Functional analytic methods for discrete approximations of subwavelength resonator systems
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2021
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914961539727360 |
|---|---|
| author | Ammari, Habib Davies, Bryn Hiltunen, Erik Orvehed |
| author_facet | Ammari, Habib Davies, Bryn Hiltunen, Erik Orvehed |
| contents | We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by re-framing the Helmholtz equation as a non-linear eigenvalue problem in terms of integral operators. In the subwavelength limit, resonant states are described by the eigenstates of the generalised capacitance matrix, which appears by perturbing the elements of the kernel of the limiting operator. Using this formulation, we are able to describe subwavelength resonance and related phenomena. In particular, we demonstrate large-scale effective parameters with exotic values. We also show that these systems can exhibit localised and guided waves on very small length scales. Using the concept of topologically protected edge modes, such localisation can be made robust against structural imperfections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_12301 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Functional analytic methods for discrete approximations of subwavelength resonator systems Ammari, Habib Davies, Bryn Hiltunen, Erik Orvehed Analysis of PDEs Mathematical Physics 35J05, 35C20, 35P20, 74J20 We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by re-framing the Helmholtz equation as a non-linear eigenvalue problem in terms of integral operators. In the subwavelength limit, resonant states are described by the eigenstates of the generalised capacitance matrix, which appears by perturbing the elements of the kernel of the limiting operator. Using this formulation, we are able to describe subwavelength resonance and related phenomena. In particular, we demonstrate large-scale effective parameters with exotic values. We also show that these systems can exhibit localised and guided waves on very small length scales. Using the concept of topologically protected edge modes, such localisation can be made robust against structural imperfections. |
| title | Functional analytic methods for discrete approximations of subwavelength resonator systems |
| topic | Analysis of PDEs Mathematical Physics 35J05, 35C20, 35P20, 74J20 |
| url | https://arxiv.org/abs/2106.12301 |