Generalized optical theorem to a multipole source excitation in the scattering theory

In the present paper, the Optical Theorem is generalized to the case of a penetrable obstacle excited by a multipole of arbitrary order in the presence of a transparent substrate. This generalization allows one to test computer modules when wave scattering by lossless penetrable obstacle is considered. Besides, it enables one to evaluate the absorption cross-section by subtracting the scattering cross-section from the extinction cross-section. This seems to be important because, in this particular case, the far field does not involve a Sommerfeld integral.