Poynting theorem in terms of beam shape coefficients and applications to axisymmetric, dark and non-dark, vortex and non-vortex, beams

Highlights: • Poynting theorem is expressed in terms of beam shape coefficients. • Axisymmetric, dark and non-dark, beams are considered as special cases. • A review of the applications in the literature of the above results is provided, including for vortex and non-vortex beams. - Abstract: Electromagnetic arbitrary shaped beams may be described by using expansions over a set of basis functions, with expansion coefficients containing sub-coefficients called beam shape coefficients which encode the structure of the beam. In this paper, the Poynting theorem is expressed in terms of these beam shape coefficients. Special cases (axisymmetric, dark and non-dark beams) are thereafter considered, as well as specific applications to paradigmatic examples, from trivial cases (plane waves and spherical waves) to the more sophisticated case of vortex beams.