TWIST PHASE IN GAUSSIAN-BEAM OPTICS

The recently discovered twist phase is studied in the context of the f ull ten-parameter family of partially coherent general anisotropic Gau ssian Schell-model beams. It is shown that the nonnegativity requireme nt on the cross-spectral density of the beam demands that the strength of the twist phase be bounded from above by the inverse of the transv erse coherence area of the beam. The twist phase as a two-point functi on is shown to have the structure of the generalized Huygens kernel or Green's function of a first-order system. The ray-transfer matrix of this system is exhibited. Wolf-type coherent-mode decomposition of the twist phase is carried out. Imposition of the twist phase on an other wise untwisted beam is shown to result in a linear transformation in t he ray phase space of the Wigner distribution. Though this transformat ion preserves the four-dimensional phase-space volume, it is not sympl ectic and hence it can, when impressed on a Wigner distribution, push it out of the convex set of all bona fide Wigner distributions unless the original Wigner distribution was sufficiently deep into the interi or of the set. (C) 1998 Optical Society of America.