A darkness theorem for the beam shape coefficients and its relationship to higher-order non-vortex Bessel beams

•A theorem in terms of Beam Shape Coefficients is established.•It allows one to decide whether a beam is dark or non-dark.•The theorem is related with the existence of higher-order non-vortex Bessel beams.

Within the framework of generalized Lorenz-Mie theories and other light scattering theories such as the Extended Boundary Condition Method, the illuminating electromagnetic beam is described in terms of beam shape coefficients. We establish a darkness theorem in terms of the shape coefficients, allowing one to establish whether the beam intensity is zero on an axis (i.e. dark) or not. This theorem allows one to predict the existence of higher-order nonvortex Bessel beams. A proposal for similar studies concerning other types of beams is provided, as a possible extension of the present work.