Generalization of the Optical Theorem to the multipole source excitation

•We extended the Optical Theorem to the case of a penetrable particle excited by a multipole source.•The extinction cross-section can be evaluated from the scattered field at the point of the multipole location.•The Generalized Optical Theorem can be applied to test computer models for non-absorbing particles.

Based on classic Maxwell׳s theory and the Gauss Theorem we extended the Optical Theorem to the case of a penetrable particle excited by a multipole source. We demonstrate that the derived extinction cross-section can be evaluated via calculation of some specific derivatives from the scattered field at the point of the multipole location. The obtained relation between extinction cross-section and scattering cross-section can be employed to estimate the corresponding absorption cross-section.