Space-Time Wave Localisation in Systems of Subwavelength Resonators
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912182553280512 |
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| author | Ammari, Habib Hiltunen, Erik Orvehed Rueff, Liora |
| author_facet | Ammari, Habib Hiltunen, Erik Orvehed Rueff, Liora |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10100 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Space-Time Wave Localisation in Systems of Subwavelength Resonators Ammari, Habib Hiltunen, Erik Orvehed Rueff, Liora Analysis of PDEs Numerical Analysis Mathematical Physics Optics 35L51, 35P25, 35C20, 74J05 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. |
| title | Space-Time Wave Localisation in Systems of Subwavelength Resonators |
| topic | Analysis of PDEs Numerical Analysis Mathematical Physics Optics 35L51, 35P25, 35C20, 74J05 |
| url | https://arxiv.org/abs/2409.10100 |