Generalized optical theorem for scattering in inhomogeneous media

The scattering of scalar waves by objects embedded in an inhomogeneous medium contained by a bounded volume is discussed using the method of pseudopotentials. The scattering amplitude for the object in an extended uniform medium is assumed known and used as input. The scattering process is described by using an expansion of the scattering amplitude in terms of spherical harmonics. An appropriate multipole decomposition of the Green function in the bounded medium is developed and the effective scattering amplitude in this environment is defined. The generalized optical theorem obeyed by this effective scattering amplitude is obtained and analyzed. The scattering problem is formulated entirely and explicitly in terms of the bounded medium's Green functions. This approach is thus very flexible in regards to the choice of incident field. In the case of waveguides the connection between propagation and scattering is explicit. At the same time it still allows for independent computation of the propagation and scattering aspects of the problem. This is the main advantage of using as input the scattering amplitude in an extended uniform medium.