Mathematical Synthesis and Analysis of Nonlinear Metasurfaces

TL;DR

This paper develops a theoretical framework for designing and analyzing second-order nonlinear metasurfaces, deriving synthesis conditions, exploring nonreciprocal behavior, and validating results with numerical simulations.

Contribution

It introduces synthesis expressions for nonlinear metasurfaces and analyzes their scattering properties, including nonreciprocity, using perturbation theory and FDTD simulations.

Findings

Derived synthesis expressions relating susceptibilities to fields.

Identified conditions for no reflection and nonreciprocity.

Validated theoretical results with numerical simulations.

Abstract

We propose a discussion on the synthesis and scattering analysis of nonlinear metasurfaces. For simplicity, we investigate the case of a second-order nonlinear isotropic metasurface possessing both electric and magnetic linear and nonlinear susceptibility components. We next find the synthesis expressions relating the susceptibilities to the specified fields, which leads to the definition of the nonlinear metasurface conditions for no reflection, themselves revealing the nonreciprocal nature of such structures. Finally, we provide the approximate expressions of the scattered fields based on perturbation theory and compare the corresponding results to finite-difference time-domain simulations.