All-optical image edge detection based on the two-dimensional photonic spin Hall effect in anisotropic metamaterial

Optical image processing based on the photonic spin Hall effect (SHE) has been gaining significant attention as a convenient and an accurate way for image edge detection. However, the recent edge imaging techniques depending on optical differentiation is mainly achieved by modulation of one-dimensional photonic SHE. Here, we theoretically predict the two-dimensional photonic SHE in the anisotropic metamaterial, and find that its longitudinal and transverse displacements exhibit spin-dependent property at filling factors with increasing incidence angle. As the transverse and in-plane displacements induced by the photonic SHE can be controlled by the filling factor of the crystal structure, the optical axis angle, and the incident angle, this intrinsical effect can be used to realize a tunable edge imaging. Interestingly, by changing the optical axis of the anisotropic metamaterial, the in-plane displacements are equal to the transverse displacements for a certain filling factor and the corresponding incident angle. Therefore, we propose a two-dimensional image edge detection method based on the photonic SHE in anisotropic metamaterial. Further numerical results validate the theoretical proposal.