Conservation of extremal ellipticity and analytical expressions for astigmatism and asymmetry in Gaussian beam transformations

Abstract

A Gaussian beam with initial astigmatism, waist, and $M^2$ asymmetry 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.

© 2017 Optical Society of America

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