Long- and short-term average intensity for multi-Gaussian beam with a common axis in turbulence

With the help of the extended Huygens-Fresnel principle and the short-term mutual coherence function, the analytical formula of short-term average intensity for multi-Gaussian beam (MGB) in the turbulent atmosphere has been derived. The intensity in the absence of turbulence and the long-term average intensity in turbulence can both also be expressed in this formula. As special cases, comparisons among short-term average intensity, long-term average intensity, and the intensity in the absence of turbulence for flat topped beam and annular beam are carried out. The effects of the order of MGB, propagation distance and aperture radius on beam spreading are analysed and discussed in detail.