Propagation factors of standard and elegant Laguerre Gaussian beams in non-Kolmogorov turbulence

Analytical formulae are derived for the propagation factors (M2-factors) of standard Laguerre Gaussian (SLG) beam and elegant Laguerre Gaussian (ELG) beam in non-Kolmogorov turbulence based on the extended Huygens-Fresnel principle and second order moments of the Wigner distribution function. The M2-factors of SLG beam and ELG beam in non-Kolmogorov turbulence have been discussed numerically and comparatively. It is shown that the relative M2-factors of ELG beam are more affected by the turbulence and keep the better beam quality in comparison with that of SLG beam. Furthermore, the normalized M2-factors of SLG beam and ELG beam with higher orders, longer wavelength, larger waist width, larger inner scale of turbulence and the generalized exponent parameter, smaller outer scale of turbulence and smaller the generalized structure parameter are less affected by the non-Kolmogorov turbulence.