Effective radius of curvature of Hermite–Gaussian beams propagating through non-Kolmogorov turbulence

By using the extended Huygens–Fresnel principle and non-Kolmogorov spectrum, the analytical expression for the effective radius of curvature of Hermite–Gaussian (H–G) beams propagating through non-Kolmogorov turbulence is derived. It is shown that the effective radius of curvature of H–G beams in non-Kolmogorov turbulence depends on the generalized exponent parameter α, inner scale l0, outer scale L0, and propagation distance z. The effective radius of curvature of H–G beams increases with decreasing outer scale L0 for 3.6 < α < 4 and the increasing inner scale l0, but dose not monotonously vary with increasing exponent parameter α and propagation distance z. The results are interpreted physically.