Orbital angular momentum of superposition of two generalized Hermite–Gaussian laser beams

We have obtained an expression for complex amplitude of the generalized paraxial Hermite-Gaussian (HG) beams. At certain parameters these beams become well-known HG modes and elegant HG beams. We calculated an orbital angular momentum (OAM) of linear combination of two generalized HG beams with transposed adjacent indices and with phase delay of p/2. It has been shown that for a sum of two HG modes the OAM is integer, while for two elegant HG beams it is always unitary and for two hybrid HG beams it is fractional.