Two-dimensional optical multiple-order differentiations based on spatial spectrum modulation

Abstract

Optical differential operations have recently attracted considerable attention owing to the capabilities of ultrafast speed and low power consumption. The transfer function, which embodies the frequency-domain characteristics of differential systems, plays an important role in differentiator design. Here, we report a super-Gaussian aperture differential filter, and we reveal unique characteristics of odd- and even-order transfer functions and corresponding differential effects via spatial spectrum modulation. We show that the feature of the transfer function is well maintained, and more precise differentiation can be achieved using the designed filter. Two-dimensional first- to fifth-order full and partial differentiations are implemented both theoretically and experimentally. Our work provides an approach for engineering customized multiple-order differentiators and promotes the advancements of related areas such as optical analog computing and image processing.