Convergent finite-modal representations improve electromagnetic scattering accuracy
Finite-Modal Realization and Operator-Norm Convergence of a Source-to-Observation Electromagnetic Scattering Green Operator
Information Theory
Summary
Predicting how electromagnetic waves scatter in complex environments is tricky because existing methods use simplified models that don’t always capture the full picture. The authors created a mathematical framework that accurately represents these scattering effects using a finite number of modes, ensuring reliable predictions across many conditions. They showed that their approach converges uniformly and preserves important channel information, verified with computational experiments involving two spheres. This work helps engineers better model and understand electromagnetic interactions in multiple-scattering setups.
What this means in practice
- •For antenna designers: Model electromagnetic interactions in complex environments to improve antenna placement and performance predictions using reliable finite-modal scattering operators.
- •For wireless communication engineers: Analyze communication modes in multi-scattering environments with precise source-to-observation models ensuring accurate channel characterization.
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.