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

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.