Orbital angular momentum of an elliptic optical vortex embedded into the Gaussian beam

We consider an elliptic optical vortex embedded into a Gaussian beam. For such a beam, explicit closed-form expressions are derived for the complex amplitude and the normalized orbital angular momentum (OAM). It is shown that the elliptic Gaussian vortex (EGV) has a fractional OAM. The maximal OAM value equal to the vortex topological charge $n$ is achieved at zero ellipticity of the vortex. The major axis of the intensity ellipse in the beam cross section rotates in propagation, turning by a 90-degree angle from the initial plane to the focal plane of a spherical lens. There are n intensity nulls on the major axis of the EGV intensity ellipse. The distance between the nulls varies during the beam propagation and with changing degree of ellipticity. At a fixed degree of ellipticity, the distance between the intensity nulls is maximal in the focal plane. At zero ellipticity, all nulls are "gathering" into a single on-axis n-times degenerate intensity null. The experimental results are consistent with the theory.