{"title":"Space-Time Wave Localisation in Systems of Subwavelength Resonators","authors":"Habib Ammari, Erik Orvehed Hiltunen, Liora Rueff","doi":"arxiv-2409.10100","DOIUrl":null,"url":null,"abstract":"In this paper we study the dynamics of metamaterials composed of\nhigh-contrast subwavelength resonators and show the existence of localised\nmodes in such a setting. A crucial assumption in this paper is time-modulated\nmaterial parameters. We prove a so-called capacitance matrix approximation of\nthe wave equation in the form of an ordinary differential equation. These\nformulas set the ground for the derivation of a first-principles\ncharacterisation of localised modes in terms of the generalised capacitance\nmatrix. Furthermore, we provide numerical results supporting our analytical\nresults showing for the first time the phenomenon of space-time localised waves\nin a perturbed time-modulated metamaterial. Such spatio-temporal localisation\nis only possible in the presence of subwavelength resonances in the unperturbed\nstructure. We introduce the time-dependent degree of localisation to\nquantitatively determine the localised modes and provide a variety of numerical\nexperiments to illustrate our formulations and results.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"17 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10100","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.