Theory of resonances in the electromagnetic scattering by macroscopic bodies

The electromagnetic scattering resonances of a collection of macroscopic bodies with uniform electric properties are used to construct a spectral representation for the scattered field. The resonances and their weights are found by solving for the eigenvalues and eigenstates of a non-Hermitian, linear integral operator Γ. A scheme is developed for doing this by diagonalizing a matrix that represents Γ by the set of individual grain eigenstates---the diagonal elements are individual grain eigenvalues while the off-diagonal elements are overlap integrals of eigenstates from two different grains. For a system of spherical scatterers, this scheme leads to a reasonable method of calculating numerically the scattered field in cases where the multiple scattering is important. As an example, the scattering by a pair of identical spheres is worked out analytically for a limiting case. Sum rules for the weights in the spectral representation are derived and discussed.