Space-Time Wave Localisation in Systems of Subwavelength Resonators

TL;DR

This paper investigates space-time localized wave modes in time-modulated metamaterials with subwavelength resonators, providing analytical characterizations and numerical evidence of their existence and properties.

Contribution

It introduces a capacitance matrix approximation for wave equations in time-modulated metamaterials, enabling first-principles analysis of localized modes.

Findings

Existence of space-time localized waves in perturbed time-modulated metamaterials.

Analytical characterization of localized modes using a capacitance matrix approach.

Numerical validation of space-time localization phenomena.

Abstract

In this paper we study the dynamics of metamaterials composed of high-contrast subwavelength resonators and show the existence of localised modes in such a setting. A crucial assumption in this paper is time-modulated material parameters. We prove a so-called capacitance matrix approximation of the wave equation in the form of an ordinary differential equation. These formulas set the ground for the derivation of a first-principles characterisation of localised modes in terms of the generalised capacitance matrix. Furthermore, we provide numerical results supporting our analytical results showing for the first time the phenomenon of space-time localised waves in a perturbed time-modulated metamaterial. Such spatio-temporal localisation is only possible in the presence of subwavelength resonances in the unperturbed structure. We introduce the time-dependent degree of localisation to quantitatively determine the localised modes and provide a variety of numerical experiments to illustrate our formulations and results.