Hermite-Gaussian laser beams with orbital angular momentum

We consider vortex Hermite-Gaussian modes (VHG-modes) with their complex amplitude being proportional to an n-th order Hermite polynomial dependant on a real parameter a. When |a| 0). If |a| > 1, the VHB-mode has analogous isolated s on the vertical axis. When |a| = 1, all n isolated s appear on the opti-cal axis in the center of the beam and generate an n-th order optical vortex. In this case, the VHG-mode coincides with a Laguerre-Gaussian mode of order (0, n). For a = 0, the VHG-mode coincides with a Hermite-Gaussian mode of order (0, n). We calculate the orbital angular momentum of the VHB-modes, which depends on a parameter a and varies from 0 (at a = 0 and a → ∞) to n (at a = 1).