Laser beam self-focusing in the atmosphere

The abundance of solar energy outside the Earth makes attractive the electricity production in space. Initial proposals have been based on the energy transportation by microwaves. However, recent progress in laser science has stimulated research into the feasibility of using laser-based orbit systems in which laser radiation is utilyzed for transport of converted solar energy to the ground [1, 2]. Note that for even for diffraction limited beams one must have precision focusing optics in the space and a large ground-based receiver to facilitate efficient power transport and collection. Here we 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 we 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 we consider a laser beam propagating vertically through the earth's atmosphere from space to ground. The nonlinear refractive index change is proportional to density variation. Introducing the density at sea level as ρ<inf>0</inf>, the corresponding nonlinear refractive index at an arbitrary height is, n<inf>2</inf>(z)=n<inf>2</inf>(0)ρ/ρ<inf>0</inf>;ρ=ρ<inf>0</inf>e^−z/h. Here the refractive index on the ground is n<inf>2</inf>(0)=5.6×⁻¹⁹ cm²/W. Self-focusing in homogeneous media starts when the beam power exceeds the critical value, P<inf>cr</inf>=0.93λ<inf>0</inf>²/2πn<inf>0</inf>n<inf>2</inf>. The two key parameters we vary in our simulations are the mirror radius and the beam power. Figure 1 shows the intensity distribution on the ground for a mirror radius R<inf>0</inf> = 1m and for several beam powers. One can observe a strong (factor of five) beam compression in comparison with linear propagation without any indication of filamentation. Figure 2 presents results of modelling of the beam radius evolution in the atmosphere for different mirror radii.