Space-Time Wave Localisation in Systems of Subwavelength Resonators
<|reference_start|>Space-Time Wave Localisation in Systems of Subwavelength Resonators: 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.<|reference_end|>
@article{ammari2024space-time,
    title={Space-Time Wave Localisation in Systems of Subwavelength Resonators},
    author={Habib Ammari, Erik Orvehed Hiltunen, Liora Rueff},
    journal={arXiv preprint arXiv:2409.10100},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.10100},
    primaryClass={math.AP cs.NA math-ph math.MP math.NA physics.optics}
}