by an effective Aubry-André-Harper bichromatic potential,” APL Photonics 2(5), 056102 (2017).
[Crossref]

Appl. Phys. Express (1)

T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” Appl. Phys. Express 12(6), 062005 (2019).
[Crossref]

Appl. Phys. Lett. (5)

F. Alpeggiani, L. C. Andreani, and D. Gerace, “Effective bichromatic potential for ultra-high Q-factor photonic crystal slab cavities,” Appl. Phys. Lett. 107(26), 261110 (2015).
[Crossref]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79(15), 2312–2314 (2001).
[Crossref]

A. Slobozhanyuk, A. V. Shchelokova, X. Ni, S. H. Mousavi, D. A. Smirnova, P. A. Belov, A. Alù, Y. S. Kivshar, and A. B. Khanikaev, “Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces,” Appl. Phys. Lett. 114(3), 031103 (2019).
[Crossref]

M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, I. Farrer, J. Heffernan, M. S. Skolnick, and L. R. Wilson, “A semiconductor topological photonic ring resonator,” Appl. Phys. Lett. 116(6), 061102 (2020).
[Crossref]

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87(6), 061107 (2005).
[Crossref]

Appl. Phys. Rev. (1)

D. Smirnova, D. Leykam, Y. Chong, and Y. Kivshar, “Nonlinear topological photonics,” Appl. Phys. Rev. 7(2), 021306 (2020).
[Crossref]

Commun. Phys. (1)

Y. Ota, R. Katsumi, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Topological photonic crystal nanocavity laser,” Commun. Phys. 1(1), 86 (2018).
[Crossref]

J. Appl. Phys. (1)

M. S. Rider, S. J. Palmer, S. R. Pocock, X. Xiao, P. A. Huidobro, and V. Giannini, “A perspective on topological nanophotonics: Current status and future challenges,” J. Appl. Phys. 125(12), 120901 (2019).
[Crossref]

J. Lightwave Technol. (1)

Laser Photonics Rev. (2)

J. Ma, X. Xi, and X. Sun, “Topological photonic integrated circuits based on valley kink states,” Laser Photonics Rev. 13(12), 1900087 (2019).
[Crossref]

X. Zhou, Z.-K. Lin, W. Lu, Y. Lai, B. Hou, and J.-H. Jiang, “Twisted quadrupole topological photonic crystals,” Laser Photonics Rev. 14(8), 2000010 (2020).
[Crossref]

Light: Sci. Appl. (5)

W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, “Low-threshold topological nanolasers based on the second-order corner state,” Light: Sci. Appl. 9(1), 109 (2020).
[Crossref]

D. Smirnova, A. Tripathi, S. Kruk, M.-S. Hwang, H.-R. Kim, H.-G. Park, and Y. Kivshar, “Room-temperature lasing from nanophotonic topological cavities,” Light: Sci. Appl. 9(1), 127 (2020).
[Crossref]

S. Arora, T. Bauer, R. Barczyk, E. Verhagen, and L. Kuipers, “Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths,” Light: Sci. Appl. 10, 9 (2021) .
[Crossref]

C Han, M. Lee, S. Callard, C. Seassal, and H. Jeon, “Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array,” Light: Sci. Appl. 8(1), 40 (2019).
[Crossref]

M. Kim, Z. Jacob, and J. Rho, “Recent advances in 2D, 3D and higher-order topological photonics,” Light: Sci. Appl. 9(1), 130 (2020).
[Crossref]

Nanophotonics (1)

Y. Ota, K. Takaka, T. Ozawa, A. Amo, Z. Jia, B. Kante, M. Notomi, Y. Arakawa, and S. Iwamoto, “Active Topological Photonics,” Nanophotonics 9(3), 547–567 (2020).
[Crossref]

Nat. Commun. (7)

M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
[Crossref]

W. -Jie Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5(1), 5782 (2014).
[Crossref]

S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey, “Crystalline metamaterials for topological properties at subwavelength scales,” Nat. Commun. 8(1), 16023 (2017).
[Crossref]

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref]

H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, “Topological hybrid silicon microlasers,” Nat. Commun. 9(1), 981 (2018).
[Crossref]

X.-T. He, E.-T. Liang, J.-J. Yuan, H.-Y. Qiu, X.-D. Chen, F.-L. Zhao, and J.-W. Dong, “A silicon-on-insulator slab for topological valley transport,” Nat. Commun. 10(1), 872 (2019).
[Crossref]

B. Midya, H. Zhao, and L. Feng, “Non-Hermitian photonics promises exceptional topology of light,” Nat. Commun. 9(1), 2674 (2018).
[Crossref]

Nat. Mater. (3)

Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, “Parity–time symmetry and exceptional points in photonics,” Nat. Mater. 18(8), 783–798 (2019).
[Crossref]

X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, “Robust reconfigurable electromagnetic pathways within a photonic topological insulator,” Nat. Mater. 15(5), 542–548 (2016).
[Crossref]

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Nat. Nanotechnol. (3)

Z. Shao, H. Chen, S. Wang, X. Mao, Z. Yang, S. Wang, X. Wang, X. Hu, and R. Ma, “A high-performance topological bulk laser based on band-inversion-induced reflection,” Nat. Nanotechnol. 15(1), 67–72 (2020).
[Crossref]

M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, “Robust topologically protected transport in photonic crystals at telecommunication wavelengths,” Nat. Nanotechnol. 14(1), 31–34 (2019).
[Crossref]

S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, “Nonlinear light generation in topological nanostructures,” Nat. Nanotechnol. 14(2), 126–130 (2019).
[Crossref]

Nat. Photonics (12)

S. Mittal, V. V. Orre, G. Zhu, M. A. Gorlach, A. Poddubny, and M. Hafezi, “Photonic quadrupole topological phases,” Nat. Photonics 13(10), 692–696 (2019).
[Crossref]

Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang, M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics for on-chip communication,” Nat. Photonics 14(7), 446–451 (2020).
[Crossref]

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, “Topological protection of photonic mid-gap defect modes,” Nat. Photonics 12(7), 408–415 (2018).
[Crossref]

A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” Nat. Photonics 13(10), 697–700 (2019).
[Crossref]

M. Li, D. Zhirihin, M. Gorlach, X. Ni, Dmitry Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, “Higher-order topological states in photonic kagome crystals with long-range interactions,” Nat. Photonics 14(2), 89–94 (2020).
[Crossref]

H. Kim, R. Bose, T. C. Shen, G. S. Solomon, and E. Waks, “A quantum logic gate between a solid-state quantum bit and a photon,” Nat. Photonics 7(5), 373–377 (2013).
[Crossref]

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, and S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11(12), 763–773 (2017).
[Crossref]

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
[Crossref]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[Crossref]

Nat. Phys. (3)

F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, and B Zhang, “Topologically protected refraction of robust kink states in valley photonic crystals,” Nat. Phys. 14(2), 140–144 (2018).
[Crossref]

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulide, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14(1), 11–19 (2018).
[Crossref]

J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13(6), 611–617 (2017).
[Crossref]

Nature (7)

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

S. Mittal, E. A. Goldschmidt, and M. Hafezi, “A topological source of quantum light,” Nature 561(7724), 502–506 (2018).
[Crossref]

C. W. Peterson, W. A. Benalcazar, T. L. Hughes, and G. Bahl, “A quantized microwave quadrupole insulator with topologically protected corner states,” Nature 555(7696), 346–350 (2018).
[Crossref]

Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y Chong, and Q. J. Wang, “Electrically pumped topological laser with valley edge modes,” Nature 578(7794), 246–250 (2020).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref]

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541(7638), 473–480 (2017).
[Crossref]

New J. Phys. (2)

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

Opt. Commun. (1)

M. Notomi, K. Nozaki, A. Shinya, S. Matsuo, and E. Kuramochi, “Toward fJ/bit optical communication in a chip,” Opt. Commun. 314, 3–17 (2014).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Opt. Mater. Express (1)

Optica (7)

Phys. Rev. A (3)

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics,” Phys. Rev. A 93(4), 043827 (2016).
[Crossref]

M. J. Collins, F. Zhang, R. Bojko, L. Chrostowski, and M. C. Rechtsman, “Integrated optical Dirac physics via inversion symmetry breaking,” Phys. Rev. A 94(6), 063827 (2016).
[Crossref]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[Crossref]

Phys. Rev. B (9)

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[Crossref]

X.-D. Chen, F.-L. Zhao, M. Chen, and J.-W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
[Crossref]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96(20), 201402 (2017).
[Crossref]

A. Mock, L. Lu, and J. O’Brien, “Space group theory and Fourier space analysis of two-dimensional photonic crystal waveguides,” Phys. Rev. B 81(15), 155115 (2010).
[Crossref]

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, “Effects of symmetry reduction in two-dimensional square and triangular lattices,” Phys. Rev. B 69(23), 235112 (2004).
[Crossref]

F. Liu, H.-Y. Deng, and K. Wakabayashi, “Topological photonic crystals with zero Berry curvature,” Phys. Rev. B 97(3), 035442 (2018).
[Crossref]

