Propagation of Coherently Combined Beams in turbulent atmosphere: analytical approach

The performance of laser weapon system based on Coherent Beam Combining (CBC) depends on its propagation properties in atmosphere. The appropriate semi-analytical model based on partial coherent beam combination for assumed coherence coefficients between beams in CBC lattice was developed. To simulate atmospheric turbulences the Kolmogorov-Fried model of partial coherence and Hufnagel-Valley model of C-n(2) dependence on atmosphere parameters were implemented. The approximated formula on CBC performance in dependence on Fried radius was proposed. The results of CBC modeling were compared to known analytical solutions of Gaussian beam propagation in turbulent atmosphere. The dependence of CBC performance on C-n(2) parameter, elevation angle and range was analyzed. The general conclusion is that application of CBC has not practical sense for propagation on medium and long ranges without effective adaptive optics system.