Extension of the van Cittert–Zernike theorem for completely polarized incoherent electromagnetic beam propagating through non-Kolmogorov turbulence

Based on the 2 × 2 cross-spectral density matrix, the van Cittert–Zernike extended theorem is developed for the completely polarized incoherent beams propagation through the paraxial non-Kolmogorov turbulence. On the consequence of the extended theorem and the definition of general spectral degree of cross-polarization of a beam, we found that the spectral degree of cross-polarization of the resultant field is independent of the refractive index structure constant of atmospheric turbulence. We investigated the influences of the propagation distance and the distance of two detection points on the degree of coherence and the spectral degree of cross-polarization.