Higher-order moments and overlaps of rotationally symmetric beams

We introduce a closed-form expression for the overlap between two different circular beams (CiBs) with azimuthal symmetry. A full description of the propagation of the higher-order moments of the CiBs through paraxial ABCD systems is presented. Our formalism can be easily applied to calculate relevant beam parameters such as the normalization constants, the M^2 factors, the kurtosis parameters, the expansion coefficients of the CiBs, and therefore of all its relevant special cases, including the standard, elegant, and generalized Laguerre–Gaussian beams, Bessel–Gaussian beams, hypergeometric–Gaussian beams, quadratic Bessel–Gaussian beams, and optical vortex beams, among others.