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.

► Expression for M2-factor of the radial GSM beam array in non-Kolmogorov turbulence is derived.
► An optimum ring radius, corresponding to a minimum M2-factor, is obtained and explained in detail.
► Optimizing effect of r0 on M2-factor has great dependence on α   and C˜n2.
► Tradeoff between superposition of the intensity and superposition of CSDF should be considered.