Landscape of wave focusing and localisation at low frequencies

TL;DR

This paper develops a landscape theory for high-contrast wave systems at low frequencies, enabling prediction of wave focusing and localisation in complex three-dimensional resonator arrangements.

Contribution

It introduces an asymptotic framework based on the generalised capacitance matrix to predict wave focusing and localisation in high-contrast, subwavelength resonator systems.

Findings

Predicts wave focusing locations in 3D systems

Provides a discrete approximation for complex scattering problems

Validates predictions in random and non-periodic configurations

Abstract

High-contrast scattering problems are special among classical wave systems as they allow for strong wave focusing and localisation at low frequencies. We use an asymptotic framework to develop a landscape theory for high-contrast systems that resonate in a subwavelength regime. Our from-first-principles asymptotic analysis yields a characterisation in terms of the generalised capacitance matrix, giving a discrete approximation of the three-dimensional scattering problem. We develop landscape theory for the generalised capacitance matrix and use it to predict the positions of three-dimensional wave focusing and localisation in random and non-periodic systems of subwavelength resonators.