In this paper, we investigate the correlation tensor for stochastic electromagnetic fields modulated by a depolarizer consisting of a rough-surfaced retardation plate. Under the assumption that the microstructure of the scattering surface on the depolarizer is as fine as to be unresolvable in our observation region, we have derived a relationship between the polarization matrix/coherency matrix for the modulated electric fields behind the rough-surfaced retardation plate and the coherence matrix under the free space geometry. This relation is regarded as entirely analogous to the van Cittert-Zernike theorem of classical coherence theory. Within the paraxial approximation as represented by the ABCD-matrix formalism, the three-dimensional structure of the generated polarization speckle is investigated based on the correlation tensor, indicating a typical carrot structure with a much longer axial dimension than the extent in its transverse dimension.
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Ning Ma, Juan Zhao, Steen G. Hanson, Mitsuo Takeda, Wei Wang, "3D polarisation speckle as a demonstration of tensor version of the van Cittert-Zernike theorem for stochastic electromagnetic beams," Proc. SPIE 10022, Holography, Diffractive Optics, and Applications VII, 100222F (31 October 2016);