TWISTED GAUSSIAN SCHELL-MODEL BEAMS .1. SYMMETRY STRUCTURE AND NORMAL-MODE SPECTRUM

We present a comprehensive normal-mode decomposition analysis for the recently introduced [J. Opt. Soc. Am. A 10, 95 (1993)] class of twiste d 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 fie lds to achieve the mode decomposition and to determine the spectrum. T he twist phase is nonseparable in nature, rendering it nontrivially tw o dimensional. The cosequences of this, resulting in the need to use L aguerre-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.