Spectrum of the Volume Integral Operator of Electromagnetic Scattering

The spectrum of the volume integral operator of 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 an exact outline of the essential spectrum for any inhomogeneous anisotropic scatterer with Hölder 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.