On the relationship between the singularity expansion method and the mathematical theory of scattering

The so-called natural frequencies in the singularity expansion method (SEM) consist of two nonintersecting sets of wavenumber parameters: namely, a set of interior resonant frequencies which occur on the negative imaginary axis of the plane and a set of those which reside in the left half of the plane off the imaginary axis. It is shown that only the latter set can be interpreted as intrinsic to the scatterer. It corresponds to the set of complex poles of the scattering matrix of the problem and also to the set of complex eigenvalues of the related exterior homogeneous boundary value problem. Finally, some doubts about the eigenmode expansion method (EEM) formalism are raised, and a possible justification, based on nonself-adjoint theory, is suggested.