Abstract

Chiral light–matter interaction is currently revolutionizing the fundamental research on light and its applications. This interaction has traditionally faced the challenges of low directionality and efficiency based on the spin–orbit interaction of light in microscopic waveguides. It is important to exploit photonic integrated circuits to efficiently engineer photonic chiral behavior. In this paper, we propose and demonstrate ultra-directional high-efficiency chiral coupling in silicon photonic circuits based on low-to-high-order mode conversion and interference. We show that the directionality of chiral coupling can, in principle, approach ±1 with circular polarization inputs by benefiting from the underlying mechanism of complete destructive and constructive interference. The efficiency of chiral coupling can exceed 70%, with negligible scattering to unguided modes, and this is considerably higher than the efficiency of conventional coupling mechanisms. Moreover, chiral silicon photonic circuits can function as perfect 3 dB power splitters for arbitrarily linear polarization inputs. These offer the possibility of on-chip chirality determination and management using photonic integrated circuits for flourishing development in chiral optics.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Chiral optics has promoted the development of fundamental research on light and its applications over the past few years. It is associated with optical polarization handedness or spin angular momentum (SAM), which determines the chiral (spin-dependent) behavior of light–matter interactions. Analogous to the electric spin Hall effect (SHE) that characterizes the spin-dependent transport of electrons, and the quantum SHE version related to unidirectional edge spin transport, recently discovered photonic counterparts called photonic (quantum) SHEs feature the representative phenomenon of chiral optics [13]. It emerges as the manifestation of spin-dependent splitting or a shift in light beams and the spin-controlled unidirectional excitation of surface plasmon–polariton or waveguide modes. The physical mechanism underlying them is the general spin–orbit interaction of light in metasurfaces, gradient-index media, or strongly confined nanowaveguides [49]. In particular, the chiral effects of light–matter interactions in photonic nanostructures may offer a robust opportunity for developing chiral quantum optics, and thus promoting quantum information processing and computing [1015]. Moreover, more research related to chiral optics covers chiral imaging [16], optical storage [17], all-optical magnetic recording [18], and valley information processing [19,20].

Photonic chiral behavior has been studied in metasurfaces [21], nanostructures [7,9], and various optical interfaces, such as air–glass [22] and metal–dielectric interfaces [5]. For the nanophotonic waveguides, the strongly confined guided modes naturally manifest as non-negligible longitudinal polarization components. Accordingly, this gives rise to a large intrinsically transverse spin that induces the remarkable spin-momentum locking phenomenon of light [2325]. Based on this effect of nanophotonic waveguides, on-chip chiral resolution, chiral photonic circuit emission, and the nonreciprocal phenomenon have been recently discovered and investigated via silicon microdisks [26], dipole emission [14], and photonic crystal waveguides with embedded quantum dots [11,15]. It is worth noting that most reported photonic chiral behaviors face significant challenges in terms of low directionality and efficiency, fundamentally limited by their chiral mechanisms. Because there is substantial coupling to unguided modes, chiral coupling efficiency is lowered by the dipole emitter and the silicon microdisk scatter [5,7,26], except in the case of chiral emission utilizing quantum dots, but with the requirement of inducing the magnetic field [11]. As is well known, for scalable photonic integration and even quantum internet in the future, silicon photonics provides a promising platform to solve the problems of miniaturization, cost of fabrication, and compatibility with mature complementary metal-oxide semiconductor (CMOS) technologies [27,28]. Over the past few decades, the conventional fundamental transverse electrical (TE) and transverse magnetic (TM) mode management in silicon photonic circuits has been well studied, such as the cases of splitting/rotating [29] and sorting [30] linear polarization (LP) beams. However, the analogue to management for circularly polarized light has received little attention on silicon platforms. Moreover, returning to the chiral optics scheme, it is significant to exploit a new method to efficiently engineer photonic chiral behavior in silicon photonic circuits.

In this paper, we propose and demonstrate ultra-directional and high-efficiency chiral coupling in silicon photonic circuits based on low-to-high-order mode conversion and interference. The chiral coupling in photonic integrated circuits manifests as remarkably directional coupling that depends on the polarization handedness of the incident light. It removes the conventional restrictions on coupling of only LP inputs to silicon photonic circuits. The underlying mechanism enabling chiral coupling is optical interference, a well-known phenomenon and the cornerstone of numerous applications of optics. Spin-controlled directional coupling based on the interference principle has previously been demonstrated for plasmon polaritons emission [5,31]. We exploit interference with different mode orders to achieve high directionality of chiral coupling because of complete destructive and constructive interference. Furthermore, chiral coupling based on guided-mode interference possesses high efficiency, notably much higher than the mechanism originating from the spin-momentum locking of light at nanowaveguide interfaces. Moreover, the proposed chiral silicon photonic circuits enable exact on-chip chirality determination for the polarization handedness of light, and can also function as perfect 3 dB power splitters for LP incident light with arbitrary polarization orientation, which, to the best of our knowledge, has not yet been demonstrated before in polarization-sensitive silicon nanophotonic devices.