B. -Y Xie, H.-F. Wang, H. -X Wang, X.-Y Zhu, J.-H. Jiang, M.-H. Lu, and Y. -F. Chen, “Second-order photonic topological insulator with corner states,” Phys. Rev. B 98(20), 205147 (2018).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators,” Phys. Rev. B 96(24), 245115 (2017).
[Crossref]

S. Barik, A. Karasahin, S. Mittal, E. Waks, and M. Hafezi, “Chiral quantum optics using a topological resonator,” Phys. Rev. B 101(20), 205303 (2020).
[Crossref]

Phys. Rev. Lett. (17)

A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, “Topological optical waveguiding in silicon and the transition between topological and trivial defect states,” Phys. Rev. Lett. 116(16), 163901 (2016).
[Crossref]

J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989).
[Crossref]

W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979).
[Crossref]

B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y. -F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” Phys. Rev. Lett. 122(23), 233903 (2019).
[Crossref]

X.-D. Chen, W.-M. Deng, F.-L. Shi, F.-L Zhao, M. Chen, and J. -W. Dong, “Direct observation of corner states in second-order topological photonic crystal slabs,” Phys. Rev. Lett. 122(23), 233902 (2019).
[Crossref]

K. Takata and M. Notomi, “Photonic topological insulating phase induced solely by gain and loss,” Phys. Rev. Lett. 121(21), 213902 (2018).
[Crossref]

D. Smirnova, S. Kruk, D. Leykam, E. Melik-Gaykazyan, D.-Y. Choi, and Y. Kivshar, “Third-harmonic generation in photonic topological metasurfaces,” Phys. Rev. Lett. 123(10), 103901 (2019).
[Crossref]

Y. Hatsugai, “Chern number and edge states in the integer quantum Hall effect,” Phys. Rev. Lett. 71(22), 3697–3700 (1993).
[Crossref]

Z.-Q. Yang, Z.-K. Shao, H.-Z. Chen, X.-R. Mao, and R.-M. Ma, “Spin-momentum-locked edge mode for topological vortex lasing,” Phys. Rev. Lett. 125(1), 013903 (2020).
[Crossref]

H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
[Crossref]

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref]

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Phys. Rev. Lett. 106(9), 093903 (2011).
[Crossref]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[Crossref]

S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, “Topologically robust transport of photons in a synthetic gauge field,” Phys. Rev. Lett. 113(8), 087403 (2014).
[Crossref]

J. Noh, S. Huang, K. P. Chen, and M. C. Rechtsman, “Observation of photonic topological valley Hall edge states,” Phys. Rev. Lett. 120(6), 063902 (2018).
[Crossref]

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018).
[Crossref]

Phys. Rev. Res. (1)

E. Sauer, J. P. Vasco, and S. Hughes, “Theory of intrinsic propagation losses in topological edge states of planar photonic crystals,” Phys. Rev. Res. 2(4), 043109 (2020).
[Crossref]

Phys. Rev. X (1)

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

Proc. IEEE (1)

T. Asano and S. Noda, “Photonic crystal devices in silicon photonics,” Proc. IEEE 106(12), 2183–2195 (2018).
[Crossref]

Rev. Mod. Phys. (1)

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Sci. Adv. (1)

N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, “Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing,” Sci. Adv. 6(10), eaaw4137 (2020).
[Crossref]

Sci. Bull. (1)

J. Wang and Y. Long, “On-chip silicon photonic signaling and processing: a review,” Sci. Bull. 63(19), 1267–1310 (2018).
[Crossref]

Sci. Rep. (1)

A. P. Slobozhanyuk, A. B. Khanikaev, D. S. Filonov, D. A. Smirnova, A. E. Miroshnichenko, and Y. S. Kivshar, “Experimental demonstration of topological effects in bianisotropic metamaterials,” Sci. Rep. 6(1), 22270 (2016).
[Crossref]

Science (8)

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359(6381), eaar4005 (2018).
[Crossref]

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum interface,” Science 359(6376), 666–668 (2018).
[Crossref]

B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, “Nonreciprocal lasing in topological cavities of arbitrary geometries,” Science 358(6363), 636–640 (2017).
[Crossref]

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vučković, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 (2008).
[Crossref]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, “Quantized electric multipole insulators,” Science 357(6346), 61–66 (2017).
[Crossref]

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref]

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref]

Other (2)

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Che, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett.34(11), 1633 (2009).
[Crossref]

