Spectrum of the volume integral operator of electromagnetic scattering

TL;DR

This paper analyzes the spectrum of the volume integral operator in 3D electromagnetic scattering, revealing how its essential spectrum and eigenvalues vary with frequency and material properties, supported by theoretical and numerical results.

Contribution

It provides explicit spectral characterization of the operator for inhomogeneous anisotropic scatterers and derives bounds on eigenvalues for different physical scenarios.

Findings

Essential spectrum dominates at low frequencies

Eigenvalues spread at higher frequencies

Numerical results agree with theoretical predictions

Abstract

Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out at higher ones. The explicit expression of the operator's symbol provides exact outline of the essential spectrum for any inhomogeneous anisotropic scatterer with Holder continuous constitutive parameters. Geometrical bounds on the location of discrete eigenvalues are derived for various physical scenarios. Numerical experiments demonstrate good agreement between the predicted spectrum of the operator and the eigenvalues of its discretized version.