2. PRINCIPLE AND DESIGN

We first study the helicity of optical polarization handedness. The complex electric field of light with polarization handedness can be described as

E=A[ex+m·exp(iδ)·ey]exp[i(kzωt)],
where A is wave amplitude, ex and ey denote the unit vectors of the corresponding axes, m indicates the ratio of the amplitude of the y-polarized to the x-polarized components of the electric field, δ describes the phase retardation between them, and k=ω/c is the wavenumber, with ω the angular frequency and c the speed of light in a vacuum. The helicity of polarization handedness is given by [23,32]
σ=2·Im(Ex·Ey*)|Ex|2+|Ey|2=2m·sinδ1+m2.
In the above, σ[1,1], especially, the integers σ=1, 1, and 0, describe left-handed circular polarization (LCP) σ1, right-handed circular polarization (RCP) σ+1, and LP states of light, respectively, correspondingly carrying the mean SAM of , +, and 0 per photon, where denotes Planck’s constant divided by 2π.

The chiral effect of light–matter interactions is illustrated in Fig. 1(a). It is characterized by the spin-dependent splitting of light or its directional emitting, scattering, and coupling. Its mechanisms include the wave interference [5,31], spin–orbit coupling [4,8], and spin-momentum locking [2,7,11] of light. In our scheme, the chiral photonic device is formed on a silicon-on-insulator (SOI) platform. As shown in Fig. 1(b), the incident light in the LCP or RCP state is injected into a polymer (SU8)-assisted inversely tapered Y-branch silicon waveguide for chiral coupling. This specific waveguide structure for chiral coupling can be divided into three parts, i.e., a thick wire polymer waveguide covering an inversely tapered silicon waveguide at the bottom (part I), a subsequent adiabatic inverse taper structure after the polymer waveguide (part II), and a Y-branch waveguide at the end of the inverse taper structure (part III). The insets in Fig. 1(b) show zoomed-in details of the three parts of the designed device.

 

Fig. 1. Principle and design of chiral silicon photonic circuits. (a) Schematic illustration of chiral effect of light–matter interactions. The polarization handedness of incident light determines the chiral behavior of light–matter interactions. (b) 3D view of chiral silicon photonic circuits (polymer-assisted inversely tapered Y-branch silicon waveguide) for chiral coupling based on low-to-high-order mode conversion and interference. (c) Calculated effective refractive index versus the silicon waveguide width. In the adiabatic inverse taper structure with the waveguide width varying from 600 to 840 nm, the TE0 mode remains unchanged, while the TM0 mode evolves into the TE1 mode due to mode hybridization.

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Despite the mirror symmetry relative to the YZ plane, the waveguide structure, consisting of an upper cladding of air and buffer layer of SiO2, breaks the mirror symmetry relative to the XZ plane [30]. Such asymmetry can be understood as a fundamental requirement for chirality sorting with circular polarization. More specifically, the working principle of the chiral silicon photonic device relies on low-to-high-order mode conversion and interference, briefly described as follows. For incident light, the x-polarization component excites the fundamental TE0 mode of the polymer waveguide with high efficiency. It is then coupled into the inversely tapered silicon waveguide sitting at the bottom of the polymer waveguide, and maintained in a subsequent adiabatically tapered silicon waveguide as the TE0 mode. The y-polarization component excites the TM0 mode coupling from the polymer waveguide to the inversely tapered silicon waveguide at the bottom. The subsequent adiabatic inverse taper structure after the polymer waveguide converts the TM0 mode into the first-order TE1 mode because of mode hybridization with structural asymmetry relative to the XZ plane [33], as shown in Fig. 1(c), which enables the transfer of guided modes from quasi-vertical polarization to the quasi-horizontal polarization.

