In this paper, we study the propagation properties of twisted Hermite–Gaussian Schell- model (THGSM) beams propagating in a uniaxial crystal orthogonal to the optical axis. We derive the concrete analytical expression of the cross-spectral density (CSD) function in the crystal and simulate the evolution characteristics of such beams, including normalized spectral intensity, the spectral degree of coherence (DOC), and effective beam width. We find that the spectral intensity distribution exhibits a non-circular symmetric self-splitting while rotating, and the distribution of the spectral DOC is non-circular symmetric rotationally distorted, which is quite different from that in an isotropic medium. The initial beam parameters and crystal parameters both affect the distribution of spectral intensity and DOC. Furthermore, increasing the twist factor and adjusting the ratio of the extraordinary light refractive index and the ordinary light refractive index n_e/n_o of the uniaxial crystal can suppress the beam expansion as propagating in the crystal. Our results show that the uniaxial crystal can be used to determine whether light beams carry a twist phase or not, and to modulate the characteristics of light beams.

This study examines the evolution of Shannon entropy, a key measure of uncertainty and disorder, in a Laguerre-Gaussian correlated Schell-model (LGcSM) beam under ocean turbulence. We explore how the spatial coherence distribution of the LGcSM beam influences its Shannon entropy in both free space and ocean turbulent conditions. Our results show that tailoring the optical coherence distribution can significantly control spatial disorder, enabling the beam to restore order under turbulence. Furthermore, we analyze the impact of various ocean turbulence parameters on Shannon entropy evolution, offering a potential strategy to mitigate performance degradation in optical communication systems affected by turbulence.