ИСТИНА

One of the fundamental results in wave scattering theory is the Optical Theorem (OT) which is known as well as the Extinction Theorem. In case of plane wave excitation the OT relates the extinction cross-section to the forward scattering complex amplitude of scattering diagram. Similar results take place in acoustics, seismics and quantum mechanics. One great advantage of the OT is that it eliminates the need to integrate the field energy flux around the object. In this paper we extended the OT to the case of a penetrable obstacle excited by a multipole of arbitrary order. We employ classic Maxwell's theory and the Gauss Theorem. It has been shown that the extinction cross-section can be evaluated via the calculation of some specific derivatives from the scattered field at the point of the multipole location. The universal formula for estimating the amount of energy which an obstacle can extract from the exciting multipole field has been obtained.