Numerical simulation of laser beam propagation in three-dimensional random media: beam splitting and patch formation

The results of numerical simulations of far-field, focused beam propagation in a homogeneous, Kolmogorov field are compared with theoretical predictions. It is shown that the spot structure at the focal plane depends on two parameters: the diffraction parameter ηD, which is defined as the ratio of the Fresnel length 2Z/kD 0 to the initial beam diameter D 0, and an analogous turbulence parameter ηtu=2Z/k(ρ0 LT)2, where Z is the focal distance, k is the wavenumber in vacuum, and ρ0 LTis the long-term far-field coherence length. For ηtu≫1 the beam is broken into multiple patches of typical size that is smaller than the transmitter diffraction scale. It is found that patches are also formed when ηtu≤1 provided the initial diameter D 0 is much bigger than ρ0 LT. The structure of the spot when ηtu≪1 depends on the value of ηD. For ηD≫1, the beam intensity pattern can be very distorted, however the spot is not dispersed.