The analytical expression of the cross-spectral density function of a twisted anisotropic Gaussian Schell-model (TAGSM) beam transmitting in turbulent ocean is derived by applying a tensor method. The statistical properties, including spectral density, the strength of twist and beam width of the propagating beam are studied carefully through numerical examples. It is demonstrated that the turbulence of ocean has no effect on the rotation direction of the beam spot during propagation. However, the beam shape will degrade into a Gaussian profile under the action of oceanic turbulence with sufficiently long propagation distance, and a beam with a larger initial twist factor is more resistant to turbulence-induced degeneration. As oceanic turbulence becomes stronger, the beam spot spreads more quickly while the twist factor drops more rapidly upon propagation. The physical mechanisms of these phenomena are addressed in detail. The obtained results will be helpful in optical communication systems underwater.

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.