Finite-Modal Realization and Operator-Norm Convergence of a Source-to-Observation Electromagnetic Scattering Green Operator
Abstract
Source-to-observation operators provide reusable environment-level descriptions for multi-query electromagnetic (EM) prediction and communication-mode analysis. However, in practical multiple-scattering models, these operators are represented with finitely many angular modes, and agreement for selected excitations or between successive truncation orders does not establish uniform accuracy of the full map or reliability of its singular channels. To close this gap, we formulate the environment-induced response as a scattering Green operator on fixed continuous source and observation spaces and derive an exact trace-space factorization that reconstructs the Maxwell scattered field. For fixed, pairwise-disjoint enclosing trace spheres and a well-posed collective problem, nested vector spherical wave function (VSWF) realizations converge in operator norm. A structural bound separates external modal tails from collective-resolvent sensitivity, and operator-norm convergence guarantees uniform convergence of the singular values. We further construct a finite metric core that preserves the nonzero singular values of each finite-order operator and reconstructs matched orthonormal source--field channels without introducing external-support discretization degrees of freedom (DoF) into the spectral problem. Full-wave benchmarks verify the finite-order implementation. A controlled near-resonant two-sphere study shows that adjacent-order agreement can precede resolution of the dominant high-order collective direction. It further shows that only part of the internal amplification appears in externally accessible gains and that resonance promotes a distinct high-order channel pair above an otherwise preserved low-order family. The resulting framework provides a convergent, metric-consistent finite-modal representation of multiple-scattering source-to-observation operators and their accessible channels.
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BibTeX
@misc{wang2026finitemodal,
title = {{Finite-Modal Realization and Operator-Norm Convergence of a Source-to-Observation Electromagnetic Scattering Green Operator}},
author = {Zhukang Wang and Da Li and Ruifeng Li and Jinyan Ma and Jiarun Hu and Jiahui Wang and Anqi Xia and Tengjiao Wang and Said Mikki and Er-Ping Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08229},
eprint = {2609.08229},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08229},
}
RIS
TY - UNPB
TI - Finite-Modal Realization and Operator-Norm Convergence of a Source-to-Observation Electromagnetic Scattering Green Operator
AU - Zhukang Wang
AU - Da Li
AU - Ruifeng Li
AU - Jinyan Ma
AU - Jiarun Hu
AU - Jiahui Wang
AU - Anqi Xia
AU - Tengjiao Wang
AU - Said Mikki
AU - Er-Ping Li
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08229
UR - https://arxiv.org/abs/2609.08229
AB - Source-to-observation operators provide reusable environment-level descriptions for multi-query electromagnetic (EM) prediction and communication-mode analysis. However, in practical multiple-scattering models, these operators are represented with finitely many angular modes, and agreement for selected excitations or between successive truncation orders does not establish uniform accuracy of the full map or reliability of its singular channels. To close this gap, we formulate the environment-induced response as a scattering Green operator on fixed continuous source and observation spaces and derive an exact trace-space factorization that reconstructs the Maxwell scattered field. For fixed, pairwise-disjoint enclosing trace spheres and a well-posed collective problem, nested vector spherical wave function (VSWF) realizations converge in operator norm. A structural bound separates external modal tails from collective-resolvent sensitivity, and operator-norm convergence guarantees uniform convergence of the singular values. We further construct a finite metric core that preserves the nonzero singular values of each finite-order operator and reconstructs matched orthonormal source--field channels without introducing external-support discretization degrees of freedom (DoF) into the spectral problem. Full-wave benchmarks verify the finite-order implementation. A controlled near-resonant two-sphere study shows that adjacent-order agreement can precede resolution of the dominant high-order collective direction. It further shows that only part of the internal amplification appears in externally accessible gains and that resonance promotes a distinct high-order channel pair above an otherwise preserved low-order family. The resulting framework provides a convergent, metric-consistent finite-modal representation of multiple-scattering source-to-observation operators and their accessible channels.
ER -