title: Conservation of extremal ellipticity and analytical expressions for astigmatism and asymmetry in Gaussian beam transformations.
abstract: A Gaussian beam with initial astigmatism, waist, and M2asymmetry propagates through a simple optical system consisting of a single thin, aberration-free lens. We derive simple analytical expressions for the asymmetry, astigmatism, and ellipticity of the beam after the lens, and show that the maximal ellipticity of the beam is a conserved quantity that is solely dependent on these input parameters. This appears to still hold for general astigmatic Gaussian beams. Our simple, analytical results conveniently determine the trade-off between astigmatism and asymmetry of a laser for a given output maximum ellipticity requirement pre- or post-lenses.
authors.forename: Ho W
authors.initials: HW
authors.lastname: Lo
authors.forename: Jan
authors.initials: J
authors.lastname: Kleinert
authors.forename: Michaela
authors.initials: M
authors.lastname: Kleinert