Study of SPGD-based phase compensation for atmospheric thermal blooming in the upward transmission of high-energy lasers

Atmospheric thermal blooming (TB) is a critical nonlinear effect that degrades the propagation of high-energy lasers. While adaptive optics (AO) technology can partially mitigate TB-induced phase distortions, the positive feedback between AO correction and TB leads to phase compensation instability (PCI), thereby limiting the performance of the AO system. Under severe TB conditions, traditional phase compensation approaches become ineffective. We developed an enhanced stochastic parallel gradient descent (SPGD) algorithm and integrated it into the TB phase compensation process to identify effective phase compensation solutions. Numerical results show that enhanced SPGD compensation achieves near-diffraction-limited performance over a broad range of thermal distortion numbers ( N D < 1000) and remains free of PCI at very high thermal distortion numbers ( N D < 1600). Mode decomposition of the phase variations during compensation reveals that the enhanced SPGD algorithm predominantly adjusts specific characteristic phase modes. These findings suggest that TB phase compensation should prioritize such modes, as the inclusion of excessively complex modes increases the probability of PCI.