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.

Presenting the intensity development of a circular Laguerre-cosh-Gaussian (CLChG) beam in turbulent mouse biological tissues is the major goal of the current work. Using the power spectrum refractive index from Schmitt's model and the extended Huygens-Fresnel integral, the propagation formula of the CLChG beam is produced. In order to determine the spreading properties of the studied beam, analytical expressions of the CLChG beam's effective beam size in turbulent mouse biological tissues are constructed. Some graphical representations have to be carried out in order to discover the impacts of beam and biological turbulence parameters on this sort of beam. The findings show that the transformation of the CLChG beam into a Gaussian-like beam in the far field occurs more quickly when the beam passes through the deep dermis of the mouse. The shape of the CLChG beam can also be changed by choosing a specific value for the parameter linked to the cosh-part. Because the effective beam spot radius along the x- and y-axis are equal, we also see that the beam spot in biological tissues takes on a circular shape.

This work examines several analytical evaluations of the Voigt profile, which is a convolution of the Gaussian and Lorentzian profiles, theoretically and numerically. Mathematical derivations are performed concisely to illustrate some closed forms of the considered profile. A representation in terms of special function and a simple and interesting approximation of the Voigt function are well demonstrated, which could have promising applications in several fields of physics, e.g., atmospheric radiative transfer, neutron reactions, molecular spectroscopy, plasma waves, and astrophysical spectroscopy.