Laser beam self-focusing in the atmosphere

The authors propose to exploit a self-focusing effect in the atmosphere to assist delivering powerful laser beams. Usually, for beams with power exceeding the critical power for self-focusing, uncontrolled beam filamentation and beam break up takes place. In this work the authors demonstrate that when the self-focusing length is comparable with the atmosphere height, the catastrophic self-focusing can be greatly suppressed and a smooth compression of the whole beam is possible. To illustrate the idea, without loss of generality the authors consider a laser beam propagating vertically through the Earth's atmosphere from space to ground.