On the basis of the extended Huygens–Fresnel principle and the spatial power spectrum of the refractive index fluctuations of ocean water, a propagation formula for on-axis average intensity of hollow Gaussian beams (HGBs) in oceanic turbulence is analytically obtained. Furthermore, the propagation properties of an HGB in oceanic turbulence are studied numerically in detail. The numerical results indicate that the initial beams with a higher beam order, longer blue–green wavelength, and larger waist width are helpful in mitigating the influence of turbulent ocean. Meanwhile, an HGB may propagate a much longer distance in weak oceanic turbulence by decreasing the dissipation rate of mean-square temperature and the ratio of temperature and salinity, as well as increasing the dissipation rate of turbulent kinetic energy per unit mass of fluid. The simulations also verify that HGBs have more resiliency to oceanic turbulence effects than ordinary Gaussian beams. Our research is expected to provide useful guidance for understanding the propagation characteristics of structured light beams in turbulent media.
The analytical expressions of mode probability density (MPD) and crosstalk probability density (CPD) for LaguerreGaussian correlated Schell-mode (LGCSM) beams propagating through oceanic turbulence are established based on the geometrical optics approximation. Using the derived formulae and numerical simulation, the propagation characteristics of a single LGCSM beam in turbulent ocean are quantificationally analyzed in detail. The numerical results for the effects of all kinds of parameters on the MPD and CPD curves of a LGCSM beam propagating in the ocean environment are presented and illustrated. This research is expected to provide a convenient way and useful guidance to describe and treat the propagation of laser beam in turbulent medium.