Acoustic scattering and "failure" of the optical theorem.

Abstract

For plane wave scattering by an obstacle, the optical theorem relates the scattering cross section to the far-field scattered field in the forward direction. This simple and useful result fails to hold when the incident field is not a plane wave. "Failures" of this kind are explored. For scattering by a sphere, an explicit formula for the scattering cross section is obtained, applicable to arbitrary incident fields.