In this paper, the relation between the spectral degree of coherence and degree of polarization of random electromagnetic beams is derived by the Stokes parameters. And the concept of polarization singularity is extended from spatially fully coherent beams to partially coherent electromagnetic beams. Theoretical analysis shows that correlation vortices are linearly polarized singularities. The results are illustrated by numerical examples.
Polarization singularities in the near-field of Gaussian vortex beams diffracted by a circular aperture are studied by a rigorous electromagnetic theory. It is shown that there exist C-points and L-lines, which depend on off-axis displacement parameters along the x and y directions, waist width, wavelength, and topological charge of the diffracted Gaussian vortex beam, as well as on propagation distance. The results are illustrated by numerical calculations.
We have derived the analytical expression of the electric cross-spectral density in the near- field of partially coherent vortex beams diffracted by an aperture. Taking the Caussian Schell-model vortex beam as a typical example of partially coherent vortex beams, the spatial correlation properties and correlation vortices in the near-field of partially coherent vortex beams diffracted by a rectangle aperture are studied. It is shown that the off-axis displacement, spatial degree of coherence parameter, propagation distance, and the opening factor of the aperture affect the spectral degree of coherence and positions of correlation vortices. With the optimization algorithm, we obtain the symmetric distributing coherent vortex.