The simulated transverse mode pattern evolution at six positions [1, 2, 3, 4, 5, 6 marked in Fig. 1(b)] along the waveguide is shown in Fig. 2(a) for both the incident x-polarized and y-polarized light. In the adiabatic inverse taper structure, TE0 and TE1 modes both with quasi-horizontal polarization produce spatial interference in the case of circular polarization inputs, giving rise to quasi-periodic up-and-down oscillation of field density along the direction of propagation [Fig. 1(b)]. The power evolution of up-and-down oscillating interference fields can be deduced by integrating the field density along the upper and lower half of the field region (see Supplement 1) as follows:

Iu=ξ+m2·ψ+2m·ζ·cos(Δβ·zδ).
Id=ξ+m2·ψ2m·ζ·cos(Δβ·zδ).
In the above, ξ and ψ are integral coefficients for the TE0 and TE1 modes on the upper and lower half of the field region, respectively, and ζ indicates that of the superposition term. Δβ=Δneffk is the propagation constant difference between the TE0 and TE1 modes at the end of the adiabatic inverse taper structure, with Δneff the effective index difference. Accordingly, the up-and-down oscillating interference fields completely determine directional coupling to output of the following Y-branch waveguide. Note that a similar function of the Y-branch waveguide might be achieved by multimode interference (MMI) couplers [34,35].

 

Fig. 2. Results of numerical simulation. (a) Transverse mode pattern evolution at six positions [1, 2, 3, 4, 5, 6 in Fig. 1(b)] along the waveguide for both the x- and y-polarization component inputs. (b)–(d) Simulation results of chiral coupling in silicon photonic circuits when the incident polarization handedness is (b) RCP, (c) LCP, and (d) LP, respectively.

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The power splitting here highly depends on the phase retardation δ and amplitude ratio m, and thus is eventually associated with the helicity (σ) of the incident light. The directionality of chiral coupling is calculated by

D=IuIdIu+Id=2m·ζ·cos(Δβ·zδ)ξ+m2·ψ.
Remarkably, a high directionality of chiral coupling for the inputs σ1 and σ+1 of polarization handedness (m=1) can be obtained provided that the interference is completely destructive and constructive on the condition of ξψζ (see Supplement 1). Under such an approximation, when suitably setting the joint location of the Y-branch structure to obtain Δβ·z=(2n+1/2)π (n=0,1,2), the directionality can be simplified as
D2m·sinδ1+m2=σ,
which is directly linked to the helicity of the polarization handedness of the incident light. Analogously, when Δβ·z=(2n1/2)π (n=0,1,2), directionality is given by Dσ. This is the primary goal of the study. Note that the chiral coupling for circular polarization states can be extended to any two orthogonal polarization states, such as elliptical polarizations based on a similar design principle (see Supplement 1).

We numerically verify the chiral coupling and show the results by using 3D finite-difference time-domain (3D-FDTD) simulations for three polarization handedness inputs, as shown in Figs. 2(b)2(d). For σ+1 RCP incident light (δ=π/2), Iu is maximal and Id minimal; hence, D1 [Fig. 2(b)]. For σ1 LCP incident light (δ=π/2), Iu is minimal but Id maximal, and thus D1 [Fig. 2(c)]. For LP incident light with a ±45° diagonal orientation (δ=0 or π), IuId, yielding D0 [Fig. 2(d)]. The LP states have other polarization orientations, such as pure x polarization (m=0) and y polarization (m), but all these cases of LP inputs feature similar phenomena to that in Fig. 2(d) with D0 (see Supplement 1). From another perspective, an LP state with orientation angle α can be regarded as a linear combination of orthogonal LCP and RCP. The expansion using the Jones vector can be explicitly written as

[cosαsinα]=12(cosαisinα)[1i]+12(cosα+isinα)[1i].
Hence, the chiral silicon photonic device can act as a perfect 3 dB power splitter for arbitrary LP inputs in the case of high-directional chiral coupling for circular polarization inputs. Apparently, this proposed chiral coupling scheme also allows for the determination of the polarization handedness of light.