G. Arregui, J. Gomis-Bresco, C. M. Sotomayor-Torres, and P. D. Garcia, “Quantifying the robustness of topological slow light,” arXiv:2007.15606 (2020).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1. Semiconductor-based topological PhCs with (a) broken and (b) with preserved time-reversal symmetry, corresponding to photonic quantum Hall and photonic quantum spin Hall systems, respectively. (a) Adapted from [46] with permission from AAAS. Copyright 2017. (b) Adapted from [51] with permission from AAAS. Copyright 2018.
Fig. 2.
Fig. 2. (a) Unit cell of a honeycomb PhC with equilateral triangular air holes and corresponding first Brillouin zone. (b) unit cells of VPhCs with opposite Berry curvatures. (c) TE-mode photonic band structures for the structure shown in (a) (black dashed curves) and for the structures shown in (b) (red curves). Band structures were calculated by two-dimensional plane-wave expansion method using a semiconductor refractive index of 3.4. Note that the two structures in (b) have the same band structure.
Fig. 3.
Fig. 3. (a) Zigzag and bearded interfaces. (b) Projected band diagram for interfaces with LL= 1.3a/$\sqrt {3}$ and LS=0.9a/$\sqrt {3}$, where a is the period. Red and blue curves are dispersion curves for edge states at zigzag and bearded interfaces, respectively. Shaded regions show bulk modes. Dashed lines represent light line. Optical modes above the light line couple with radiation modes. Band diagram was calculated using two-dimensional plane-wave expansion method. Refractive index of 3.4 was used for the calculations.
Fig. 4.
Fig. 4. Silicon VPhCs: (a) VPhC waveguide formed in a silicon membrane. (b) SOI VPhC waveguide. (c) topological photon router composed of a microdisk and two VPhC waveguides. (d) Si-based VPhC cavity and (e) beam splitter. (a): Adapted from [70] with permission from Springer Nature: Nature Nanotechnology, Copyright (2019). (b) and (c): Adapted from [73] under a Creative Commons Attribution 4.0 International license. (d) and (e): Adapted from [75] with permission, Copyright (2019).
Fig. 5.
Fig. 5. III-V VPhCs with light emitter: (a) SEM image of GaAs VPhC embedding QD light emitters as internal light sources (top) and PL image (bottom). (b) SEM image of VPhC laser with quantum well gain (top), emission spectra at different pumping power (middle), and emission patterns measured at pumping powers indicated in middle panel (bottom). (a): Adapted from [78]. Copyright (2019) The Japan Society of Applied Physics. (b): Adapted with permission from [79] © The Optical Society.
Fig. 6.
Fig. 6. Topological nanocavities based on edge states in 1D systems. (a) SSH chain comprising L3 nanocavities (top) and emission spectra (bottom) for edge mode lasing (red) and for bulk mode lasing (blue). (b) Schematic of topological nanocavity formed in PhC nanobeam. Blue and red regions have Zak phases of π and 0, respectively. (c) SEM image of topological nanobeam cavity and calculated field distribution of in-gap localized mode. (d) Emission spectra below and above the laser threshold. (a) Adapted from [87] under a Creative Commons Attribution 4.0 International license. (b-d) Adapted from [88] under a Creative Commons Attribution 4.0 International license.
Fig. 7.
Fig. 7. Nanocavity formed in effective bichromatic potential in a PhC waveguide. (a) Schematic of the structure. (b) SEM image of a nanocavity with a bichiromatic potential. (c) Measured spectrum indicating the presence of a high Q cavity. Adapted from [92] under a Creative Commons Attribution 4.0 International license.
Fig. 8.
Fig. 8. PhC nanocavity based on a topological corner state. (a) Schematic of a corner structure constructed using topological and trivial PhCs with square lattice along with a calculated field distribution of a corner mode. (b) Definitions of unit cells for topological and trivial PhCs. Corresponding Brillouin zone is also shown. (c) Photonic band structure for the PhCs with (d1,d2)=(0.7a, 0.1a). (d) Field distributions at X point for the first two bands in trivial (upper) and topological (lower) PhCs. (e) SEM image of a GaAs nanocavity based on a corner state. (f) µ-PL spectrum measured at cryogenic temperature. The peak around 1075 nm is originated form the corner state. Adapted with permission from [100] © The Optical Society.
Fig. 9.
Fig. 9. Topological nanocavity lasers based on corner states. (a) SEM images of nanocavity laser based on a corner state in a square lattice (top). Emission spectra from a corner pumped with different pump powers (bottom). (b) SEM image of topological nanocavity laser in a VPhC (top left). Emission pattern of the triad mode (top right). Far field patters (bottom) measured through apertures show in the middle. (a) Adapted from [102] with permission. Copyright (2020) American Chemical Society. (b): Adapted from [109] under a Creative Commons Attribution 4.0 International license.

Tables (1)

Tables Icon

Table 1. Topological waveguides and nanocavities realized in semiconductor-based PhCs