In this work, we develop a hybrid-order Poincaré sphere to describe the evolution of polarization states of wave propagation in inhomogeneous anisotropic media. We extend the orbital Poincaré sphere and high-order Poincaré 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 Poincaré sphere. Similar to that in previously proposed Poincaré spheres, the Berry curvature can be regarded as an effective magnetic field with monopole centered at the origin of sphere and the Berry connection can be interpreted as the vector potential. Both the Berry curvature and the Pancharatnam-Berry phase on the hybrid-order Poincaré sphere are demonstrated to be proportional to the variation of total angular momentum. Our scheme provides a convenient method to describe the spin-orbit interaction in inhomogeneous anisotropic media.
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.
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 Poincaré 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.
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.
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.
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