The optical theorem for local source excitation of a particle near a plane interface

•We extended the Optical Theorem to a particle excited by a dipole on an interface.•The Extinction Cross-Section includes the scattering from the interface.•The absorption cross-section is not needed to find the optical antenna efficiency.

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 local source deposited near a plane interface. We demonstrate that the derived Extinction Cross-Section involves the total point source radiating cross-section and some definite integrals responsible for the scattering by the interface. The derived extinction cross-section can be employed to estimate the quantum yield and the optical antenna efficiency without computation of the absorption cross-section.