Echo scattering characteristics: Vortex beams reflected by rough surface in ocean turbulence

Optical field echo scattering characteristic is one of the essential technologies for the future integration of underwater laser communication and detection. Vortex beam (e.g. Laguerre-Gaussian (LG) beam) with a helical wavefront structure is better suited to reduce the effects of ocean turbulence. A double-path transmission model of LG beam scattering through rough surface in ocean turbulence is innovatively established. We developed a closed analytical expression for the echo speckle intensity of LG beams reflected by a rough surface with a Gaussian distribution in ocean turbulence based on the generalized Huygens-Fresnel principle. The autocorrelation function of intensity and complex degree of coherence (DOC) of echo speckle field were numerically simulated and analyzed. From the results we found a rule that when coherence length of rough surfaces (rho h) is greater than the coherence length (rho 0) of spherical waves propagating across ocean turbulence, the impact of a rough surface on DOC is much less than that of ocean turbulence. This conclusion provides the theoretical basis that the echo wave field cannot be obtained in target detection under ocean turbulence.