光学学报, 2010, 30 (6): 1542, 网络出版: 2010-06-07
复宗量厄米高斯光束在大气湍流中的传输特性
Propagation Properties of Elegant Hermite-Gaussian Beams in Atmospheric Turbulence
大气光学 传输特性 二阶矩 M2因子 复宗量厄米高斯光束 atmospheric optics propagation properties second moments M2-factor elegant Hermite-Gaussian (EHG) beams
摘要
采用广义惠更斯菲涅耳衍射积分方法和Wigner分布函数的二阶矩定义,推导出在直角坐标系下激光光束经大气湍流传输的远场发散角、束宽以及M2因子的解析表达式,并以复宗量厄米高斯(EHG)光束为例,定量分析了EHG光束在大气湍流中的传输特性。研究表明,光束在大气湍流中传输后的M2因子与入射面上的M2因子、入射面的二阶矩、传输距离、波数以及湍流的影响因子有关;随着在大气湍流中传输距离的增加,EHG光束的远场发散角、束宽和M2因子均会逐渐增大;大气湍流对高阶EHG光束的远场发散角、束宽和M2因子的影响更小;EHG光束在大气湍流中的M2因子与传输距离、湍流的折射率结构参数、光束波长、光束阶数以及基模高斯光束的束腰宽度密切相关。
Abstract
The analytical expressions of the far-field divergence angle,the beam width and the M2-factor in rectangular coordinate systems for laser beams propagating in atmospheric turbulence are derived by using the extended Huygens-Fresnel principle and the definition of the second moments of the Wigner distribution function. Taking the elegant Hermite-Gaussian (EHG) beams as typical examples of laser beams,the propagation properties of the EHG beams in turbulence are analyzed quantitatively. It can be shown that the M2-factor of the laser beams in atmospheric turbulence is related to the M2-factor of the incident plane,the second moments of the incident plane,the propagation distance in turbulence,wavenumber and the influence factor of the atmospheric turbulence. Specially,the far-field divergence angle,the beam width and the M2-factor of the EHG beams increase with the propagation distance in turbulence. And the influences of the atmospheric turbulence on the far-field divergence angle angle,the beam width and the M2-factor of the EHG beams with higher beam order are smaller. The M2-factor of the EHG beams depends on the propagation distance,the structural constant of the refractive index fluctuations of the turbulence,the wavelength,the beam order and the waist width of the fundamental-mode Gaussian beam.
乔娜, 但有全, 张彬. 复宗量厄米高斯光束在大气湍流中的传输特性[J]. 光学学报, 2010, 30(6): 1542. Qiao Na, Dan Youquan, Zhang Bin. Propagation Properties of Elegant Hermite-Gaussian Beams in Atmospheric Turbulence[J]. Acta Optica Sinica, 2010, 30(6): 1542.