Self-focusing effect of annular beams propagating in the atmosphere.
The self-focusing effect of annular beams propagating in the atmosphere to assist delivering powerful laser beams from orbit to the ground is studied in detail. It is found the annular beam is compressed more strongly due to the self-focusing effect as the beam obscure ratio increases. On the other hand, the self-focusing effect between annular, flat-topped and Gaussian beams is compared. It is shown that the self-focusing effect on the annular beam is stronger than that on flat-topped and Gaussian beams. However, the threshold critical power values of annular, flat-topped and Gaussian beams should be in sequence from small to large. Furthermore, the expression of the B integral of annular beams propagating from orbit to the ground in the atmosphere is derived, and the fitting equation related to the B integral of annular beams for maximal compression without filamentation is presented.