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Photonic spin Hall effect (SHE) manifests itself as spin-dependent shift or splitting of a light beam, which is derived from spin–orbit interactions, and can be realized by breaking the rotation symmetry of light–matter interaction systems. Here, we demonstrate the observation of a photonic SHE by breaking the rotation symmetry of the optical field, while keeping the rotation symmetry of the inhomogeneous waveplate. The inhomogeneous waveplate constructed by dielectric nanostructures, introduces a spin-dependent Pancharatnam–Berry phase to the two spin components of the input beam, i.e., the left- and right-circular polarization components acquire exactly opposite vortex phases. During beam propagation, they experience opposite azimuthal rotations, and induce a four-lobe spin-dependent splitting in the azimuthal direction. In addition, the spin-dependent splitting becomes more evident upon beam propagation, and can be enhanced by increasing the topological orders of the nanostructures. For comparison, we also examine that no spin-dependent splitting can be observed when keeping the rotation symmetry of the incident optical field.

We systematically study the role of Weyl cone tilting in the spin Hall effect of light (SHEL) in doped Weyl semimetals (WSMs), and propose a new scheme to determine the type of a WSM and to sense the tilt degree of Weyl cones precisely. It is found that in the case of a small amount of doping, the SHEL in type-I WSMs shows almost no dependence on the tilt degree of Weyl cones, while the SHEL in type-II WSMs is extremely sensitive to variations in the degree of tilt. However, in the case of a large amount of doping, not only the SHEL in type-II WSMs but also the SHEL in type-I WSMs show strong dependences on the tilt degree. These trends are mainly attributed to the variation of the real part of the Hall conductivity with the tilt degree. Remarkably, by using a quantum weak measurement, the tiny SHEL shifts can be amplified and detected to a desirable accuracy. Based on the obviously different tilt-dependent characteristics of amplified SHEL shifts in WSMs, we propose a new scheme to determine the type of a WSM and to sense the tilt degree precisely. By adjusting the doping level, the sensing sensitivity can reach up to 1461.55 µm per degree of tilt. This study may provide an application reference for the fabrication of WSM parameter sensors and other topological photoelectric devices.

The photonic spin Hall effect (SHE) originates from the interplay between the photon-spin (polarization) and the trajectory (extrinsic orbital angular momentum) of light, i.e. the spin-orbit interaction. Metasurfaces, metamaterials with a reduced dimensionality, exhibit exceptional abilities for controlling the spin-orbit interaction and thereby manipulating the photonic SHE. Spin-redirection phase and Pancharatnam-Berry phase are the manifestations of spin-orbit interaction. The former is related to the evolution of the propagation direction and the latter to the manipulation with polarization state. Two distinct forms of splitting based on these two types of geometric phases can be induced by the photonic SHE in metasurfaces: the spin-dependent splitting in position space and in momentum space. The introduction of Pacharatnam-Berry phases, through space-variant polarization manipulations with metasurfaces, enables new approaches for fabricating the spin-Hall devices. Here, we present a short review of photonic SHE in metasurfaces and outline the opportunities in spin photonics.

In this work, we propose a simple approach to realize addition and subtraction operation of optical orbital angular momentum (OAM) based on dielectric metasurfaces. The spin–orbit interaction of light in spatially inhomogeneous and anisotropic metasurfaces results in the spin-to-orbital angular momentum conversion. The subtraction system of OAM consists of two cascaded metasurfaces, while the addition system of OAM is constituted by inserting a half waveplate (HWP) between the two metasurfaces. Our experimental results are in good agreement with the theoretical calculation. These results could be useful for OAM-carrying beams applied in optical communication, information processing, etc.

Based on transformation optics, we propose a method to realize an arbitrary wavefront transformation through an impedance-matched nonmagnetic slab. First, we follow the principle of equal optical path length to realize arbitrary phase transformations by a flat configuration, adopt a nonlinear coordinate transformation to ensure impedance match, and preserve the dispersion relation to render the device nonmagnetic. Applying this method, a phase transformer is designed such that both the wave shape and propagation direction can be changed. Second, we choose distinct deflection angles for two orthogonal polarizations and combine the two sets of material parameters into an anisotropic slab, whereby a wavefront-controllable polarization splitter is achieved. The results are further validated by numerical simulations. The method proposed can be used to develop all-dielectric, lossless and broadband devices that can be easily constructed at optical frequencies.

