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In this paper, we give a review of the tensor method for treating the propagation of scalar and electromagnetic Gaussian Schell-model (GSM) beams. Partially coherent complex curvature tensor is introduced to describe a scalar astigmatic partially coherent GSM beam with twisted phase (i.e., twisted anisotropic GSM beam). A tensor ABCD law for treating the propagation of scalar twisted anisotropic GSM beam through a paraxial astigmatic optical system is derived. The tensor method is then applied to treat the propagation of a scalar twisted anisotripic GSM beam through an apertured optical system, fractional Fourier transform optical system, dispersive and absorbing media, turbulent media. Furthermore, we applied the tensor method to treat the propagation of an electromagnetic GSM beam. Propagation formulae for an electromagnetic GSM beam passing through a paraxial astigmatic optical system in free space and in turbulent atmosphere are derived. The propagation properties of an electromagnetic GSM beam in a Gaussian cavity and in turbulent atmosphere are also reviewed.

Tensor Method for Treating the Propagation of Scalar and Electromagnetic Gaussian Schell-Model Beams: A Review~!2009-09-07~!2009-12-02~!2010-03-09~!