3. EXPERIMENTAL RESULTS

We fabricate the chiral photonic device on a silicon platform (see Supplement 1) and demonstrate chiral coupling in the fabricated silicon photonic circuits. The experimental setup and results are shown in Fig. 3 to measure the chiral coupling outputs from the silicon photonic circuits. The inset of Fig. 3(b) shows the measured optical microscope image of the fabricated chiral silicon photonic circuits (silicon thickness, 220 nm). The input and output ports of the silicon photonic circuits are all covered by a square polymer (SU8) waveguide (3.5μm×3.5μm) to facilitate efficient excitation and output of light. Note that the polymer waveguide at two output ports is not shown in Fig. 1(b) for simplicity. The silicon waveguide (length, 240 μm) covered by the input polymer waveguide is inversely tapered with its width slowly increasing from 80 to 600 nm, enabling high-efficiency mode coupling into the waveguide. When exiting from the polymer waveguide, the silicon waveguide is further adiabatically tapered with a length of 16 μm and varying width from 600 to 840 nm, enabling the conversion from the TM0 mode to the TE1 mode for the y-polarization component of incident light. At the branching point of the Y-branch waveguide, two output branches are equally split with small bending radii (bending radius, 1.5 μm), and then connected to the large bending waveguides to guarantee a relatively long distance (50μm) between output branches. Note that the initial bending radii of the output branches need to be sufficiently small to effectively separate the oscillating interference fields, and thus achieve high directionality of chiral coupling, despite possibly increasing the insertion loss of the device.

 

Fig. 3. Experimental setup and results for measurements of chiral coupling outputs. (a) Experimental schematic diagram with an inset of an optical microscope image. Pol, polarizer; HWP, half-wave plate; QWP, quarter-wave plate; OL, objective lens; L, lens. (b)–(k) Measured spin-dependent output from chiral silicon photonic circuits under different incident polarization handedness values with helicity (b), (g) σ=1, (c), (h) σ= 0.5, (d), (i) σ= 0, (e), (j) σ= 0.5, and (f), (k) σ= 1, respectively, at two wavelengths [λ1: (b)–(f), λ2: (g)–(k)] with opposite directionality.

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In the measurement setup for free-space coupling, the polarization handedness of incident light is controlled by a group of polarizer and wave plates. The quarter-wave plate (QWP) determines the helicity of polarization handedness as σsin2θ (see Supplement 1), where θ is the rotation angle between the optical axis of the QWP and the polarization direction of light after the half-wave plate (HWP). For light coupling from free space to the waveguide, an objective lens (OL) is used to focus the incident light on the facet of the polymer waveguide, and vice versa, for light output from the waveguide.

The handedness-dependent output from chiral silicon photonic circuits is photographed by a camera under different polarization handedness values of incident light with helicity σ=1, 0.5, 0, 0.5, and 1, respectively, at two wavelengths of λ1 in Figs. 3(b)3(f) and λ2 in Figs. 3(g)3(k) with opposite directionality. One can clearly see the distinct chiral coupling to different output ports of the Y-branch waveguide is determined by the helicity of incident polarization handedness. Note that the measured intensity profiles from two output ports of the Y-branch waveguide feature dark concentric rings, which might be induced by the aberration of the lens for large divergent fields outside the waveguide.

We characterize the directionality of chiral coupling in silicon photonic circuits based on Eq. (5) and measure power from two output ports of the Y-branch waveguide, as shown in Fig. 4. The adjustable polarization state of incident light by controlling the rotation angle of the QWP is shown on the top in Fig. 4. The measured results under different incident polarization handedness values at two wavelengths (λ1, λ2) with opposite directionality are in good agreement with the theoretical values. In particular, the absolute values of measured directionality |D| exceed 0.92 under complete LCP (σ1) and RCP (σ+1) inputs, indicating the high directionality of chiral silicon photonic circuits.

 

Fig. 4. Measured directionality of chiral coupling under different incident polarization handedness at two wavelengths (λ1, λ2) with opposite directionality. The top of the figure shows the incident polarization handedness that varies with rotation angle of the QWP. The measured results in the experiment (balls) are in good agreement with the predicated values by theory (dashed lines).

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We further study the performance of chiral coupling in silicon photonic circuits as a function of wavelength. We measure power from two output ports of the Y-branch waveguide and assess the directionality by sweeping the incident wavelength. For easy measurement of the sweeping spectra, a pair of lensed fibers is used for fiber–chip–fiber coupling (see Supplement 1). The output lensed fiber is connected to an optical power meter to record the sweeping spectra. Figures 5(a) and 5(b) show the measured normalized power from two output ports of the Y-branch waveguide under incident LCP (σ1) light, while Figs. 5(d) and 5(e) plot the measured results under incident RCP (σ+1) light. Figures 5(c) and 5(f) depict the calculated directionality of chiral coupling under incident LCP (σ1) and RCP (σ+1) light, respectively. One can see the interesting quasi-periodic phenomena of the sweeping spectra. It can be explained with the fact that the propagation constant difference (Δβ) between the TE0 and TE1 modes in Eq. (5) due to waveguide dispersion is wavelength dependent, leading to a variation in power and directionality with wavelength. Note that two wavelengths (1542 nm, 1551 nm) with opposite directionality are marked in Figs. 5(b) and 5(e), respectively. To increase the wavelength range with high directionality, one may shorten the inversely tapered silicon waveguide (see Supplement 1). Moreover, it is possible to implement wavelength-tunable chiral coupling in practical applications assisted by the thermal-optic tuning technique.

