为了探究矢量椭圆多高斯-谢尔模(EEMGSM)光束的传输特性, 基于广义惠更斯-菲涅耳原理和维格纳分布函数的二阶矩理论, 理论推导了EEMGSM光束在各向异性湍流中传输的质量因子解析表达式。通过数值计算和分析, 探究了初始偏振度、初始相干度、腰宽、波长和湍流结构常数等与质量因子的变化规律。结果表明,EEMGSM光束的质量因子随着阶数、波长和腰宽的增大而减小; 随着初始相干度和湍流结构常数的减小而减小; 在相同条件下, 具有大初始偏振度的EEMGSM光束的光束质量受各向异性的影响小于具有小初始偏振度的EEMGSM光束的光束质量; 且在相同条件下, EEMGSM光束的质量因子比标量椭圆高斯-谢尔模(EGSM)光束小, 即EEMGSM光束具有缓解各向异性湍流影响的优点。所得结论对于自由空间光通信的研究具有一定的理论参考价值。

In order to investigate the propagation characteristics of electromagnetic elliptical multi-Gaussian-Schell mode (EEMGSM) beams, based on the generalized Huygens-Fresnel principle and the second moment theory of Wigner distribution function, the analytical expression of M2 factor of EEMGSM beams propagating in anisotropic turbulence was derived theoretically. Through numerical calculation and analysis, the variations of initial polarization, initial coherence, waist width, wavelength and turbulence structure constant with M2 factor were investigated. The results show that, M2 factor of EEMGSM beam decreases with the increase of order, wavelength and waist width. It decreases with the decrease of initial coherence and turbulence structure constant. Under the same conditions, the beam quality of EEMGSM beams with large initial polarization is less affected by anisotropy than that of EEMGSM beams with small initial polarization. Under the same conditions, the quality factor of EEMGSM beam is smaller than that of scalar elliptical Gaussian-Schell mode (EGSM) beam. EEMGSM beam has the advantage of alleviating the influence of anisotropic turbulence. The study has certain theoretical reference value for the research of free space optical communication.