General Metasurface Synthesis Based on Susceptibility Tensors

TL;DR

This paper introduces a fast, vectorial susceptibility tensor-based method for synthesizing metasurfaces capable of transforming arbitrary incident waves into desired reflected and transmitted waves, enabling advanced electromagnetic control.

Contribution

It presents a novel, closed-form, vectorial synthesis approach for metasurfaces, capable of handling complex wave transformations and relating susceptibilities to scattering parameters.

Findings

Method is fast and provides closed-form solutions.

Capable of transforming up to four independent wave triplets.

Demonstrated applications include refraction, polarization rotation, vortex beams, and angular momentum multiplexing.

Abstract

A general method, based on susceptibility tensors, is proposed for the synthesis of metasurfaces transforming arbitrary incident waves into arbitrary reflected and transmitted waves. The proposed method exhibits two advantages: 1)it is inherently vectorial, and therefore better suited for full vectorial (beyond paraxial) electromagnetic problems, 2) it provides closed-form solutions, and is therefore extremely fast. Incidentally, the method reveals that a metasurface is fundamentally capable to transform up to four independent wave triplets (incident, reflected and refracted waves). In addition, the paper provides the closed-form expressions relating the synthesized susceptibilities and the scattering parameters simulated within periodic boundary conditions, which allows one to design the scattering particles realizing the desired susceptibilities. The versatility of the method is illustrated by examples of metasurfaces achieving the following transformations: generalized refraction, reciprocal and non-reciprocal polarization rotation, Bessel vortex beam generation, and orbital angular momentum multiplexing.