On the description of electromagnetic arbitrary shaped beams: The relationship between beam shape coefficients and plane wave spectra

•Electromagnetic beams may be described by using beam shape coefficients or plane wave spectra.•Beam shape coefficients are expressed in terms of plane wave spectra.•Plane wave spectra are expressed in terms of beam shape coefficients.

A strong effort has been devoted during the last three decades, and more, to the study of electromagnetic scattering of arbitrary shaped beams by particles. For this topic, the most important issue concerns the description of the illuminating beam as an expansion over a basis of functions. There are essentially two kinds of expansions that have been used: (i) a discrete expansion involving beam shape coefficients and (ii) a continuous expansion in terms of plane wave spectra. In this paper, we provide a formal relationship between these two kinds of expansions.