The Rayleigh range of elegant Hermite–Gaussian beams in non-Kolmogorov turbulence

Based on the two types of definitions for the Rayleigh range, and in consideration of the effect of non-Kolmogorov turbulence, analytical expressions for the Rayleigh range of elegant Hermite–Gaussian (EHG) beams passing through non-Kolmogorov turbulent atmosphere defined by the mean-squared beam width and by the effective radius of curvature are derived and compared, where the effect of non-Kolmogorov turbulence on the Rayleigh range is stressed upon. It is shown that the Rayleigh range in non-Kolmogorov turbulence varies non-monotonically with increasing generalized exponent parameter α for beams with shorter wavelength, lower beam order and larger beam waist. With decreasing inner scale of turbulence for 3<α<4 and increasing outer scale of turbulence for 3.8≤α<4, the Rayleigh range defined by the mean-squared beam width decreases, whereas the Rayleigh range defined by the effective radius of curvature increases. Usually, the two types of Rayleigh range in turbulence are unequal, and the difference between them is relatively smaller in the region 3.8≤α<4.

► The Rayleigh range of laser beams passing in non-Kolmogorov turbulence is studied. ► The effect of non-Kolmogorov turbulence on the Rayleigh range is stressed. ► Usually, zR(α  ) and z′R(α)z′R(α) are unequal, but the difference between them is smaller in the region 3.8≤α<4.