Poynting vector and beam shape coefficients: On new families of symmetries (non-dark axisymmetric beams of the second kind and dark axisymmetric beams)

Abstract

On the one hand, some electromagnetic symmetries of laser beams are reflected in symmetry properties of the Poynting vector. On the other hand, these symmetries are in turn embedded in symmetries relating the beam shape coefficients which encode the structure of laser beams. The present paper extends the beam shape coefficient symmetries of laser beams, already uncovered, to new families. Examples and counter-examples are furthermore provided to illustrate these symmetries and formal laboratories are proposed as a way to discover still more symmetries.