Statistical propagation of vortex beams in depth-dependent oceanic turbulence along slant paths

Optical wave propagation in the ocean constitutes a challenging random-medium problem due to the combined effects of depth-dependent absorption, scattering, and refractive-index fluctuations induced by oceanic turbulence. In this work, we develop a depth-dependent statistical propagation model for vortex beams along slant paths by coupling realistic chlorophyll-induced attenuation profiles with an inclined-path oceanic turbulence spectrum. Based on this framework, the evolution of spatial coherence radius, beam attenuation, and orbital-angular-momentum (OAM) modal crosstalk of Bessel-Gaussian vortex beams is systematically investigated as functions of ocean depth, propagation distance, and turbulence parameters. The results reveal a pronounced depth dependence of beam attenuation governed by the vertical distribution of chlorophyll, as well as significant turbulence-induced degradation of spatial coherence leading to enhanced intermodal coupling among OAM states. As an illustrative application, the proposed model provides a quantitative prediction of the optical power required to sustain long-range underwater propagation, and demonstrates that appropriate optimization of beam parameters can effectively mitigate OAM crosstalk in inhomogeneous oceanic turbulence. These results provide a unified statistical framework for analyzing the propagation and modal evolution of structured optical fields in depth-varying oceanic random media.