The singular function expansion in time-dependent scattering

A class of linear initial-boundary-value problems relevant to time-dependent scattering is solved exactly in terms of the complete, orthogonal set of singular functions of the appropriate integral operator. The method is primarily presented as a mathematically defensible alternative to the eigenmode expansion method. The results extend the singularity expansion method to include the steady-state response at source frequencies and provide a connection between resonance behavior in the steady-state and low-loss natural modes. The method furthermore leads to an efficient automatic algorithm for the determination of natural modes and natural frequencies by observation of the singular values. The conclusions are supported by numerical calculations