Orbital angular momentum of paraxial propagation-invariant laser beams

For propagation-invariant laser beams represented as a finite superposition of the Hermite-Gaussian beams with the same Gouy phase and with arbitrary weight coefficients, we obtain an analytical expression for the normalized orbital angular momentum (OAM). This expression is represented also as a finite sum of weight coefficients. We show that a certain choice of the weight coefficients allows obtaining the maximal OAM, which is equal to the maximal power of the Hermite polynomial in the sum. In this case, the superposition describes a single-ringed Laguerre-Gaussian beam with a topological charge equal to the maximal OAM and to the maximal power of the Hermite polynomial.