We examine the geometric phase Doppler effect that appears when a structured light interacts with a rotating structured material. In our scheme the structured light possesses a vortex phase and the structured material works as an inhomogeneous anisotropic plate. We show that the Doppler effect manifests itself as a frequency shift which can be interpreted in terms of a dynamic evolution of Pancharatnam-Berry phase on the hybrid-order Poincare sphere. The frequency shift induced by the change rate of Pancharatnam-Berry phase with time is derived from both the Jones matrix calculations and the theory of the hybrid-order Poincare sphere. Unlike the conventional rotational Doppler effect, the frequency shift is proportional to the variation of total angular momentum of light beam, irrespective of the orbital angular momentum of input beams.

Perfect vortex beams are the orbital angular momentum (OAM)-carrying beams with fixed annular intensities, which provide a better source of OAM than traditional Laguerre- Gaussian beams. However, ordinary schemes to obtain the perfect vortex beams are usually bulky and unstable. We demonstrate here a novel generation scheme by designing planar Pancharatnam-Berry (PB) phase elements to replace all the elements required. Different from the conventional approaches based on reflective or refractive elements, PB phase elements can dramatically reduce the occupying volume of system. Moreover, the PB phase element scheme is easily developed to produce the perfect vector beams. Therefore, our scheme may provide prominent vortex and vector sources for integrated optical communication and micromanipulation systems., Comment: 14 pages, 5 figures, accepted for publication in Scientific Reports

Development of spin-photonic devices requires the integration of abundant functions and the miniaturization of the elements. Pancharatnam-Berry phase elements have fulfilled these requirements and can be attained by using dielectric metasurfaces with subwavelength nanostructures. Here, we review some of our works on Pancharatnam- Berry phase elements and make an introduction of some integrated spin-photonic devices. We propose to integrate Pancharatnam-Berry phase lens into dynamical phase lens, which can be conveniently used to modulate spin states of photons. By integrating a Pancharatnam-Berry phase lens into a conventional plano-concave lens, we can obtain spin-filtering of photons. Moreover, we demonstrate that the generation of complex wavefronts characterized with different spin states can be implemented by the Pancharatnam-Berry phase lens. Further, based on the spin-dependent property of Pancharatnam-Berry phase element, we realize the three-dimensional photonic spin Hall effect with lateral and longitudinal spin-dependent splitting simultaneously. We foresee that this optical integration concept of designing Pancharatnam-Berry phase elements, which circumvents the limitations of bulky optical components in conventional integrated optics, will significantly impact multipurpose optical elements, particularly spin-based photonics devices.

We examine the spin-dependent manipulating of vector beams by tailoring the inhomogeneous polarization. The spin-dependent manipulating is attributed to the spin-dependent phase gradient in vector beams, which can be regarded as the intrinsic feature of inhomogeneous polarization. The desired polarization can be obtained by establishing the relationship between the local orientation of polarization and the local orientation of the optical axis of waveplate. We demonstrate that the spin-dependent manipulating with arbitrary intensity patterns can be achieved by tailoring the inhomogeneous polarization.

We propose a photonic spin filter whose structure is similar to that of conventional spatial filter, but the two plano-convex lenses are replaced by Pancharatnam-Berry phase ones. The dielectric metasurface with high transmission and conversion efficiency is designed to work as Pancharatnam-Berry phase lens. The photonic spin filter can sort desired spin photons from the input beam with mixed spin states, and thereby facilitate possible applications in spin-based photonics.

We propose and realize a radial spin Hall effect (SHE) of light by using a dielectric metasurface. The metasurface with radially varying optical axes introduces a Pancharatnam--Berry (PB) geometrical phase to the incident light. The spatial gradient of PB phase accounts for a shift in the momentum space and thus leads the light to split radially into two concentric rays with opposite spin in the position space, which is called a radial SHE. Further experiments verify that the magnitude of the splitting increases with the rotation rate of the optical-axis orientation and the propagation distance, thereby allowing for macroscopic observation of the SHE. We also find that the phase of the incident light influences the profiles of the two split rays, while the polarization determines their intensities. The results provide methods to tune the SHE of light by engineering metasurfaces and modulating the incident light, and this radial SHE may be extrapolated to other physical systems.

