Abstract
Optical spatial differentiation is important for applications in massively parallel computing and real-time image processing. This study makes use of the generalized spin Hall effect of light to perform optical spatial differentiation. Importantly, this scheme generally accompanies oblique light reflection and refraction at $a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}y$ planar interface, regardless of material compositions or angles of incidence. Moreover, this spin-optical approach offers robust image processing to extract the boundaries of objects, where two distinct images can be stored in two different polarization states.
Highlights
Planar interfaces between two isotropic materials are the simplest optical structures but fundamentally reveal the nature of wave optics, such as Snell’s law, Fresnel coefficients, and the Brewster angle
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
Summary
Planar interfaces between two isotropic materials are the simplest optical structures but fundamentally reveal the nature of wave optics, such as Snell’s law, Fresnel coefficients, and the Brewster angle. It was observed that optical beams totally reflected by planar interfaces exhibit different transverse shifts dependent on polarization state [1,2]. Until recently, such an effect was first theoretically studied in the context of a geometric phase (Berry phase) [3,4,5,6] and later as total angular momentum conservation [7,8]. We experimentally demonstrate that under paraxial approximation, by analyzing specific orthogonal polarization states, the beam profiles reflected and refracted at a single optical planar interface correspond to spatial differentiation of incident field. The frequency bandwidth of the spatial differentiation computing is unlimited, which enables an optically fast operation speed
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