Generalized optical theorem for an arbitrary incident field

A formalism of optical theorem extended for an arbitrarily shaped wave field is presented. The formalism concerns only time-harmonic scattering in free space. The theorem relates the extinction cross section to the imaginary part of the total scattering amplitude at the forward direction of the individual plane wave components multiplied by the corresponding plane wave amplitude in the angular spectrum of the incident wave. A differential extinction cross section is defined from the theorem. An alternative formalism relating the total cross section to plane wave scattering is also presented. Physical interpretation is provided and applications are discussed.