Complex scaling for open waveguides
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911001557860352 |
|---|---|
| author | Epstein, Charles L. Goodwill, Tristan Hoskins, Jeremy Quinn, Solomon Rachh, Manas |
| author_facet | Epstein, Charles L. Goodwill, Tristan Hoskins, Jeremy Quinn, Solomon Rachh, Manas |
| contents | In this work we analyze the complex scaling method applied to the problem of time-harmonic scalar wave propagation in junctions between `leaky,' or open dielectric waveguides. In [arXiv:2302.04353, arXiv:2310.05816, arXiv:2401.04674, arXiv:2411.11204], it was shown that under suitable assumptions the problem can be reduced to a system of Fredholm second-kind integral equations on an infinite interface, transverse to the waveguides. Here, we show that the kernels appearing in the integral equation admit a rapidly decaying analytic continuation on certain natural totally real submanifolds of $\mathbb{C}^2.$ We then show that for suitable, physically-meaningful, boundary data the resulting solutions to the integral equations themselves admit analytic continuation and satisfy related asymptotic estimates. By deforming the integral equation to a suitable contour, the decay in the kernels, density, and data enable straightforward discretization and truncation, with an error that decays exponentially in the truncation length. We illustrate our results with several representative numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complex scaling for open waveguides Epstein, Charles L. Goodwill, Tristan Hoskins, Jeremy Quinn, Solomon Rachh, Manas Numerical Analysis 65N80, 35Q60, 35C15, 35P25, 45B05, 31A10, 30B40, 65R20 In this work we analyze the complex scaling method applied to the problem of time-harmonic scalar wave propagation in junctions between `leaky,' or open dielectric waveguides. In [arXiv:2302.04353, arXiv:2310.05816, arXiv:2401.04674, arXiv:2411.11204], it was shown that under suitable assumptions the problem can be reduced to a system of Fredholm second-kind integral equations on an infinite interface, transverse to the waveguides. Here, we show that the kernels appearing in the integral equation admit a rapidly decaying analytic continuation on certain natural totally real submanifolds of $\mathbb{C}^2.$ We then show that for suitable, physically-meaningful, boundary data the resulting solutions to the integral equations themselves admit analytic continuation and satisfy related asymptotic estimates. By deforming the integral equation to a suitable contour, the decay in the kernels, density, and data enable straightforward discretization and truncation, with an error that decays exponentially in the truncation length. We illustrate our results with several representative numerical examples. |
| title | Complex scaling for open waveguides |
| topic | Numerical Analysis 65N80, 35Q60, 35C15, 35P25, 45B05, 31A10, 30B40, 65R20 |
| url | https://arxiv.org/abs/2506.10263 |