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

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. (C) 2014 Elsevier Ltd. All rights reserved.