Two-Dimensional Isotropic Spatial Differentiation Through Complete Polarization Control

Abstract

Optical image processing has emerged as an alternative to digital processing due to its high speed and reduced electronic burden. Among its various functions, spatial differentiation is particularly important because it provides essential structural information for image analysis. Reflection at planar interfaces enables two-dimensional (2D) isotropic spatial differentiation without nanofabrication. However, previous demonstrations of this approach have been limited to specific incident conditions, such as the Brewster angle or a specific angle under total internal reflection at a lossless dielectric interface. Here, we demonstrate, via complete polarization control, that 2D isotropic edge detection at planar interfaces can be achieved over a wide range of incident angles by extending the output polarization from linear to elliptical. The resulting transfer function exhibits a linear amplitude profile and a first-order phase vortex, corresponding to isotropic first-order spatial differentiation. Relaxing the incident-angle restriction allows the angle to be chosen to achieve desired performance, with near-normal incidence being advantageous over a broad spectral range and large angles being favorable for higher edge-detection efficiency. The 2D isotropic edge detection is experimentally verified using a BK7 prism and further extended to a metal-coated mirror, showing that our principle remains valid for both dielectric and metallic reflectiveinterfaces. © 2026 The Author(s). Advanced Optical Materials published by Wiley-VCH GmbH.