Objective Free-space optical communication has attracted wide attention due to its advantages, such as large information capacity, high transmission rate, strong anti-interference ability, small system size and low power consumption. Being an important part of the free-space optical communication, atmospheric laser communication is facing technical bottlenecks, such as unsatisfactory reception efficiencies and large energy jitters. Fiber coupling can effectively solve these technical bottlenecks. Coupling with optical fiber is the most common method; however, multi-mode fiber limits the usage of coherent communication reception. Using a single-mode fiber will definitely reduce the coupling efficiency under atmospheric turbulence conditions. Recently, pre-amplification of few-mode fiber or few-mode multi-core fiber has become essential to improve the reception performance of atmospheric laser communication. However, a turbulent atmosphere will have effects, such as spot distortion, arrival angle fluctuation, beam expansion and light intensity flicker. These effects seriously affect the coupling efficiency between the space light and few-mode fiber. In this study, we first studied the relationship between few-mode fiber parameters, turbulence intensity, tracking error and the coupling efficiency of space light to the few-mode fiber under the conditions of atmospheric turbulence and tracking error. Then, we established a coupling model of the space light to the few-mode fiber under the conditions of atmospheric turbulence and tracking error. Finally, we established an experimental platform under this condition to verify the coupling performance of the few-mode fiber. We hope our results can provide a technical reference for the design of the atmospheric laser communication pre-amplifiers.

Methods Based on the coupling model of space light to few-mode fiber, an approximate calculation of step-type few-mode fiber optical field was performed using the Laguerre-Gaussian (LG) distribution and LG beam as the free-space light. We obtained the optical field distribution of the LP and LG modes. According to the acquisition tracking pointing model and Von Karman turbulence spectrum model, we established the coupling model by superimposing the optical field distribution of the LP and LG modes under atmospheric turbulence and tracking error. We studied the relationship between the coupling efficiency of the few-mode fiber and the intensity of atmospheric turbulence, the angle of aiming error under different fiber V values. A self-made turbulence simulator was used to simulate the atmospheric turbulence of different intensities and experimentally study the relationship between the coupling efficiency and fiber V values under atmospheric turbulence.

Results and Discussions We obtained the relationship between the coupling efficiency and the V value of the fiber under different atmospheric turbulence intensities and different tracking error angles (Fig. 2, Fig. 5) using simulation. The coupling efficiency increases with the increase of the V value. When Cn2=0, as the V value increases to 4.85, the coupling efficiency reaches a maximum of 0.98, and any further increase in the V value decreases the coupling efficiency. This is because as the fiber V value increases, the number of spatial modes supported by the fiber also increase. Thus, a large number of modes cause crosstalk between modes. Therefore, there is an optimal V value to maximize the coupling efficiency of space light to the few-mode fiber, and as the turbulence intensity increases, the optimal V value gradually increases. We also obtained the relationship between the coupling efficiency and the V value of few-fiber under different atmospheric turbulence and tracking error angles (Figs.6--9). In the traditional free-space optical communication system, the tracking error angle is 3 μrad. Currently, under the weak turbulence of Cn2=10 ^-15 and Cn2=5×10 ^-15, the best coupling efficiencies can be obtained when the fiber V value is 5, which are 0.74 and 0.732, respectively; under the strong turbulence of Cn2=10 ^-14 and Cn2=5×10 ^-14, the best coupling efficiencies can be obtained when the fiber V value is 5.2, which are 0.715 and 0.7, respectively. The coupling experiment of space light to few-mode fibers under simulated turbulence has been completed, and the results are shown in Table 1 and Fig.13, which is consistent with the simulation results.

Conclusions We have established a coupling model of space light to the few-mode fiber under the conditions of atmospheric turbulence and tracking error, based on the acquisition tracking pointing model and the Von Karman turbulence spectrum model. This study shows the optimal V value of few-mode fiber that makes the coupling efficiency the best under the influence of atmospheric turbulence, non-linear effects and crosstalk between modes. As the V value of the fiber increases, its ability to resist tracking error also increases. Considering that the tracking error is 3 μrad, for Cn2=5×10 ^-15and Cn2=10 ^-15, the fiber V value is 5 and the best coupling efficiencies are 0.74 and 0.732; for Cn2=5×10 ^-14and Cn2=10 ^-14, the fiber V value is 5.2 and the best coupling efficiencies are 0.715 and 0.7. The coupling experiment of the space light to the few-mode fibers under simulated turbulence has been completed, the coupling efficiency of the experiment is consistent with the trend of the simulation results. The feasibility of the simulation results in practical applications is verified, providing a reference for the research of free-space optical communication.