Generalized Spatial Differentiation from the Spin Hall Effect of Light and Its Application in Image Processing of Edge Detection

Abstract

Optics naturally provides us with some powerful mathematical operations. Here, we experimentally demonstrate that during reflection or refraction at a single optical planar interface, the optical computing of spatial differentiation can be realized by analyzing specific orthogonal polarization states of light. We show that the spatial differentiation is intrinsically due to the spin Hall effect of light and generally accompanies light reflection and refraction at any planar interface, regardless of material composition or incident angles. The proposed spin-optical method takes advantages of a simple and common structure to enable vectorialfield computation and perform edge detection for ultrafast image processing.

Meta-optics for spatial optical analog computing

“…Several other proposals and demonstrations using spin Hall effect (SHE) of light [65], prism coupling configuration [66], reflective hybrid plasmonic-dielectric metasurfaces [48], periodic plasmonic metasurfaces covered by graphene [67], multiinput-multioutput computational metasurfaces [68], ultrathin bianisotropic metasurfaces [69], polarization-insensitive structured surfaces with tailored nonlocality [70], and engineering the spatial dispersion of the electric dipole resonance in dielectric metasurfaces [71] to perform mathematical operators based on GF approach have been reported in the literature.…”

“…Recently, Zhu et al [65] experimentally demonstrated spatial differentiation of the incident beam when reflected or refracted at a single optical planar interface under paraxial approximation. They employed SHE of light, i.e.…”

Monolithic metasurface spatial differentiator enabled by asymmetric photonic spin-orbit interactions

“…Notably, optical spatial computing based on metamaterials including differentiators, integrators, and equation solvers is proposed by Silva et al in 2014 [34], opening new avenues for optical analog computing. Since then, various differentiator metasurfaces are developed based on photonic crystals [5,35], spin Hall effect [36], surfaces plasmons [37], high-contrast gratings [8], and Pancharatnam-Berry (PB) phase [38,39]. However, additional prisms or lenses are still required for plasmon coupling or Fourier transform in those applications [37,40], which is incompatible with the flat and compact optical systems.…”

“…However, additional prisms or lenses are still required for plasmon coupling or Fourier transform in those applications [37,40], which is incompatible with the flat and compact optical systems. Besides, many metasurface spatial differentiators work only in 1D edge detection [8,9,35,36], restricting the practical applications in image recognition and processing.…”

Revealing topological phase in Pancharatnam–Berry metasurfaces using mesoscopic electrodynamics

“…However, a vectorial theoretical framework is still required to clearly explain why the generalized Snell's law occurs in the cross-polarized transmitted fields in PB metasurface system in the -1st or 1st diffraction orders only. To overcome these difficulties, the concept of geometric phase (PB phase), which is responsible for the conversion of the polarization state in the linearly birefringent medium [32][33][34][35][36], is introduced. Several works have shown that the transmission matrix which describes the birefringent response can be separated into co-polarized and cross-polarized beams in the circular basis by applying the PB phase induced by the orientation of nano-antennas [31,37,38].…”