The propagation formula of a partially coherent Generalized Flattened Hermite-Cosh-Gaussian (GFHChG) beam in maritime atmospheric turbulence is derived with the help of the extended Huygens–Fresnel principle. In addition, the analytical expression for the beam width of a partially coherent GFHChG beam in the considered environment is investigated. From the numerical results based on the analytical formulae, we find that the analyzed beam can take different shapes of the profile, depending on the turbulence and beam parameters. And also, it can significantly resist turbulence with small wavelength and waist width values. On the other hand, when the medium becomes turbulent, the beam loses its characteristics and its resistance to fluctuations. Furthermore, the results reveal that the beam spreads more rapidly with the increase of the strength of turbulence, the outer scale size, and the decrease of the inner scale size. We should mention that the results gained represent a general form of numerous partially coherent laser beams such as Generalized Flattened Hermite Gaussian, Generalized Flattened Cosh-Gaussian, Hermite-Cosh-Gaussian, Cosh-Gaussian, Hermite-Gaussian and Gaussian Schell model beams.

We derive the received intensity of astigmatic hyperbolic sinusoidal Gaussian(AHSG) beam propagating through oceanic turbulence. Huygens–Fresnel integral is evaluated to reach the expression at the receiver side. Effect of variations on turbulence parameters such as the rate of dissipation of the mean square temperature, the rate of dissipation of the turbulent kinetic energy per unit mass of fluid, and relative strength of the temperature and salinity fluctuations are examined. We observe that beam has a view having rings at close range but beam evolves into circular shape at a short/long distance depending on the parameters of oceanic turbulence. This evolution occurs faster when the rate of dissipation of the mean square temperature raises. We hope that our results will be used in underwater communication, imaging or range measurement applications.