Enhanced optical spatial differential operations via strong spin-orbit interactions in an anisotropic epsilon-near-zero slab

Several works on optical higher-order differential operations have recently attracted attention, particularly in image processing for edge detection. However, the inefficient differential operation leads to barriers to practical applications. Here, we report an anisotropic epsilon-near-zero slab to significantly enhance the transmission efficiency of second-order differentiators and discuss the Berry phase mechanism of this optical calculation process. Through a rigorous full-wave analysis of the process, we find that the conversion efficiency of differential operation depends on the spin-orbit interactions. Our scheme can strengthen the spin-orbit interaction by introducing anisotropy, which significantly enhances the transmission efficiency. We finally give transfer functions to reveal how to improve the efficiency and compare the quadratic coefficient among different systems. This highly efficient differentiation operation may develop significant applications in fast, compatible, and power-efficient ultrathin devices for data processing and biological imaging.