Extinction theorem for object scattering in a stratified medium

Abstract

A simple relation for the rate at which energy is extinguished from the incident wave of a far-field point source by an obstacle of arbitrary size and shape in a stratified medium is derived from wave theory. This relation generalizes the classical extinction theorem, or optical theorem, that was originally derived for plane wave scattering in free space and greatly facilitates extinction calculations by eliminating the need to integrate energy flux about the obstacle. The total extinction is shown to be a linear sum of the extinction of each waveguide mode. Each modal extinction involves a sum over all incident modes that are scattered into the extinguished mode and is expressed in terms of the object’s plane wave scatter function in the forward azimuth and equivalent plane wave amplitudes of the modes. The only assumptions are that multiple scattering between the object and waveguide boundaries is negligible, and the object lies within a constant sound-speed layer. Calculations for a shallow-water waveguide show that the extinction cross section is highly dependent on measurement geometry, and medium stratification, as well as the scattering properties of the object and may be significantly modified by the presence of absorption in the medium.