Focusability of coherently combined beams propagating downwards in the turbulent atmosphere

The focusability of coherently combined beams (CCBs) propagating from orbit through the turbulent atmosphere to the ground is studied, where the diffraction, self-focusing and turbulence effects are considered. It is shown that the spot size on the ground of CCBs is much smaller than that of incoherently combined beams (ICBs). The analytical expression of the B integral of CCBs propagating in the turbulent atmosphere is derived, and an effective design rule for the CCB power transportation without filamentation is presented. It is found that the focusability of CCBs propagating in the turbulent atmosphere can be improved by the gradient power distribution method, and the spot size on the ground can always be reduced below the diffraction limit. Furthermore, the optimal gradient power distribution to reach the highest focusability on the ground without filamentation is presented.