Beam propagation factor of radial Gaussian-Schell model beam array in non-Kolmogorov turbulence

The analytical expression for the beam propagation factor (M²-factor) of a radial Gaussian-Schell model (GSM) beam array propagating in non-Kolmogorov turbulence is derived. The influences of beam number, ring radius and generalized exponent on the M²-factor are investigated. The results indicate that the M²-factor has great dependence on the generalized exponent and the beam number. Moreover, there is an optimum ring radius, which leads to a minimum M²-factor and increases with increase in beam number. Further, the M²-factor for the superposition of the intensity is larger than that for the superposition of the cross-spectral density function (CSDF). However, the M²-factor for the superposition of the intensity is less sensitive to the turbulence than that for the superposition of the CSDF.