Objective  Satellite-ground laser communication has the potential for high-bandwidth communication, but atmospheric turbulence can significantly affect the capabilities of communication systems. Outdoor experiments of satellite-ground communication systems are expensive and difficult to reproduce. Most of the existing numerical simulations are based on horizontal uniform paths, and are not suitable for turbulence paths of non-uniform satellite-ground links. In order to evaluate the impact of turbulence on communication systems, it is very important to develop numerical simulations suitable for satellite-ground links. In numerical simulation, simulating with too many phase screens will increase the complexity of the system. Therefore, it is necessary to develop a simple and reliable numerical simulation model for ground-satellite or satellite-ground turbulence path.

  Methods   The phase screens under the Kolmogorov spectrum and the non-Kolmogorov spectrum are simulated by Fourier inversion method, and the subharmonic compensation method is used to compensate the phase screens. By calculating the constraints of the numerical simulation, a three-layer transmission simulation model is proposed. In order to verify the model, the laser transmission under the traditional Kolmogorov turbulence spectrum model with 2, 3, 6, 11 and 21 layers is simulated on the basis of the split-step method.

  Results and Discussions  Simulations of phase screens under the Kolmogorov spectrum and the non-Kolmogorov spectrum show that the spectral index has a great influence on the phase screen simulation (Fig.4-5). Different spectral indices have different requirements for subharmonic compensation (Fig.6). The mutual coherence factor of the optical field on the observation surface is calculated, and compared with the theoretical value (Fig.7). The mean square error was used to measure the distortion between simulation and theory for different layers of phase screens (Tab.2). It is found that the three-layer model can ensure the accuracy of transmission and reduce the complexity of the system. The changes in the amplitude profile of Gaussian beam (Fig.11) and the changes in the coherence of the received beam under different turbulence spectrum models (Kolmogorov spectrum and non-Kolmogorov spectrum) (Fig.12) are analyzed, the simulation results show that under the same atmospheric conditions, the Gaussian beam in the non-Kolmogorov spectrum will produce obvious amplitude attenuation and beam spread, and the coherence of the optical field at the observation plane will decrease faster.

  Conclusions  In this study, a simple and reliable numerical simulation model for ground-satellite turbulence path system is designed. In this model, the turbulent path is divided into three layers, and each layer is described by different spectral indices according to the characteristics of atmospheric turbulence. The mutual coherence factors were calculated and compared with the theoretical value under the traditional Kolmogorov spectrum with 2, 3, 6, 11 and 21 phase screens. The feasibility of the three-layer transmission model was verified, the proposed model can ensure the simulation accuracy and the efficiency of computer simulation. Based on the proposed three-layer transmission model, the transmission process of the traditional Kolmogorov spectrum and the non-Kolmogorov spectrum with the spectral index varying with the height are simulated, and the changes of the optical amplitude and the observation plane coherence are compared between the two. The results show that under the same atmospheric conditions, the Kolmogorov spectrum in the near-surface region is basically consistent with the results of the non-Kolmogorov spectrum, while with the increase of transmission distance, the Gaussian beam uplink will generate obvious amplitude attenuation and beam spread in the non-Kolmogorov spectrum. The coherence of the light field on the observation surface decrease faster at the same time. The proposed simulation model can be used to evaluate the optical transmission characteristics of the ground-satellite uplink under the influence of complex atmospheric turbulence with fewer phase screens and simulation time, which provides convenience for predicting the expected wavefront behavior at the aperture of the satellite optical receiver.