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 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
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 [1–3]. 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 [4–9]. 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 [10–15]. Moreover, more research related to chiral optics covers chiral imaging , optical storage , all-optical magnetic recording , and valley information processing [19,20].
Photonic chiral behavior has been studied in metasurfaces , nanostructures [7,9], and various optical interfaces, such as air–glass  and metal–dielectric interfaces . 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 [23–25]. 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 , dipole emission , 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 . 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  and sorting  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 as23,32]
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 -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 -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.
Despite the mirror symmetry relative to the YZ plane, the waveguide structure, consisting of an upper cladding of air and buffer layer of , breaks the mirror symmetry relative to the XZ plane . 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 -polarization component excites the fundamental 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 mode. The -polarization component excites the 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 mode into the first-order mode because of mode hybridization with structural asymmetry relative to the XZ plane , 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 -polarized and -polarized light. In the adiabatic inverse taper structure, and 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:34,35].
The power splitting here highly depends on the phase retardation and amplitude ratio , and thus is eventually associated with the helicity () of the incident light. The directionality of chiral coupling is calculated bySupplement 1). Under such an approximation, when suitably setting the joint location of the -branch structure to obtain (), the directionality can be simplified as 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 RCP incident light (), is maximal and minimal; hence, [Fig. 2(b)]. For LCP incident light (), is minimal but maximal, and thus [Fig. 2(c)]. For LP incident light with a diagonal orientation ( or ), , yielding [Fig. 2(d)]. The LP states have other polarization orientations, such as pure polarization () and polarization (), but all these cases of LP inputs feature similar phenomena to that in Fig. 2(d) with (see Supplement 1). From another perspective, an LP state with orientation angle can be regarded as a linear combination of orthogonal LCP and RCP. The expansion using the Jones vector can be explicitly written as
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 () 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 mode to the mode for the -polarization component of incident light. At the branching point of the -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 () 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.
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 (see Supplement 1), where 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 , , 0, 0.5, and 1, respectively, at two wavelengths of in Figs. 3(b)–3(f) and in Figs. 3(g)–3(k) with opposite directionality. One can clearly see the distinct chiral coupling to different output ports of the -branch waveguide is determined by the helicity of incident polarization handedness. Note that the measured intensity profiles from two output ports of the -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 -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 (, ) with opposite directionality are in good agreement with the theoretical values. In particular, the absolute values of measured directionality exceed 0.92 under complete LCP () and RCP () inputs, indicating the high directionality of chiral silicon photonic circuits.
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 -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 -branch waveguide under incident LCP () light, while Figs. 5(d) and 5(e) plot the measured results under incident RCP () light. Figures 5(c) and 5(f) depict the calculated directionality of chiral coupling under incident LCP () and RCP () 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 () between the and 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.
The simulation results in Figs. 5(c) and 5(f) show an ultrahigh directionality that approaches , and the measured values of 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 . The results shown in Figs. 3–5 demonstrate the successful implementation of ultra-directional and high-efficiency chiral coupling in silicon photonic circuits.
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 -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.
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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