A Breakthrough in Resonance Analysis for Complex Multilayered Structures in Small, High-Contrast Nonlinear Media with Kerr Effect

TL;DR

This paper introduces a novel asymptotic method to analyze resonances in small, high-contrast multilayered nonlinear media with Kerr effect, providing a comprehensive characterization that advances understanding in wave behavior in complex layered systems.

Contribution

It presents the first general asymptotic characterization of resonances in small, high-contrast nonlinear layered media with Kerr effect, linking resonances to material, geometric, and nonlinear properties.

Findings

Provides an asymptotic approximation for resonances

Links resonance behavior to material and geometric parameters

Offers new insights into multilayered structure wave dynamics

Abstract

Scattering resonances play a crucial role in understanding wave behavior in various physical systems. While significant progress has been made in analyzing resonances in high-contrast and nonlinear media, a general characterization of resonances in small, high-contrast nonlinear media with the Kerr effect, particularly in layered configurations, has remained an open problem. In this paper, we present a novel asymptotic approach that addresses this gap by providing an approximation for resonances in terms of material properties, geometry, and nonlinearity. Our results offer new insights into the dependence of resonances on these factors, particularly for complex multilayered structures, making this the first general characterization of its kind.