Phase space conservation and selection rules for astigmatic mode converters

An astigmatic mode converter consists of a pair of cylindrical lenses which, when properly located and oriented, can transform a Hermite-Gauss mode (HG(nm)) with rectangular symmetry into a Laguerre-Gauss mode (LG(nm)) with cylindrical symmetry (see E. Abramochkin, V. Volstnikov, Opt. Commun. 83 (1991) 123; M.W. Beijersbergen, L. Alien, H.E.L.O. van der Veen, J.P. Woerdman, Opt. Commun. 96 (1993) 123; M.J. Padgett, J. Arlt, N. Simpson, Am. J. Phys. 64 (1996) 77; and J. Courtial, M.J. Padgett, Opt. Commun. 159 (1999) 13). In this paper we discuss how the conservation of phase space area determines the selection rules on which mode conversions are possible. A discussion of the beam quality factor M-2 is also given for both Hermite-Gauss and Laguerre-Gauss modes. (C) 1999 Published by Elsevier Science B.V. All rights reserved.