Isotropic Topological Second-Order Spatial Differentiator Operating in Transmission Mode

TL;DR

This paper introduces an isotropic, transmission-mode topological second-order spatial differentiator that operates at normal incidence, offering robust edge detection capabilities for integrated optical systems.

Contribution

It presents a novel topological differentiator functioning in transmission mode with symmetry-protected topological charge, advancing optical computing and integration.

Findings

Operates in transmission mode at normal incidence

Exhibits a topological charge of ±2

Performs second-order differentiation effectively

Abstract

Differentiation has widespread applications, particularly in image processing for edge detection. Significant advances have been made in using nanophotonic structures and metamaterials to perform such operations. In particular, a recent work demonstrated a topological differentiator in which the transfer function exhibits a topological charge, making the differentiation operation robust to variation of operating conditions. The demonstrated topological differentiator, however, operates in the reflection mode at off-normal incidence and is difficult to integrate into compact imaging systems. In this work, we design a topological differentiator that operates isotropically in transmission mode at normal incidence. The device exhibits an optical transfer function with a symmetry-protected, topological charge of $\pm 2$ and performs second-order differentiation. Our work points to the potential of harnessing topological concepts for optical computing applications.