In practice, the beam produced by a high-energy laser is more nearly elliptical in its cross section, such as a semiconductor laser and a spectral beam combining system. When a high-energy laser propagates in the atmosphere, a fraction of the laser power is absorbed by the atmosphere along the propagation path. The absorbed power first heats the air and alters the refraction index of the path, and then causes laser distortion and divergence. This self-induced effect is called thermal blooming. Moreover, the energy transmission efficiency of a high-energy laser is severely limited by the thermal blooming effect. Thermal blooming depends on the distribution of the laser beam and the state of the atmosphere. Until now, the effect of thermal blooming on an elliptical Gaussian beam (EGB) propagating in the atmosphere has not been reported. In this paper, the beam quality optimization of an EGB under wind-dominated thermal blooming is studied analytically and numerically. The results obtained in this paper are useful for the applications of high-energy lasers propagating in the atmosphere.

Thermal blooming of a laser beam propagating through atmosphere can be described by the paraxial wave equation and the hydrodynamic equation. When the diffraction effect is neglected under the geometric optics approach, the intensity expression for steady-state thermal blooming and the distortion parameter of an EGB propagating in the atmosphere are respectively derived, and their correctness is proved. Besides, numerical simulation is very useful to study thermal blooming. We design 4D computer code of the time-dependent atmospheric propagation of a focused EGB by using the multi-phase screen method and the finite difference method. A grid size of 512×512 is used. The numerical calculation results remain almost constant when the number of grid size increases. The transient-state thermal blooming and steady-state thermal blooming are investigated in this paper.

In this paper, the intensity expressions for steady-state thermal blooming and the distortion parameter of an EGB propagating in the atmosphere are derived, respectively. It is proved that the distortion parameter (Eq. (4)) we obtained is valid. In the atmosphere, as the beam width in the windward direction of the source plane is large (the same spot area), the distortion parameter is small and the thermal blooming effect on the EGB is weak (Figs.1 and 2). The relative peak intensity of an EGB and its displacement at the target are discussed. As the beam width in the windward direction of the source plane is large, the relative peak intensity at the target is large, and its displacement is small (Fig. 3). The 4D computer code of the time-dependent atmospheric propagation of a focused EGB is designed. It is found that in free space, the long and short axes of an EGB are interchanged at the target. In particular, in free space, the focused EGBs with the same spot areas return to the symmetric Gaussian beam at a certain propagation distance, whose formula is derived (Eq. (13)). However, in the atmosphere, different EGBs do not become symmetrical at a certain propagation distance because of thermal blooming (Fig. 5). Due to the astigmatism of an EGB, the influence of atmospheric thermal blooming on its propagation depends on the wind direction. The thermal blooming can be weakened by making the short axis of a focused EGB along the general wind direction. As the beam width in the windward direction of the source plane is large (the same spot area), the thermal blooming effect on a focused EGB is weak, which results in a better symmetrical spot (Fig. 6) and a small focal shift (Fig. 8). The time required to achieve the steady-state thermal blooming for a focused EGB is proportional to the beam width along the wind direction in the source plane (Fig.10).

In this paper, the beam quality optimization of an elliptical Gaussian beam under wind-dominated thermal blooming is studied analytically and numerically. The expression of distortion parameter of an elliptical Gaussian beam propagating in the atmosphere is derived, and its correctness is proved. Due to the astigmatism of an elliptical Gaussian beam, the influence of atmospheric thermal blooming on its propagation depends on the wind direction. Thermal blooming can be weakened by making the short axis of a focused EGB along the general wind direction. In the atmosphere, as the beam width in the windward direction of the source plane is large (the same spot area), the thermal blooming effect on the EGB is weak, which results in a better symmetrical spot and energy focus ability at the target, i.e. better beam quality at the target. The time required to achieve steady-state thermal blooming for a focused elliptical Gaussian beam is proportional to the beam width along the wind direction in the source plane.