We present a comprehensive normal-mode decomposition analysis for the recently introduced [ J. Opt. Soc. Am. A 10, 95 ( 1993)] class of twisted Gaussian Schell-model fields in partially coherent beam optics. The formal analogies to quantum mechanics in two dimensions are exploited. We also make effective use of a dynamical SU(2) symmetry of these fields to achieve the mode decomposition and to determine the spectrum. The twist phase is nonseparable in nature, rendering it nontrivially two dimensional. The consequences of this, resulting in the need to use Laguerre–Gaussian functions rather than products of Hermite–Gaussians, are carefully analyzed. An important identity involving these sets of special functions is established and is used in deriving the spectrum.
© 1993 Optical Society of America
Original Manuscript: October 30, 1992
Revised Manuscript: March 25, 1993
Manuscript Accepted: January 19, 1993
Published: September 1, 1993
R. Simon, N. Mukunda, and K. Sundar, "Twisted Gaussian Schell-model beams. I. Symmetry structure and normal-mode spectrum," J. Opt. Soc. Am. A 10, 2008-2016 (1993)