 

Fig. 5. Measured and simulated performance of chiral coupling in silicon photonic circuits versus wavelength. (a), (b), (d), (e) Normalized power from (a), (d) up and (b), (e) down output ports of the Y-branch waveguide. (c), (f) Directionality of chiral coupling in silicon photonic circuits. (a)–(c) LCP (σ1) incident light. (d)–(f), RCP (σ+1) incident light. Solid lines, experiment. Dashed lines, theory.

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The simulation results in Figs. 5(c) and 5(f) show an ultrahigh directionality that approaches ±1, and the measured values of |σ| can be over 0.98. For efficiency of chiral coupling, the simulation results show that the insertion loss can be less than 30% (see Supplement 1). In the experiment, the measured insertion loss of the chiral silicon photonic circuits is estimated to be approximately 5dB. The results shown in Figs. 35 demonstrate the successful implementation of ultra-directional and high-efficiency chiral coupling in silicon photonic circuits.

4. CONCLUSION

We propose and demonstrate simple silicon photonic circuits for on-chip chiral coupling with impressive performance. The underlying mechanism of chiral coupling is low-to-high-order mode conversion and interference. The mode interference enables high directionality owing to the complete destructive and constructive interference. The polymer-assisted coupling and guided-mode interference improve the efficiency of chiral coupling with negligible scattering to unguided modes. The high directionality and efficiency of chiral photonic behavior have not yet been achieved before, to the best of the our knowledge of other reported mechanisms. With further improvement, the directionality and efficiency can be enhanced through the optimization of geometric parameters of the inversely tapered silicon waveguide structure and the bending radius of the Y-branch waveguide. In addition, the chiral silicon photonic circuits can be used as a perfect 3 dB power splitter for LP light with arbitrary polarization orientation, which has not yet been reported before in polarization-sensitive silicon nanophotonic devices. Apparently, the chiral silicon photonic circuits also can be exploited to determine the helicity of the polarization handedness of light, providing a means for high-performance chip-scale photonic spin sorting and other spin-related applications. It is believed that photonic integrated circuits will play an increasingly important role in chip-scale chiral optics and other emerging chirality-related applications.

Funding

National Natural Science Foundation of China (NSFC) (61761130082, 11774116, 11574001, 11274131, 61222502); National Basic Research Program of China (973 Program) (2014CB340004); Royal Society-Newton Advanced Fellowship; National Program for Support of Top-notch Young Professionals; Natural Science Foundation of Hubei Province (2018CFA048); Program for Huazhong University of Science and Technology (HUST) Academic Frontier Youth Team (2016QYTD05).

 

See Supplement 1 for supporting content.

