Nonlinear subwavelength resonances in three dimensions

TL;DR

This paper develops a discrete model for three-dimensional nonlinear Helmholtz resonances in subwavelength regimes, capturing nonlinear effects and additional eigenmodes observed experimentally.

Contribution

It introduces a novel discrete formulation for nonlinear resonances that works in both weak and strong regimes, extending linear models to include nonlinear eigenmodes.

Findings

Discrete model accurately predicts nonlinear eigenmodes

Model valid across different nonlinear regimes

Captures experimentally observed nonlinear effects

Abstract

In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators with Kerr-type nonlinearities. Our discrete formulation is valid in both weak and strong nonlinear regimes. Compared to the linear formulation, it characterizes the extra eigenmodes induced by the non-linearlity that have recently been experimentally observed.