Propagation of multi-Gaussian beams in incoherent combination through turbulent atmosphere and their beam quality

Based on the extended Huygens–Fresnel principle, the propagation of M?×?N multi-Gaussian beams in incoherent combination through turbulent atmosphere, and their beam quality are studied. The power in the bucket (PIB), β parameter and strehl ratio (S_R ) are taken as the characteristic parameters of beam quality, and analytical expressions for PIB and S_R are derived. It is shown that multi-Gaussian beams in turbulent atmosphere undergo three stages of evolution with increasing propagation distance z, and turbulence accelerates the evolution of the three stages which multi-Gaussian beams undergo. The turbulence results in a degradation of the beam quality, and multi-Gaussian beams with higher numbers M and N are less sensitive to the effects of turbulence than those with lower M and N.