Generalization of the optical theorem for a multipole based on integral transforms

Based on integral transforms for wave fields, we obtain a generalization of the optical theorem for the case in which a local inhomogeneity is excited by a multipole source of arbitrary order. This generalization permits determining the total scattered and absorbed energy analytically by computing the derivatives of the scattered field at a single point. This relation can be used to compute the absorption cross-section in problems related to plasmonic structures and also to test computer modules when multipole radiation is scattered by transparent bodies.