Self-focusing effect on the beam quality of Hermite–Gaussian beams propagating upwards through the inhomogeneous atmosphere

The self-focusing effect on the beam quality of Hermite–Gaussian beams propagating upwards through the inhomogeneous atmosphere is studied. The analytical formula of the beam width is derived, and its validity is confirmed. Furthermore, the analytical formulas of the actual focal length and -factor are also derived. It is found that the self-focusing effect in the inhomogeneous atmosphere results in beam quality degradation. Under the same initial beam width and the same beam power, as the beam order increases, the actual focal length is farther away from the target, and the spot size on the target and the -factor increase; namely, the beam quality degrades further. In addition, it is shown that the beam quality can be improved by the phase compensation.