Fresnel scattering for open waveguide networks
Abstract
This paper concerns the Helmholtz scattering problem for open waveguide networks, extending the analysis from [arXiv:2302.04353, arXiv:2310.05816, arXiv:2401.04674] to plane-wave incident data. We first reduce the problem to a Fredholm second-kind integral equation on an infinite interface. This produces an integral representation of the solution to the original scattering problem, which is then used to obtain detailed asymptotic estimates of the solution at infinity. To leading order and away from the waveguides, the scattered field is itself a plane wave. Its amplitude and phase shift exhibit a jump across a critical polar angle depending on the direction of the incident plane-wave. Our estimates also imply that the scattered field is outgoing in a weak sense, allowing us to establish a uniqueness result. We conclude by calculating the waveguide-mode contributions to the scattered field in a perturbative regime.
Related
- Solving the scattering problem for open wave-guide networks, II: Outgoing estimates
- Solving the scattering problem for open wave-guide networks, I: Fundamental solutions and integral equations
- Method of Spectral Mappings for Nonselfadjoint Boundary-Value Problems Associated with Resonance Scattering by Open Structures
- Radiation Conditions and Uniqueness Theorems for Open Wave-guide Networks
- Recurrence and transience of open Jackson networks with balanced nodes
BibTeX
@misc{quinn2026fresnel,
title = {{Fresnel scattering for open waveguide networks}},
author = {Solomon Quinn and Charles L. Epstein},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17398},
eprint = {2610.17398},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17398},
}
RIS
TY - UNPB
TI - Fresnel scattering for open waveguide networks
AU - Solomon Quinn
AU - Charles L. Epstein
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17398
UR - https://arxiv.org/abs/2610.17398
AB - This paper concerns the Helmholtz scattering problem for open waveguide networks, extending the analysis from [arXiv:2302.04353, arXiv:2310.05816, arXiv:2401.04674] to plane-wave incident data. We first reduce the problem to a Fredholm second-kind integral equation on an infinite interface. This produces an integral representation of the solution to the original scattering problem, which is then used to obtain detailed asymptotic estimates of the solution at infinity. To leading order and away from the waveguides, the scattered field is itself a plane wave. Its amplitude and phase shift exhibit a jump across a critical polar angle depending on the direction of the incident plane-wave. Our estimates also imply that the scattered field is outgoing in a weak sense, allowing us to establish a uniqueness result. We conclude by calculating the waveguide-mode contributions to the scattered field in a perturbative regime.
ER -