Modeling and Simulation of High-Energy Laser Propagation for High-Speed Moving Targets with Coupled Linear Attenuation, Turbulence, and Thermal Blooming

Accurately predicting high-energy laser propagation toward fast-moving aerial targets is not straightforward, since the slant range, elevation angle, atmospheric path, accumulated turbulence, and thermal blooming all change along with target motion. Because of this coupled evolution, fixed-path or quasi-static models can hardly describe, in a complete way, the time-varying loss of beam transmission and the weakening of energy concentration. To address this problem, this paper builds on established wave-optics propagation methods to develop a dynamic multi-physics framework for high-speed moving-target engagements. The central idea is to rebuild the propagation environment at every time step according to the instantaneous target position so that the optical path can be linked with height-dependent extinction, refractive-index structure, and absorption profiles; meanwhile, relative motion is represented as an effective transverse sweeping velocity, which helps reduce the accumulation effect of thermal blooming. Based on a unified split-step Fourier method, the model combines Beer–Lambert path attenuation, Kolmogorov-spectrum multilayer phase screens, and thermal-blooming phase modulation, yielding time-resolved indicators such as transmittance, received power, peak irradiance, Strehl ratio, scintillation index, pointing error, and beam-quality factor. Simulation results show that, in a 500 m static horizontal path, the attenuation module reduces to the Beer–Lambert solution, with the maximum relative error kept below 10−14; the turbulence phase-screen implementation is validated against the absolute Kolmogorov prediction. Over the resolved inertial interval, the ensemble-averaged structure function yields a fitted exponent pfit=1.671 (theoretical: 5/3=1.667) and a relative normalization error of 2.5%, confirming that the generated screens reproduce both the Kolmogorov scaling and the prescribed turbulence strength. For a 1.064 μm, 2 kW Gaussian beam propagating over a 50 s trajectory of about 8 km, when the target speed increases from 0 to 300 m/s, the thermal-blooming-related beam-quality factor decreases from roughly 1.8 to 1.2, which indicates that dynamic geometry, turbulence, attenuation, and thermal blooming need to be considered together when evaluating laser propagation performance.