In this paper, the effect of thermal blooming of an Airy beam propagating through the atmosphere is examined, and the effect of atmospheric turbulence is not considered. The changes of the intensity distribution, the centroid position and the mean-squared beam width of an Airy beam propagating through the atmosphere are studied by using the four-dimensional (4D) computer code of the time-dependent propagation of Airy beams through the atmosphere. It is shown that an Airy beam can’t retain its shape and the structure when the Airy beam propagates through the atmosphere due to thermal blooming except for the short propagation distance, or the short time, or the low beam power. The thermal blooming results in a central dip of the center lobe, and causes the center lobe to spread and decrease. In contrast with the center lobe, the side lobes are less affected by thermal blooming, such that the intensity maximum of the side lobe may be larger than that of the center lobe. However, the cross wind can reduce the effect of thermal blooming. When there exists the cross wind velocity vx in x direction, the dependence of centroid position in x direction on vx is not monotonic, and there exists a minimum, but the centroid position in y direction is nearly independent of vx.
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