Abstract
The Wigner distribution function (WDF) matrix is introduced, and its analytical propagation expressions in free space and the corresponding far-field forms are derived for the first time. It is shown that the propagation expressions for the WDF matrix have general applicable advantages and reduce to those for the WDF of partially coherent scalar paraxial beams within the paraxial regime. The application of the WDF matrix to the partially coherent vectorial nonparaxial beams is illustrated with vectorial nonparaxial Gaussian Schell-model beams.
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