湍流大气中斜程传输部分相干光的光束扩展

运用维格纳分布函数与广义惠更斯菲涅耳原理，推导出部分相干光束在任意折射率起伏功率谱模型的大气湍流中斜程传输时，其束宽传输的一般解析表达式。在此基础上，以部分相干平顶(PCFT)光束为例，给出了PCFT光束在大气湍流中斜程传输的束宽扩展解析表达式。在合肥地区大气折射率结构常数高度分布模式下开展了数值计算和分析，并与水平传输时的结果进行了比较。研究结果表明，光束在斜程传输时的束宽不仅与光束阶数、空间相干度、束腰半径、湍流的强弱和传输距离有关，还与天顶角密切相关。光束的阶数越高，空间相干性越差，天顶角越小，则其束宽扩展受湍流的影响就越小。当天顶角小于60°时，大气湍流对斜程传输光束束宽的影响明显小于水平传输的情况。

Spreading of Partially Coherent Flat-Topped Beams Propagating Along a Slant Path in Turbulent Atmosphere

By using the Wigner distribution function and the generalized Huygens-Fresnel principle, an analytical formula, which is independent on specific spatial power spectrum of the refractive index fluctuations of atmosphere, for beam width of partially coherent beams propagating through atmospheric turbulence along a slant path is derived. Then, taking the partially coherent flat-topped (PCFT) beams as a typical example, the analytical formula for beam width spreading of PCFT beams propagating through atmospheric turbulence along a slant path is given. Consequently, numerical calculations and analysis are carried out by considering the vertical distribution models of atmospheric structure constant of refractive index in Hefei, and the results for a slant path are compared with those for a horizontal path. Research results demonstrate that the beam width is not only related to the beam order, the degree of spatial coherence, the waist radius, the intensity of turbulence and the propagation distance but also closely to the zenith angle. With the higher beam order, the worse spatial coherence of the beam and the smaller zenith angle, the spreading of beam width is less affected by the turbulence. When the zenith angle is less than 60°, the influence of the atmospheric turbulence to the beam width along the slant path is much smaller than that along the horizontal path.