Comparative Study of Two Definitions of the Turbulent Distance for Laser Beams Propagating Through Non-Kolmogorov Atmospheric Turbulence

Using two definitions of the turbulent distance to characterize the laser beam propagation through atmospheric turbulence, we derive a general analytical expression for the beam spread η depending on the turbulence parameter T(α) with the generalized exponent α and on the initial second-order beam moments in the z = 0 plane. Larger values of η correspond to a larger influence of atmospheric turbulence on the laser beam. We subsequently apply the analytical expression of η to a partially coherent Hermite–Gaussian beam propagating through non-Kolmogorov turbulence and illustrate the properties of η by numerical examples. The results show that the η values first increase, reach their maximum for a generalized exponent α ≈ 3.11, and then decrease with increase in α. Also η decreases with increasing beam order and wavelength, as well as with increasing values of the generalized refractive-index structural turbulence parameter, beam waist width, and coherence parameter.