Summary
Predicting how electromagnetic waves scatter in complex environments can be tricky when approximations only consider a limited number of directions. The paper by the authors presents a method to represent these scattering interactions more completely using mathematical operators that consider continuous sources and observations. They prove that their approach converges reliably and preserves important details even when using a finite number of angular modes. Their method also identifies how certain resonance effects appear in the scattering behavior of multiple objects. This work helps improve the accuracy and understanding of electromagnetic scattering predictions.
electromagnetic scatteringsource-to-observation operatorangular modesvector spherical wave functionsoperator norm convergencesingular valuesGreen operatormultiple scatteringresonancetrace space factorization
Authors
Zhukang Wang, Da Li, Ruifeng Li, Jinyan Ma, Jiarun Hu, Jiahui Wang, Anqi Xia, Tengjiao Wang, Said Mikki, Er-Ping Li
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.