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References

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  1. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
    [Crossref]
  2. K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348, 1448–1451 (2015).
    [Crossref]
  3. X. Ling, X. Zhou, K. Huang, Y. Liu, C. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
    [Crossref]
  4. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
    [Crossref]
  5. F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
    [Crossref]
  6. M. Khorasaninejad and K. B. Crozier, “Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter,” Nat. Commun. 5, 5386 (2014).
    [Crossref]
  7. J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
    [Crossref]
  8. K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796–808 (2015).
    [Crossref]
  9. G. Li, A. S. Sheremet, R. Ge, T. C. H. Liew, and A. V. Kavokin, “Design for a nanoscale single-photon spin splitter for modes with orbital angular momentum,” Phys. Rev. Lett. 121, 053901 (2018).
    [Crossref]
  10. P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473–480 (2017).
    [Crossref]
  11. I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
    [Crossref]
  12. M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeute, “Quantum optical circulator controlled by a single chirally coupled atom,” Science 354, 1577–1580 (2016).
    [Crossref]
  13. I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
    [Crossref]
  14. B. L. Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
    [Crossref]
  15. R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
    [Crossref]
  16. M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
    [Crossref]
  17. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
    [Crossref]
  18. C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
    [Crossref]
  19. K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7, 494–498 (2012).
    [Crossref]
  20. S. Gong, F. Alpeggiani, B. Sciacca, E. C. Garnett, and L. Kuipers, “Nanoscale chiral valley-photon interface through optical spin-orbit coupling,” Science 359, 443–447 (2018).
    [Crossref]
  21. S. Xiao, J. Wang, F. Liu, S. Zhang, X. Yin, and J. Li, “Spin-dependent optics with metasurfaces,” Nanophotonics 6, 215–234 (2017).
    [Crossref]
  22. K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
    [Crossref]
  23. K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
    [Crossref]
  24. A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9, 789–795 (2015).
    [Crossref]
  25. L. Fang and J. Wang, “Intrinsic transverse spin angular momentum of fiber eigenmodes,” Phys. Rev. A 95, 053827 (2017).
    [Crossref]
  26. F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photon. 1, 762–767 (2014).
    [Crossref]
  27. J. Wang and Y. Long, “On-chip silicon photonic signaling and processing: a review,” Sci. Bull. 63, 1267–1310 (2018).
  28. J. Wang, “Metasurfaces enabling structured light manipulation: advances and perspectives [Invited],” Chin. Opt. Lett. 16, 050006 (2018).
  29. D. Dai, L. Liu, S. Gao, D. Xu, and S. He, “Polarization management for silicon photonic integrated circuits,” Laser Photon. Rev. 7, 303–328 (2013).
    [Crossref]
  30. F. J. Rodríguez-Fortuño, D. Puerto, A. Griol, L. Bellieres, J. Martí, and A. Martínez, “Sorting linearly polarized photons with a single scatterer,” Opt. Lett. 39, 1394–1397 (2014).
    [Crossref]
  31. J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
    [Crossref]
  32. A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5, 011039 (2015).
    [Crossref]
  33. D. Dai and J. E. Bowers, “Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires,” Opt. Express 19, 10940–10949 (2011).
    [Crossref]
  34. H. Wei, J. Yu, and X. Zhang, “Compact 3-dB tapered multimode interference coupler in silicon-on-insulator,” Opt. Lett. 26, 878–880 (2001).
    [Crossref]
  35. A. Hosseini, H. Subbaraman, D. Kwong, Y. Zhang, and R. T. Chen, “Optimum access waveguide width for 1 × N multimode interference couplers on silicon nanomembrane,” Opt. Lett. 35, 2864–2866 (2010).
    [Crossref]

2018 (4)

G. Li, A. S. Sheremet, R. Ge, T. C. H. Liew, and A. V. Kavokin, “Design for a nanoscale single-photon spin splitter for modes with orbital angular momentum,” Phys. Rev. Lett. 121, 053901 (2018).
[Crossref]

S. Gong, F. Alpeggiani, B. Sciacca, E. C. Garnett, and L. Kuipers, “Nanoscale chiral valley-photon interface through optical spin-orbit coupling,” Science 359, 443–447 (2018).
[Crossref]

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

J. Wang, “Metasurfaces enabling structured light manipulation: advances and perspectives [Invited],” Chin. Opt. Lett. 16, 050006 (2018).

2017 (4)

L. Fang and J. Wang, “Intrinsic transverse spin angular momentum of fiber eigenmodes,” Phys. Rev. A 95, 053827 (2017).
[Crossref]

S. Xiao, J. Wang, F. Liu, S. Zhang, X. Yin, and J. Li, “Spin-dependent optics with metasurfaces,” Nanophotonics 6, 215–234 (2017).
[Crossref]

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

X. Ling, X. Zhou, K. Huang, Y. Liu, C. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
[Crossref]

2016 (3)

M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeute, “Quantum optical circulator controlled by a single chirally coupled atom,” Science 354, 1577–1580 (2016).
[Crossref]

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
[Crossref]

2015 (6)

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796–808 (2015).
[Crossref]

B. L. Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref]

K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348, 1448–1451 (2015).
[Crossref]

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9, 789–795 (2015).
[Crossref]

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5, 011039 (2015).
[Crossref]

2014 (6)

F. J. Rodríguez-Fortuño, D. Puerto, A. Griol, L. Bellieres, J. Martí, and A. Martínez, “Sorting linearly polarized photons with a single scatterer,” Opt. Lett. 39, 1394–1397 (2014).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (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 Photon. 1, 762–767 (2014).
[Crossref]

M. Khorasaninejad and K. B. Crozier, “Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter,” Nat. Commun. 5, 5386 (2014).
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref]

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

2013 (4)

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
[Crossref]

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

D. Dai, L. Liu, S. Gao, D. Xu, and S. He, “Polarization management for silicon photonic integrated circuits,” Laser Photon. Rev. 7, 303–328 (2013).
[Crossref]

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

2012 (1)

K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7, 494–498 (2012).
[Crossref]

2011 (1)

2010 (1)

2008 (2)

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
[Crossref]

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[Crossref]

2007 (1)

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[Crossref]

2001 (2)

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[Crossref]

H. Wei, J. Yu, and X. Zhang, “Compact 3-dB tapered multimode interference coupler in silicon-on-insulator,” Opt. Lett. 26, 878–880 (2001).
[Crossref]

Aiello, A.

