Wavefront Interpretation of Sem Resonances, Turn-On Times, and Entire Functions

Abstract

By the Singularity Expansion Method (SEM), transient scattering is analyzed in terms of the damped oscillations corresponding to the complex resonant frequencies of the scatterer. Since the resonances describe global wave fields that encompass the scattering object as a whole, the SEM series representation encounters convergence difficulties at early observation times when portions of the object are as yet unexcited. Deficiencies in this representation must then be repaired by inclusion of an entire function in the complex frequency domain. The choice of the entire function is related intimately to the excitation coefficients, called coupling coefficients, of individual resonances and also to the “turn-on” and “switch-on” times of the SEM series. By using a traveling wave formulation in terms of progressing incident, reflected and diffracted wavefronts, these constructs in the SEM can be given a cogent physical interpretation. The wavefront analysis clearly identifies those portions of the entire function that are essential (intrinsic) and those that are removable. By combining wavefronts and resonances self-consistently, one may construct a hybrid field that avoids the difficulties at early times in the SEM formulation. These concepts are illustrated for two-dimensional scattering by a circular cylinder and a flat strip.