Degree of cross-polarization of elliptical Gaussian partially coherent beams propagating in turbulent atmosphere

The cross-spectral density matrix for elliptical Gaussian partially coherent beams propagating along a slant path in non-Kolmogorov turbulence is derived based on the generalized Huygens-Fresnel principle and the quadratic approximation of the Rytov phase structure function. The spectral degree of cross-polarization (SDCP) between two distinct points of elliptical Gaussian partially coherent beams is analyzed for different source parameters, turbulence inner and outer scales, and zenith angles, and is compared with the classical degree of polarization (CDOP) when the two points coincide. The results show that the variations in the SDCP of an elliptical Gaussian partially coherent beam are more pronounced. As the relative distance between two points grows, the SDCP exhibits a "self-recovering" evolutionary trend with the off-axis distance initially declining, then rising, and ultimately stabilizing at a constant value. This stable value decreases with higher amplitude ratio and zenith angle but increases with longer coherence length and larger turbulence inner scale. Additionally, the impact of atmospheric turbulence on the SDCP becomes more significant over longer transmission distances. Finally, Monte Carlo simulations were used to validate the theoretical results. It is noted that the results have established a sound theoretical basis on the topic of improving the performance of free-space optical communication.