On the scattering cross section of bodies in inhomogeneous medium

Abstract

A theorem is proven that relates the scattering cross section of arbitrarily shaped scatterers to the scattered far field in one or two particular directions. This can be regarded as a generalization of the classical optical theorem (also known as the extinction theorem) for homogeneous medium of infinite extent. In that case, the scattering cross section is given by the far field in the forward scattering direction. For a half-space with a bounding surface of arbitrary mechanical properties, it is shown that the scattering cross section is given by the scattered far field in the specular reflection direction. For an inhomogeneous medium with abrupt density and sound-speed change at an interface, the scattering cross section is given by the far field in both the specular reflection direction and the transmission direction that obeys the Snell’s law. [Work supported by ONR.]