Thermal blooming effect and the scaling laws of partial spatially coherent beam array propagating through the atmosphere

The thermal blooming effect and the scaling laws of partially coherent beam (PCB) array propagating in the atmosphere are studied. The four-dimensional (4D) computer code of time-dependent propagation to simulate PCB array through the turbulent atmosphere is designed. Based on numerical simulation, the propagation properties of PCB array are investigated in detail. It is shown that, as the spatial coherence parameter β decreases, the relative beam width increases and the thermal blooming effect becomes more severe. However, the change of the energy Strehl ratio (SRE) versus spatial coherence parameter β is not monotonic because the energy is concentrated on the main lobe for fully coherent beam array. Besides, the scaling laws to estimate the thermal blooming effects of PCB array are investigated. The modified expression of the distortion parameter Nd of a focused PCB array is derived, which is efficient to evaluate the strength of the thermal blooming effects.