Modal approximation for time-domain elastic scattering from metamaterial quasiparticles

TL;DR

This paper develops a modal expansion approach to analyze time-domain elastic wave scattering by metamaterial quasiparticles, providing a quantitative and resonant modal approximation with error estimates.

Contribution

It introduces a novel modal expansion framework for time-dependent elastic scattering from metamaterials, including spectral analysis and resonance characterization.

Findings

Modal expansion valid in static and perturbative regimes

Resonant poles identified as polariton resonances

Low-frequency scattered field accurately approximated with error bounds

Abstract

This paper aims at quantitatively understanding the elastic wave scattering due to negative metamaterial structures under wide-band signals in the time domain. Specifically, we establish the modal expansion for the time-dependent field scattered by metamaterial quasiparticles in elastodynamics. By Fourier transform, we first analyze the modal expansion in the time-harmonic regime. With the presence of quasiparticles, we validate such an expansion in the static regime via quantitatively analyzing the spectral properties of the Neumann-Poincar\'{e} operator associated with the elastostatic system. We then approximate the incident field with a finite number of modes and apply perturbation theory to obtain such an expansion in the perturbative regime. In addition, we give polariton resonances as simple poles for the elastic system with non-zero frequency. Finally, we show that the low-frequency part of the scattered field in the time domain can be well approximated by using the resonant modal expansion with sharp error estimates.