Conservation of orbital angular momentum and extremal ellipticity for simple and general astigmatic Gaussian beams

Orbital angular momentum (OAM) of light depends on the spatial electric field amplitude and the phase structure of the beam wavefront. Light beams possessing finite OAM have been actively investigated in the context of particle micro-manipulation, microscopy, quantum informatics, etc. Recently Lo et al. [1] showed that the extremal ellipticity for a simple and general astigmatic Gaussian beam is conserved upon propagation through a rotationally invariant optical system, such as a sequence of stigmatic lenses. Here we carry forward this work and theoretically demonstrate that the conservation of extremal ellipticity for an astigmatic Gaussian beam propagating through such a medium is a direct but nontrivial consequence of the conservation of OAM of the beam. We present explicit analytical expressions for the first few moments of the beam OAM and report that apart from fundamental constants, they depend only on the beam's extremal ellipticity. Our work is expected to find use in areas where the ellipticity of the Gaussian beam is important, such as laser micromachining, lithography and imaging.

[1]  H. W. Lo et al., Appl. Opt. 56, 2523 (2017).