Orbital angular momentum of structurally stable laser beams

Abstract

For structurally stable laser beams whose amplitude can be represented as a finite sum of the Hermite-Gaussian functions with undefined weight coefficients, we obtain an analytical expression for the normalized orbital angular momentum (OAM) that is also expressed through finite sums of weight coefficients. It is shown that a certain choice of weight coefficients allows obtaining the maximal OAM, which is equal to the maximal index of the Hermite polynomial in the sum. In this case, the sum describes a single-ringed Laguerre-Gaussian beam with a topological charge equal to the maximal OAM and to the maximal order of the Hermite polynomial.