title: Measurement of the M² beam propagation factor using a focus-tunable liquid lens.
abstract: We demonstrate motion-free beam quality M² measurements of stigmatic, simple astigmatic, and general astigmatic (twisted) beams using only a focus-tunable liquid lens and a CCD camera. We extend the variable-focus technique to the characterization of general astigmatic beams by measuring the 10 second-order moments of the power density distribution for the twisted beam produced by passage through multimode optical fiber. Our method measures the same M² values as the traditional variable-distance method for a wide range of laser beam sources, including nearly TEM(00) (M²≈1) and general astigmatic multimode beams (M²≈8). The method is simple and compact, with no moving parts or complex apparatus and measurement precision comparable to the standard variable-distance method.
authors.affiliation: Department of Physics, University of Colorado, Boulder, Colorado 80309, USA. robert.niederriter@colorado.edu
authors.forename: Robert D
authors.initials: RD
authors.lastname: Niederriter
authors.forename: Juliet T
authors.initials: JT
authors.lastname: Gopinath
authors.forename: Mark E
authors.initials: ME
authors.lastname: Siemens