Generalized optical theorem for on-axis Gaussian beams

The optical theorem for an incident plane wave interacting with a finite scatterer is generalized to the case of on-axis Gaussian beams, taken as examples of shaped beams. Our results are restricted in this paper to homogeneous spheres. The beams are defined by using (i) the standard description (ii) the localized approximation and (iii) the modified localized approximation. Rigorous expressions generalizing the classical plane wave case expression are given and numerically discussed. A recently proposed approximation is investigated in order to point out assumptions underlying its validity.