Elliptical Form-invariant Gaussian Beams with a Phase Singularity

Abstract

We find a two-parameter family of astigmatic elliptical Gaussian (AEG) optical vortices, which are free space modes up to scale and rotation. We calculate their normalized orbital angular momentum, which consists of two terms (vortex and astigmatic). In any transverse plane, such a beam has an isolated $n-$ fold degenerate intensity null (an optical vortex) on the optical axis embedded into an elliptical Gaussian beam. The degenerated central intensity null in these beams does not split it into $n$ spatially separated intensity nulls, as is usually assumed for elliptical astigmatic beams.