Effective Rayleigh range of Gaussian array beams propagating through atmospheric turbulence

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