Generalized Optical Theorem and Point Sources

Abstract

A simple derivation of the general form of the optical theorem (GOT) is given for the case of a conservative scatterer in a homogeneous lossless medium, suitable for describing point sources and an observation region close to the scatterer. The presentation is based on the use of the operator approach and scalar wave equation in the limit of vanishingly small absorption. This approach does not require asymptotic estimates of rapidly oscillating integrals, does not use the integration of fluxes, which leads to the loss of information about the energy conservation law, and allows a natural generalization to the case of polarized radiation, as well as more complex multi-part fields. Such GOT generalizes the results known in the mathematical literature for models to the case of any conservative (real) scattering potential and arbitrary sources.