Perfect all-angle asymmetric transmission via normal susceptibilities: exact spatial derivative by local meta-atoms and nonlocal metasurfaces

TL;DR

This paper introduces a systematic method for designing nonlocal metasurfaces that achieve precise asymmetric all-angle transmission, enabling advanced optical analog processing through exact spatial differentiation.

Contribution

It derives closed-form susceptibility conditions for first-order spatial differentiation and provides detailed designs of local and nonlocal metasurfaces, including a multilayer PCB implementation.

Findings

Validated designs through simulations demonstrating accurate asymmetric transmission.

Established a modular approach for high-resolution nonlocal metasurfaces.

Clarified the role of nearfield coupling beyond standard homogenization.

Abstract

We present a systematic methodology for realizing accurate asymmetric all-angle transmission in nonlocal metasurfaces. As a representative example, we derive closed-form susceptibility conditions for exact first-order spatial differentiation of unity numerical aperture, clarifying the role of each underlying balance. We provide rigorous and detailed designs of physically meaningful structures that directly feature such susceptibilities: a conceptual local meta-atom and a realistic nonlocal multilayered printed circuit board (PCB). Importantly, the latter leverages an intricate system of nearfield coupling beyond standard homogenization. Validated in simulations, our results provide a general and modular route to high-resolution asymmetric nonlocal metasurfaces for optical analog processing.