  Many practical applications require the analysis of electromagnetic
scattering properties of local structures using different sources of
illumination. The Optical Theorem (OT) is a useful result in scattering theory,
relating the extinction of a structure to the scattering amplitude in the
forward direction. The most common derivation of the OT is given for plane
waves but advances in optical engineering now allow laser beam shaping, which
might require an extended theorem where the impinging source is a structured
field. In this work, we derive an expression for the optical theorem based on
classical electromagnetic theory, for probe sources given in terms of
propagation invariant beams. We obtain a general expression for the
differential scattering cross section using the integral scattering amplitude
approximation in the far field. We also analyze the scattering problem of a
zero order Bessel beam by a dielectric sphere, under the Rayleigh approximation
by varying the angle of incidence.
