The effective radius of curvature of partially coherent Hermite–Gaussian linear array beams passing through non-Kolmogorov turbulence

Abstract

Based on the extended Huygens–Fresnel principle, the definition of second-order moments of the Wigner distribution function (WDF) and the non-Kolmogorov spectrum, analytical expressions for the effective radius of curvature of partially coherent Hermite–Gaussian (PCHG) linear array beams propagating through non-Kolmogorov turbulence are derived, where the influence of non-Kolmogorov turbulent atmosphere and the array beam parameters on the effective radius of curvature is stressed, and both coherent and incoherent combination cases are taken into consideration. The results show that the effective radius of curvature of PCHG linear array beams varies non-monotonously with increasing generalized exponent parameter α and reaches a minimum at α =3.11. The effective radius of curvature of PCHG linear array beams increases with increasing beam number, but varies non-monotonically with increasing relative beam separation x0′ for x0′≤1 and increases monotonically as x0′ increases for x0′>1. Moreover, the variation behavior of the effective radius of curvature with the generalized exponent parameter, inner scale and outer scale of the turbulence is similar but is different with the relative beam separation for coherent and incoherent combination cases.