Jinghui Zhang

Slant-path propagation of laser beams through atmospheric turbulence produces beam spreading and jitter that must be rapidly predicted for system design and performance assessment. Existing scaling laws are mainly derived for horizontal paths and single-parameter variations, which limits their accuracy and applicability to realistic engagement geometries. Here, we construct a comprehensive wave-optics database for 1.064 μm truncated Gaussian beams with a 1 m aperture by traversing initial beam quality factor β₀, propagation distance L, elevation angle θ, turbulence strength Cₙ², and tracking jitter. From 46,800 turbulence-only cases, we extract the 63.2% encircled-power expansion factor and quantify the coupled influence of β₀, L, and θ on the turbulence term coefficient A in the scaling expression. A compact 3–10–1 feedforward neural network is trained to map (β₀, L, θ) to A, achieving a coefficient of determination R² = 0.948. Additional simulations without turbulence show that the jitter term coefficient B is nearly invariant over the considered parameter range, with an average value B = 3.69. Combining these results yields a unified scaling law for linear beam spreading on horizontal and slant paths. Comparison with full-wave-optics simulations demonstrates that the proposed law reproduces horizontal-path results and significantly reduces prediction errors at θ = 60° relative to existing models, providing an efficient tool for beam-quality prediction and performance evaluation in atmospheric laser propagation.

Numerical simulations were performed to rapidly predict and evaluate laser beam expansion caused by linear atmospheric transmission effects, such as turbulence and jitter, thereby enhancing the accuracy of the scaling law. Simulation results indicate that the turbulence term coefficient in the beam expansion calibration expression correlates linearly with the initial beam mass and inversely with the transmission distance. By fitting a nonlinear surface, the relationship between the turbulence term coefficient, initial beam mass, and transmission distance was established. Additionally, under turbulence-free conditions, a calibration expression relating initial beam mass to transmission distance was derived. The tracking jitter-term coefficient was determined to be 3.69, effectively characterizing beam expansion due to system jitter error. Based on simulation outcomes, a scaling law model for beam expansion induced by linear atmospheric transmission effects was clearly established. The model closely matched the simulation data, with a root mean square error (RMSE) of 3.88. Compared with existing scaling law simulations, the proposed calibration expression significantly enhances the accuracy in predicting and evaluating beam expansion caused by linear atmospheric transmission effects. It also provides a more precise characterization of variations in beam expansion during laser transmission.

Adaptive optics (AO) is an effective method to compensate the wavefront distortion caused by atmospheric turbulence and system distortion. The accuracy and speed of aberration restoration are important factors affecting the performance of adaptive optics correction. In recent years, an AO correction method based on a convolutional neural network (CNN) has been proposed for the non-iterative extraction of light intensity image features and recovery of phase information. This method can directly predict the Zernike coefficient of the wavefront from the measured light intensity image and effectively improve the real-time correction ability of the AO system. In this paper, a turbulence aberration restoration based on two frames of a light intensity image using GoogLeNet is established. Three depth scales of GoogLeNet and different amounts of data training are tested to verify the accuracy of Zernike phase difference restoration at different turbulence intensities. The results show that the training of small data sets easily overfits the data, while the training performance of large data sets is more stable and requires a deeper network, which is conducive to improving the accuracy of turbulence aberration restoration. The restoration effect of third-order to seventh-order aberrations is significant under different turbulence intensities. With the increase in the Zernike coefficient, the error increases gradually. However, there are valley points lower than the previous growth for the 10th-, 15th-, 16th-, 21st-, 28th- and 29th-order aberrations. For higher-order aberrations, the greater the turbulence intensity, the greater the restoration error. The research content of this paper can provide a network design reference for turbulence aberration restoration based on deep learning.

The decay of OAM entanglement in non-Kolmogorov turbulence has been numerically evaluated. In this work, we explore the evolution of OAM entanglement with higher-order OAM mode in the weak scintillation regime. In particular, the results of the numerical evaluation show that the OAM entanglement state with higher value of the azimuthal mode and larger radial quantum number survives over a longer distance. Meanwhile, the beam parameters and turbulence parameters usually have significant influences on OAM entanglement. In addition, it is demonstrated that the effect of turbulence on the OAM entanglement is the most serious when the generalized exponent is around 3.07.

The turbulence effect, thermal blooming effect, laser beam aberration, platform jitter, and other effects in the process of high energy laser propagation in the atmosphere will cause serious degradation of laser beam quality, which will have a negative impact on the actual application of laser propagation engineering. It is important in the engineering application of high-energy laser propagation to evaluate the far-field intensity distribution quickly. Based on the optical transfer function (OTF) theory of imaging system, the propagation process of high-energy lasers is modeled as the imaging process of point source. By using the convolution of point spread function (PSF) of jitter, turbulence, thermal blooming, and aberration of emission system, fast calculation of the far-field intensity distribution of high energy laser is realized. The calculation results are compared with those obtained by the 4D wave optics simulation program in different propagation scenarios. The results show that the calculated facula distribution and encircled energy of this method are in good agreement with the simulation results of wave optics, which can realize the fast and accurate evaluation of the far-field intensity distribution of high-energy laser propagation and provide a reference for practical engineering application.