1. Introduction . In 1961 the paraxial Hermite-Gauss beams (HGB) were first proposed theoretically as resonator modes in cavities with spherical mirrors and, about a year later, they were demonstrated experimentally [ 1 – 3 ]. Using a diffraction approach, they were presented as approximated paraxial solutions to an homogeneous Fredholm integral equation of the second kind whose actual solutions can be proportional to the angular wave functions in prolate spheroidal coordinates [ 1 ]. T...