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In this paper, the effects of turbulent biological tissues (TBT) on the propagation properties of the coherent Laguerre-Gaussian (CLG) beams are studied. Based on the turbulence theory and using the power spectrum refractive-index model, the expression formulae of the average irradiance intensity and spreading properties of a CLG beam propagating in TBT are derived. The influence of propagation distance, beam orders, wavelengths and tissue turbulence parameters are then investigated numerically. It found that, the central dark zone of the circular/elliptical LG beams rises more rapidly as the propagation distance and the structural constant of the refractive index of the biological tissue increase and the beams become eventually more like Gaussian beams in the far-field under the influence of the turbulence biological tissues. Also, the numerical results proved that the effective beam spot radius increases as turbulence, wavelength, and propagation distance are increasing.Ultimately, the beams become circular under the influence of the turbulence of the biological tissue.As found that the effective beam spot radius along the x-axis becomes equal to that of the y-axis in high TBT which explain why an elliptical LG beam is converted into a circular one in higher structural constant of the turbulent tissue. Moreover, our results show that, the influence of the beam order m slightly greater than that of l on the beam spreading.

The propagation properties for a General Model vortex Higher-order cosh-Gaussian beam (GMvHchGB) propagating in a turbulent atmosphere studied in detail. Based on the Huygens-Fresnel diffraction principle, the analytical formula of the intensity evolution for the considered beam traveling in turbulent atmosphere is derived at various propagation distances. The derived equation provides a general convenient procedure to describe the propagation characteristics to some particular beams travelling through free space/atmospheric turbulence such as a fundamental Gaussian, Cosh-Gaussian, vortex Cosh-Gaussian and higher-order Cosh-Gaussian beams. The impact of the incident parameters as Gaussian waist, Cosh parameter, wavelength, hollowness and order of the beam are numerically verified. Our study proven that the beams maintain their intensity focused over long propagation distances. Therefore, they will be useful in long-distance free-space optical communication applications.

Based on the second-order moments definition, we investigate in this paper the beam propagation factor of new mathematical model of Hollow higher-order Cosh-Gaussian (HhCG) beams. Two analytical formulae of the M 2 -factor of HhCG beams are derived. Moreover, numerical simulations are developed to illustrate the effects of the beams orders n and l, the parameter  and the beam waist on the M 2 -factor. The result shows a more general characteristic of higher-order Cosh-Gaussian, Cosh-Gaussian and the fundamental Gaussian beams can be obtained as specials cases of HhCG beams.