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9, 789–795 (2015).
[Crossref]

Alpeggiani, F.

S. Gong, F. Alpeggiani, B. Sciacca, E. C. Garnett, and L. Kuipers, “Nanoscale chiral valley-photon interface through optical spin-orbit coupling,” Science 359, 443–447 (2018).
[Crossref]

Antoniou, N.

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

Banzer, P.

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9, 789–795 (2015).
[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 Photon. 1, 762–767 (2014).
[Crossref]

Bechler, O.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

Bekshaev, A. Y.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5, 011039 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref]

Bellieres, L.

Bliokh, K. Y.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5, 011039 (2015).
[Crossref]

K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348, 1448–1451 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796–808 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
[Crossref]

Bowers, J. E.

Capasso, F.

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
[Crossref]

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

Chen, R. T.

Chen, W. T.

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
[Crossref]

Clarke, E.

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

Coles, R. J.

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

Crozier, K. B.

M. Khorasaninejad and K. B. Crozier, “Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter,” Nat. Commun. 5, 5386 (2014).
[Crossref]

Dai, D.

D. Dai, L. Liu, S. Gao, D. Xu, and S. He, “Polarization management for silicon photonic integrated circuits,” Laser Photon. Rev. 7, 303–328 (2013).
[Crossref]

D. Dai and J. E. Bowers, “Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires,” Opt. Express 19, 10940–10949 (2011).
[Crossref]

Dayan, B.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

Devlin, R. C.

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
[Crossref]

Dixon, J. E.

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

El-Ella, H.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Fang, L.

L. Fang and J. Wang, “Intrinsic transverse spin angular momentum of fiber eigenmodes,” Phys. Rev. A 95, 053827 (2017).
[Crossref]

Feber, B. L.

B. L. Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[Crossref]

Fox, A. M.

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

Gao, S.

D. Dai, L. Liu, S. Gao, D. Xu, and S. He, “Polarization management for silicon photonic integrated circuits,” Laser Photon. Rev. 7, 303–328 (2013).
[Crossref]

Garnett, E. C.

S. Gong, F. Alpeggiani, B. Sciacca, E. C. Garnett, and L. Kuipers, “Nanoscale chiral valley-photon interface through optical spin-orbit coupling,” Science 359, 443–447 (2018).
[Crossref]

Ge, R.

G. Li, A. S. Sheremet, R. Ge, T. C. H. Liew, and A. V. Kavokin, “Design for a nanoscale single-photon spin splitter for modes with orbital angular momentum,” Phys. Rev. Lett. 121, 053901 (2018).
[Crossref]

Ginzburg, P.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

Gong, S.

S. Gong, F. Alpeggiani, B. Sciacca, E. C. Garnett, and L. Kuipers, “Nanoscale chiral valley-photon interface through optical spin-orbit coupling,” Science 359, 443–447 (2018).
[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 Photon. 1, 762–767 (2014).
[Crossref]

F. J. Rodríguez-Fortuño, D. Puerto, A. Griol, L. Bellieres, J. Martí, and A. Martínez, “Sorting linearly polarized photons with a single scatterer,” Opt. Lett. 39, 1394–1397 (2014).
[Crossref]

Guendelman, G.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

Hansen, S. L.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Hansteen, F.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[Crossref]

Hasman, E.

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
[Crossref]

He, K.

K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7, 494–498 (2012).
[Crossref]

He, S.

D. Dai, L. Liu, S. Gao, D. Xu, and S. He, “Polarization management for silicon photonic integrated circuits,” Laser Photon. Rev. 7, 303–328 (2013).
[Crossref]

Heinz, T. F.

K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7, 494–498 (2012).
[Crossref]

Hilico, A.

M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeute, “Quantum optical circulator controlled by a single chirally coupled atom,” Science 354, 1577–1580 (2016).
[Crossref]

Hosseini, A.

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[Crossref]

Huang, K.

