Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams

A 4 X 4 complex curvature tensor M-1 is introduced to describe partially coherent anisotropic Gaussian-Schell model (GSM) beams. An analytical propagation formula for the cross-spectral density of partially coherent anisotropic GSM beams is derived. The propagation law of M-1 that is also derived may be called partially coherent tensor ABCD law. The analytical formulas presented here are useful in treating the propagation and transformation of partially coherent anisotropic GSM beams, which include previous results for completely coherent Gaussian beams as special cases. (C) 2002 Optical Society of America.