Dielectric metasurfaces with spatially varying birefringence and high transmission efficiency can exhibit exceptional abilities for controlling the photonic spin states. We present here some of our works on spin photonics and spin-photonic devices with metasurfaces. We develop a hybrid-order Poincare sphere to describe the evolution of spin states of wave propagation in the metasurface. Both the Berry curvature and the Pancharatnam-Berry phase on the hybrid-order Poincare sphere are demonstrated to be proportional to the variation of total angular momentum. Based on the spin-dependent property of Pancharatnam-Berry phase, we find that the photonic spin Hall effect can be observed when breaking the rotational symmetry of metasurfaces. Moreover, we show that the dielectric metasurfaces can provide great flexibility in the design of novel spin-photonic devices such as spin filter and spin-dependent beam splitter., Invited contribution to the SPIE Optics+Photonics conference "Spintronics VIII", held in San Diego, August 9-13, 2015

Observation of photonic spin Hall effect (SHE) near the phase singularity at dielectric metasurfaces is presented. The structured metasurface works as a space-variant Pancharatnam-Berry phase element and produces a vortex beam with phase singularity. The dynamical vortex phase is introduced to eliminate or enhance the phase singularity, thus realizing the manipulation of spin-dependent Pancharatnam-Berry phase. The spin-orbit coupling near the singularity of the Pancharatnam-Berry phase leads to the observation of the photonic SHE which manifests itself as spin-dependent splitting. The underlying mechanism is significantly different from previously reported cases. It thereby provides an alternative way to manipulate the spin states of photons.

In this work, we develop a hybrid-order Poincar\'{e} sphere to describe the evolution of polarization states of wave propagation in inhomogeneous anisotropic media. We extend the orbital Poincar\'{e} sphere and high-order Poincar\'{e} sphere to a more general form. Polarization evolution in inhomogeneous anisotropic media with special geometry can be conveniently described by state evolution along the longitude line on the hybrid-order Poincar\'{e} sphere. Similar to that in previously proposed Poincar\'{e} spheres, the Berry curvature can be regarded as an effective magnetic field with monopole centered at the origin of sphere and Berry connection can be interpreted as the vector potential. Both the Berry curvature and the Pancharatnam-Berry phase on the hybrid-order Poincar\'{e} sphere are demonstrated to be proportional to the total angular momentum. Our scheme provides a convenient method to describe the spin-orbit interaction in inhomogeneous anisotropic media., Comment: 6 pages, 3 figures

The polarization evolution of vector beams (VBs) generated by q-plates is investigated theoretically and experimentally. An analytical model is developed for the VB created by a general quarter-wave q-plate based on vector diffraction theory. It is found that the polarization distribution of VBs varies with position and the value q. In particular, for the incidence of circular polarization, the exit vector vortex beam has polarization states that cover the whole surface of the Poincare sphere, thereby constituting a full Poincare beam. For the incidence of linear polarization, the VB is not cylindrical but specularly symmetric, and exhibits an azimuthal spin splitting. These results are in sharp contrast with those derived by the commonly used model, i.e., regarding the incident light as a plane wave. By implementing q-plates with dielectric metasurfaces, further experiments validate the theoretical results.

We propose theoretically and verify experimentally a method of combining a q-plate and a spiral phase plate to generate arbitrary vector vortex beams on a hybrid-order Poincare sphere. We demonstrate that a vector vortex beam can be decomposed into a vector beam and a vortex, whereby the generation can be realized by sequentially using a q-plate and a spiral phase plate. The generated vector beam, vortex, and vector vortex beam are verified and show good agreement with the prediction. Another advantage that should be pointed out is that the spiral phase plate and q-plate are both fabricated on silica substrates, suggesting the potential possibility to integrate the two structures on a single plate. Based on a compact method of transmissive-type transformation, our scheme may have potential applications in future integrated optical devices.

In this letter, we propose and experimentally demonstrate a compact photonic spin filter formed by integrating a Pancharatnam-Berry phase lens (focal length of ±f) into a conventional plano-concave lens (focal length of −f). By choosing the input port of the filter, photons with a desired spin state, such as the right-handed component or the left-handed one, propagate alone its original propagation direction, while the unwanted spin component is quickly diverged after passing through the filter. One application of the filter, sorting the spin-dependent components of vector vortex beams on higher-order Poincare sphere, is also demonstrated. Our scheme provides a simple method to manipulate light, and thereby enables potential applications for photonic devices.

In the optical system, most elements such as lens, prism, and optical fiber are made of silica glass. Therefore, integrating Pancharatnam-Berry phase elements into silica glass has potential applications in the optical system. In this paper, we take a lens, for example, which integrates a Pancharatnam-Berry phase lens into a conventional plano-convex lens. The spin states and positions of focal points can be modulated by controlling the polarization states of the incident beam. The proposed lens has a high transmission efficiency, and thereby acts as a simple and powerful tool to manipulate spin photons. Furthermore, the method can be conveniently extended to the optical fiber and laser cavity, and may provide a route to the design of the spin-photonic devices.

