Elliptic Gaussian optical vortices

Abstract

We analyze an elliptic optical vortex embedded into a Gaussian beam. Explicit closed expressions for the complex amplitude and normalized orbital angular momentum (OAM) of such a beam are derived. The resulting elliptic Gaussian vortex (EGV) is shown to have a fractional OAM whose maximal value equal to the topological charge $n$ of a conventional Gauss vortex is attained for a zero-ellipticity vortex. As the beam propagates, the major axis of the intensity ellipse in the beam cross section rotates, making the angle of 90\ifmmode^\circ\else\textdegree\fi{} between the initial plane and the focal plane of a spherical lens. On the major axis of the intensity ellipse, there are $n$ intensity nulls of the EGV, with the distance between them varying with propagation distance and varying ellipticity. The distance between the intensity nulls is found to be maximal in the focal plane for a given ellipticity. For zero ellipticity, all intensity nulls get merged into a single $n$-times degenerate on-axis intensity null. The experimental results are in good agreement with theory.