Turbulence distance for laser beams propagating through non-Kolmogorov turbulence

Based on the second-order moments and the non-Kolmogorov turbulence spectrum, the general analytical expression for the turbulence distance of laser beams propagating through non-Kolmogorov turbulence is derived, which depends on the non-Kolmogorov turbulence parameters including the generalized exponent parameter α, inner scale l(0), and outer scale L(0) and the initial second-order moments of the beams at the plane of z=0. Taking the partially coherent Hermite-Gaussian linear array (PCHGLA) beam as an illustrative example, the effects of non-Kolmogorov turbulence and array parameters on the turbulence distance are discussed in detail. The results show that the turbulence distance z(Mx)(α) of PCHGLA beams through non-Kolmogorov turbulence first decreases to a dip and then increases with increasing α, and the value of z(Mx)(α) increases with increasing beam number and beam order and decreasing coherence parameter, meaning less influence of non-Kolmogorov turbulence on partially coherent array beams than that of fully coherent array beams and a single partially coherent beam. However, the value of z(Mx)(α) for PCHGLA beams first increases nonmonotonically with the increasing of the relative beam separation x0' for x0'≤1 and increases monotonically as x0' increases for x0'>1. Moreover, the variation behavior of the turbulence distance with the generalized exponent parameter, inner scale, and outer scale of the turbulence and the beam number is similar, but different with the relative beam separation for coherent and incoherent combination cases.