The optical path lengths travelled by rays across a wavefront essentially determine the resulting phase front irrespective of the shape of a medium according to the principle of equal optical path. Thereupon we propose a method for the transformation between two arbitrary wavefronts by a slab, i.e. the profile of the spatial separation between the two wavefronts is taken to be transformed to a plane surface. Interestingly, for the mutual conversion between planar and curved wavefronts, the method reduce to an inverse transformation method in which it is the reversed shape of the desired wavefront that is converted to a planar one. As an application, three kinds of phase transformation are realized and it is found that the transformation on phase is able to realize some important properties such as phase reversal or compensation, focusing, and expanding or compressing beams, which are further confirmed by numerical simulations. The slab can be applied to realizing compact electromagnetic devices for which the values of the refractive index or the permittivity and permeability can be high or low, positive or negative, or near zero, depending on the choice of coordinate transformations.

A simple and compact converter based on the dielectric metasurface is proposed for the transformation of Gaussian mode to Hermite-Gaussian and Laguerre-Gaussian modes. We establish the relationship between the phase of a desired mode and the local orientation of the optical axis based on the evolution of Pancharatnam-Berry phase on Poincaré sphere. By controlling the local orientation of the optical axis in the dielectric metasurface, we can achieve any desired higher-order laser mode.

We propose a scheme to controllably convert the wavefront of an arbitrary incident beam into a helical one by compact transformation slabs, thus enabling the output beam to carry desirable orbital angular momentum (OAM). First, based on transformation optics, a three-dimensional (3D) phase transformation between any two wavefronts by {\deg}at transformation media is established and then used to mold a wavefront of Gaussian beam into a helical one. Second, 3D FDTD simulations are performed to confirm the spiraling evolutions of the resultant field and phase, clearly demonstrating OAM generated. Further theoretical analyses show that the refractive index exhibiting a helical distribution leads to the oppositely spiral phase front and that it is feasible to produce desirable OAM by generators of unit OAM. The results not only provide an additional way to manipulate phase and photon OAM, but reciprocally shed further light on the phase structure of helical beams, which leads to a new transformation way by a surface., Comment: 6 pages, 5 figures; Phys. Rev. A, 2012

We report the realization of spin-dependent splitting with arbitrary intensity patterns based on all-dielectric metasurface. Compared to the plasmonic metasurfaces, the all-dielectric metasurface exhibit more high transmission efficiency and conversion efficiency, which make it is possible to achieve the spin-dependent splitting with arbitrary intensity patterns. Our findings suggest a way for generation and manipulation of spin photons, and thereby offer the possibility of developing spin-based nanophotonic applications., 4 pages, 5 figures

We propose a novel method for the generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases. In our scheme, the Airy beam is generated by the dynamic phase with a spatial light modulator, and the vortex phase or the vector polarization is modulated by the geometric phase with a dielectric metasurface. The modulation of the geometric phase provides an extra degree of freedom to manipulate the phase and the polarization of Airy beams. This scheme can be extended to generate any other types of optical beams with desirable phase and polarization.

We report the manipulation of spin-dependent splitting by geometric Doppler effect based on dielectric metasurfaces. The extrapolation of rotational Doppler effect from temporal to spatial coordinate gives the phase change when the local optical axes of dielectric metasurfaces are rotating in space. Therefore, the continuous variation of local optical axes in a certain direction will introduce a phase gradient in the same direction at the beam cross section. This is additive to the phase gradient appeared when breaking the rotational symmetry of linearly polarized cylindrical vector beams, which leads to the deflections of different spin components of light, i.e., photonic spin Hall effect. Hence, it is possible to manipulate the spin-dependent splitting by introducing the geometric Doppler effect. Theoretically and experimentally, we show that the magnitude and orientation of the spin-dependent splitting are both tunable when changing the spatial rotation rate of local optical axes and incident polarization.

Observation of photonic spin Hall effect (SHE) in dielectric metasurfaces whose local optical axes are spatially rotated is presented. The photonic SHE manifests itself as a spin-dependent splitting in momentum space due to the space-variant Pancharatnam-Berry phase. We show that no spin-dependent splitting occurs when keeping the rotational symmetry of local optical axes. However, the splitting can be observed when the rotational symmetry is broken. The spin-dependent splitting in position space can be observed in the far field due to the high transmission efficiency of dielectric metasurfaces. Moreover, it can be enhanced by increasing the rotation rate of local optical axes in the metasurfaces.