By analyzing the effect of the degree of polarization (DoP) of the partially coherent Gaussian Schell-model (GSM) beam on a heterodyne system of an uplink path and a downlink path, we developed an innovative and noteworthy theory according to which σ_sy (signal beam waist radius in the y direction component) and δ_Syy (coherence length of the signal beam in the yy direction component) had a more significant impact on heterodyne efficiency and DoP than the turbulence term on uplink and downlink paths. Namely, the DoP and heterodyne efficiency of an uplink path are higher than that of a downlink path when σ_sy > 0.02 m or δ_Syy ≥ 0.03 m. This innovative rule provides an efficient way for increasing the heterodyne efficiency of a signal beam propagating along an uplink or a downlink path channel in satellite-ground communication links in free-space optical heterodyne detection communication.

A novel encoding method based on the orbital angular momentum (OAM) mode and radial mode of composite vortex beams is proposed. The superposition of two vortex beams generates 32 different types of composite vortex beams: one of them is a Laguerre–Gaussian (LG) beam with a fixed OAM mode and radial mode, and the other is a LG beam containing four radial modes (p = 0, 1, 2, 3) and eight OAM modes with the same interval (l = ±3, ±5, ±7, ±9). A specially designed composite fork-shaped grating (CFG) is utilized to generate the intensity array pattern, and the received composite vortex beam is diffracted into a Gaussian beam with the relevant coordinates. Based on the coordinates and the number of bright rings in the intensity pattern, the OAM modes and radial modes of the two vortex beams composing the superposition state are determined, and finally the received composite vortex beam is decoded into the initially propagated information sequence. The correctness and effectiveness of the proposed encoding are confirmed through the comparative analysis of the correlation of the optical fields at both the transmitter and receiver in the two scenarios of interval and non-interval encoding. The proposed encoding method can significantly improve the efficiency of information transmission and its resistance to interference, holding great potential for future applications in free-space optical communication.

The modeling of light propagation in scattering media is an important topic that has attracted considerable attention in recent decades. Coupling microscopic parameters such as particle concentration, particle size, and the refractive index of the medium can broaden the applicability of the model and improve simulation accuracy. In this work, these parameters are used to regulate the anisotropy factor and the mean free path. They are then integrated into a random phase screen model constructed using the Monte Carlo and the Gerchberg–Saxton algorithm. An optical experimental setup was established, in which a Laguerre–Gaussian beam was employed as the incident light source and diffusers with mesh numbers of 1500, 600, and 220 were used as the scattering media. The model was validated through comparative analysis between simulated and experimental results. Correlation coefficients between the simulated and experimental beam profiles exceeded 0.73, and the maximum relative error in power-in-the-bucket was only 4.9%, confirming the model’s accuracy and reliability. Numerical simulations were performed based on the established model to investigate beam propagation behavior. The results indicate that increasing particle concentration and particle size both lead to enhanced beam centroid shift and beam broadening. This modeling method provides a useful tool for analyzing beam propagation in complex scattering media and holds potential applications in wavefront correction and structured beam recognition.