Propagation of multiple Bessel Gaussian beams through weak turbulence

The average intensity of the multiple Bessel Gaussian beams (mBGBs), which comprise the summation of the Bessel function and a Gaussian function, are investigated based on the extended Huygens-Fresnel principle and the Rytov theory. The weak turbulence just leads the mBGBs diverge and has no influence on the angular distribution of both the mean field and the average intensity. Therefore, the angular distribution of the average intensity depends on the average in the free space. When the order difference between any two sub beams of the mBGBs is the integer multiple of the minimum order difference, there are the symmetric side lobes of the average intensity distribution and its angular frequency is equal to the minimum order difference. Moreover, for the mBGBs with two sub beams, the initial phase change of the different sub beams could make the average intensity distribution rotate in opposite direction. This paper provides the theoretical basis for the investigation of the mBGBs propagation and the application of the sub beam detection and the beam multiplexing.