Beam propagation factor of cosh-Gaussian array beams propagating through atmospheric turbulence

The analytical formula for the beam propagation factor (M-2-factor) of cosh-Gaussian (ChG) array beams propagating through atmospheric turbulence is derived, and the influence of turbulence on the M-2-factor is studied by using the relative M-2-factor. It is shown that the M-2-factor is not a propagation invariant in turbulence, and the turbulence results in an increase of the M-2-factor. For the incoherent combination, the M-2-factor of ChG array beams increases with increasing propagation distance, beam parameter, relative beam separation distance and beam number. For the coherent combination, the M-2-factor of ChG array beams increases with oscillatory behavior as the beam parameter or the relative beam separation distance increases. For the coherent combination the M-2-factor is always smaller than that for the incoherent combination. However, for the incoherent combination the M-2-factor is always less sensitive to turbulence than that for the coherent combination. In particular, the influence of turbulence on the M-2-factor can be reduced by a suitable choice of the relative beam separation distance. With increasing beam number, the M-2-factor becomes more sensitive to turbulence for the coherent combination, while for the incoherent combination the M-2-factor becomes less sensitive to turbulence.