Laser Beam Self-Focusing in the Atmosphere

We propose to exploit a self-focusing effect in the atmosphere to assist delivering powerful laser beams from orbit to the ground. We demonstrate through numerical modeling that when the self-focusing length is comparable with the atmosphere height the spot size on the ground can be reduced well below the diffraction limits without beam quality degradation. The density variation suppresses beam filamentation and provides the self-focusing of the beam as a whole. The use of light self-focusing in the atmosphere can greatly relax the requirements for the orbital optics and ground receivers.

Figure 1

Beam intensity distribution on the ground for $R_0=1\mathrm{m}$, $C_0=15.7$: $P/P_{\mathrm{cr}}=1.0$ (red line), $P/P_{\mathrm{cr}}=1.29$ (green line), $P/P_{\mathrm{cr}}=1.66$ (blue line). The black line corresponds to the linear diffraction.

Figure 2

The beam radius at the ground versus power for the mirror radius. $R_0=1\mathrm{m}$, $C_0=15.7$ (red line) and $R_0=0.5\mathrm{m}$, $C_0=3.9$ (green line) and $R_0=0.357\mathrm{m}$, $C_0=1$ (blue line).

Figure 3

Logarithm of the field intensity $\ln I$ versus $r^2$ for $R_0=1\mathrm{m}$, $C_0=15.7$: $P/P_{\mathrm{cr}}=0.55$ (black line), $P/P_{\mathrm{cr}}=1.0$ (green line), $P/P_{\mathrm{cr}}=1.29$ (blue line), $P/P_{\mathrm{cr}}=2.0$ (red line).

Figure 4

The beam radius versus distance $z$ for mirror radius $R_0=1.5\mathrm{m}$, $C_0=35.3$ (blue line) and $R_0=1\mathrm{m}$, $C_0=15.7$ (black line) and $R_0=0.5\mathrm{m}$, $C_0=3.93$ (red line) and $R_0=0.357\mathrm{m}$, $C_0=1$ (green line).

Figure 5

The dependence $D^4(\frac{P}{P_{\mathrm{cr}}}-1)$ on power $P/P_{\mathrm{cr}}$ required to start the filamentation.