The influence of thermal blooming on the propagation properties of higher-order mode (HOM) fiber laser array is studied by using the algorithm for simulating the laser beam propagation in the atmosphere. Based on the multiphase screen method and finite-difference method, the four-dimensional (4D) computer code of time-dependent propagation is designed to simulate the propagation of HOM fiber laser array through the atmosphere. In this study, the laser energy focusability of the LP11 mode beam

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... ray is investigated in detail for different beamlet arrangements, transverse wind speed, and the content of LP01 mode under the conditions of thermal blooming. In free space, the focal shape of the LP11 mode beam array depends on the arrangement of the second circle of the initial beam array, whereas the influence of the central beamlets is weak. The number of side lobes can be tailored by changing the arrangement of the beamlets. In contrast, under the conditions of thermal blooming, the central beamlet has a significant effect on focal beam shape. It is demonstrated that the laser energy focusability can be improved by rotating the central beamlet or increasing the transverse wind speed. As the content of the LP01 mode increases, the energy is gradually concentrated from the side lobes to the center lobe. Furthermore, the effects of initial beam array arrangements on the energy focus and focal shape are investigated. The optimal arrangement for obtaining high energy focusability is discussed in detail. These results could provide useful references for applications of the HOM beam array.