Propagation of partially coherent partially phase-locked laser array in turbulent atmosphere

The mechanism for beam quality degradation in recently developed phase locking of high power solid state lasers, which is caused mainly by partially coherent property of element beam and partially phase locking of the laser array, is analyzed in detail. Analytical expression for propagation of partially coherent partially phase-locked laser array in turbulent atmosphere is obtained based on extended Huygens-Fresnel principle. The effect of coherence width, phase error and intensity of turbulence on the beam quality in the target-plane is studied in detail. The tolerance on phase error for laser array with different coherence property is analyzed. It is concluded that the laser array with better coherence is more sensitive to turbulence, and phase control can improve beam quality in the receiving plane only in the case when the element beam has good beam quality and propagates in weak turbulence.