Tunable optical spatial differentiation in the photonic spin Hall effect

Optical differential operation and image edge detection have shown some unique advantages, including faster operating speeds and lower power consumption, compared to a digital image processor. Here, we examine the origin of optical differentiator in the photonic spin Hall effect. We find that the optical differentiator in x direction is related to the beam divergence when the incident angle of the central wave vector meets Brewster's, while the optical differentiator in y direction is related to the cross polarization component. By eliminating the H-H or V-V polarization component, the H-V or V-H polarization component induced the spin-dependent splitting in the photonic spin Hall effect, which can be used for the one-dimensional optical differentiator in an arbitrary direction. Furthermore, we investigate the photonic spin Hall effect and double-peak profile near Brewster angle and predict that a perfect two-dimensional optical differentiator will become a reality.