Effective Rayleigh range of Gaussian array beams propagating through atmospheric turbulence

Abstract

The analytical expressions for the effective Rayleigh range z R of Gaussian array beams in turbulence for both coherent and incoherent combinations are derived. It is shown that z R of Gaussian array beams propagating through atmospheric turbulence depends on the strength of turbulence, the array beam parameters and the type of beam combination. For the coherent combination z R decreases due to turbulence. However, for the incoherent combination there exists a maximum of z R as the strength of turbulence varies. The z R of coherently combined Gaussian array beams is larger than that of incoherently combined Gaussian array beams, but for the coherent combination case z R is more sensitive to turbulence than that for the incoherent combination case. The larger the beam number is, the longer z R is, and the more z R is affected by turbulence. For the coherent combination z R is not monotonic versus the relative beam separation distance, and the effect of turbulence on z R is appreciable within a certain range of the relative beam separation distance.