Optical theorem for electromagnetic scattering by a three-dimensional scatterer in the presence of a lossless half space

The classical optical theorem for a scatterer in free space is useful in computing the total extinction cross section when the scattering amplitude in the forward scattering direction is known. In this letter, the classical optical theorem is extended to the case of a scatterer in the presence of a lossless half space. The extended optical theorem is derived based on energy conservation concepts, and the method of stationary phase is employed to obtain the final form. It is found that the total extinction cross section is related to the scattering amplitudes in the specular directions for reflected and transmitted fields. Numerical results are presented to illustrate use of the theorem for evaluating the energy conservation properties of an electromagnetic simulation.