Scaling law for high-energy laser slant-path propagation in a non-Kolmogorov marine atmosphere

Robust scaling laws governing high-energy laser (HEL) slant-path propagation through a non-Kolmogorov marine atmosphere are critical for rapid performance prediction in laser engineering applications. However, the derivation of accurate scaling laws remains highly challenging due to the variable application scenarios and the precision limitations of traditional scaling law models. To address this, we developed a scaling law for Gaussian beam propagation along slant paths in non-Kolmogorov marine environments by introducing the zenith angle dependence. By combining the least-squares method (LSM) and the genetic algorithm (GA) optimization method, the numerical simulation reveals distinct behaviors under independent turbulence and thermal blooming conditions. Although the zenith angle exhibits almost negligible impact on turbulence-induced beam spreading, it introduces nonlinear coupling effects with thermal blooming. To rigorously characterize these effects, we employed a modified root-sum-square (MRSS) model to establish the scaling law on the consideration of the coupling effect of turbulence and thermal blooming. Results indicate that the proposed scaling law achieves remarkable consistency with numerical simulations, with relative deviations constrained below 5.00%. This comprehensive approach not only extends the applicability of scaling laws to previously unexplored marine atmospheric conditions but also establishes what we believe to be a new benchmark for accuracy in laser propagation modeling through its integration of the zenith angle.