X. Ling, X. Zhou, K. Huang, Y. Liu, C. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
[Crossref]

Itoh, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[Crossref]

Javadi, A.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Kavokin, A. V.

G. Li, A. S. Sheremet, R. Ge, T. C. H. Liew, and A. V. Kavokin, “Design for a nanoscale single-photon spin splitter for modes with orbital angular momentum,” Phys. Rev. Lett. 121, 053901 (2018).
[Crossref]

Khorasaninejad, M.

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
[Crossref]

M. Khorasaninejad and K. B. Crozier, “Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter,” Nat. Commun. 5, 5386 (2014).
[Crossref]

Kimel, A. V.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[Crossref]

Kirilyuk, A.

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P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473–480 (2017).
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S. Gong, F. Alpeggiani, B. Sciacca, E. C. Garnett, and L. Kuipers, “Nanoscale chiral valley-photon interface through optical spin-orbit coupling,” Science 359, 443–447 (2018).
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P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473–480 (2017).
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M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeute, “Quantum optical circulator controlled by a single chirally coupled atom,” Science 354, 1577–1580 (2016).
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J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
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D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
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J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
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M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
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Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1. Principle and design of chiral silicon photonic circuits. (a) Schematic illustration of chiral effect of light–matter interactions. The polarization handedness of incident light determines the chiral behavior of light–matter interactions. (b) 3D view of chiral silicon photonic circuits (polymer-assisted inversely tapered Y -branch silicon waveguide) for chiral coupling based on low-to-high-order mode conversion and interference. (c) Calculated effective refractive index versus the silicon waveguide width. In the adiabatic inverse taper structure with the waveguide width varying from 600 to 840 nm, the TE 0 mode remains unchanged, while the TM 0 mode evolves into the TE 1 mode due to mode hybridization.
Fig. 2.
Fig. 2. Results of numerical simulation. (a) Transverse mode pattern evolution at six positions [1, 2, 3, 4, 5, 6 in Fig. 1(b)] along the waveguide for both the x - and y -polarization component inputs. (b)–(d) Simulation results of chiral coupling in silicon photonic circuits when the incident polarization handedness is (b) RCP, (c) LCP, and (d) LP, respectively.
Fig. 3.
Fig. 3. Experimental setup and results for measurements of chiral coupling outputs. (a) Experimental schematic diagram with an inset of an optical microscope image. Pol, polarizer; HWP, half-wave plate; QWP, quarter-wave plate; OL, objective lens; L, lens. (b)–(k) Measured spin-dependent output from chiral silicon photonic circuits under different incident polarization handedness values with helicity (b), (g)  σ = 1 , (c), (h)  σ = 0.5 , (d), (i)  σ = 0, (e), (j)  σ = 0.5, and (f), (k)  σ = 1, respectively, at two wavelengths [ λ 1 : (b)–(f), λ 2 : (g)–(k)] with opposite directionality.
Fig. 4.
Fig. 4. Measured directionality of chiral coupling under different incident polarization handedness at two wavelengths ( λ 1 , λ 2 ) with opposite directionality. The top of the figure shows the incident polarization handedness that varies with rotation angle of the QWP. The measured results in the experiment (balls) are in good agreement with the predicated values by theory (dashed lines).
Fig. 5.
Fig. 5. Measured and simulated performance of chiral coupling in silicon photonic circuits versus wavelength. (a), (b), (d), (e) Normalized power from (a), (d) up and (b), (e) down output ports of the Y -branch waveguide. (c), (f) Directionality of chiral coupling in silicon photonic circuits. (a)–(c) LCP ( σ 1 ) incident light. (d)–(f), RCP ( σ + 1 ) incident light. Solid lines, experiment. Dashed lines, theory.

Equations (7)

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E = A [ e x + m · exp ( i δ ) · e y ] exp [ i ( k z ω t ) ] ,
σ = 2 · Im ( E x · E y * ) | E x | 2 + | E y | 2 = 2 m · sin δ 1 + m 2 .
I u = ξ + m 2 · ψ + 2 m · ζ · cos ( Δ β · z δ ) .
I d = ξ + m 2 · ψ 2 m · ζ · cos ( Δ β · z δ ) .
D = I u I d I u + I d = 2 m · ζ · cos ( Δ β · z δ ) ξ + m 2 · ψ .
D 2 m · sin δ 1 + m 2 = σ ,
[ cos α sin α ] = 1 2 ( cos α i sin α ) [ 1 i ] + 1 2 ( cos α + i sin α ) [ 1 i ] .

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