Asymptotic behavior of angular momentum of the light field as a superposition of Hermite-Gaussian modes

An asymptotic behavior of orbital angular momentum (OAM) for the light field as superposition of Hermite-Gaussian modes is considered. An analytical formula for the OAM of such fields is obtained. For a three- and four mode superposition it was found that their OAM can be larger than the maximum index in the superposition while the structural stability of the light field is retained.