The Beam-Width Spread and Directionality of Partially Coherent Hermite-Ganssian Beams Propagating through Non-Kolmogorov Atmospheric Turbulence*

Abstract

基于广义惠更斯–菲涅耳原理和非Kolmogorov谱，推导出了部分相干厄米–高斯(H-G)光束通过非Kolmogorov大气湍流传输中束宽扩展的解析表达式，并用以研究了部分相干H-G光束通过大气湍流的束宽扩展和方向性。引入相对束宽来定量的描述光束抗拒大气湍流的能力。结果表明，空间相干长度σ0越小，光束阶束m，n越大，部分相干H-G光束的束宽扩展受大气湍流影响越小；而束腰宽度ω0受大气湍流影响与传输距离z有关，当传输距离足够远时，束腰宽度ω0越小，部分相干H-G光束的束宽扩展受大气湍流影响越小。部分相干H-G光束相对束宽随Kolmogorov大气湍流广义指数参量α增加先增加后减小。另外，存在等价部分相干H-G光束、等价完全相干H-G光束、等价高斯–谢尔模型(GSM)光束与相应的完全相干高斯光束在非Kolmogorov大气湍流和自由空间中分别具有相同的方向性，并对所得结果做了物理解释。 Based on the extended Huygens-Fresnel principle and non-Kolmogorov spectrum, analytical expressions for the beam-width spread of partially coherent Hermite-Ganssian (H-G) beams propagating through non-Kolmogorov atmospheric turbulence are derived, and used to study the beam-width spreading and directionality of partially coherent H-G beams propagating through non-Kolmogorov atmospheric turbulence. The relative width is introduced to quantitatively describe the resistance of a beam to atmospheric turbulence. It is shown that the smaller the spatial correlation length σ0, and the larger the beam order m, n, and the less the beam-width spreading of partially coherent H-G beams is affected by non-Kolmogorov atmospheric turbulence. The influence of turbulence on beam-width spreading depends on the waist width ω0 and propagation distance z, when the propagation distance is sufficiently long, the smaller the waist width ω0, the less the beam-width spreading of partially coherent H-G beams is affected by non-Kolmogorov atmospheric turbulence. The beam width of partially coherent H-G beams through non-Kolmogorov atmospheric turbulence increase with the increasing exponent parameter α, then decrease with increasing α. There exist equivalent partially coherent and fully coherent H-G beams, GSM beams, which have the same directionality as a fully coherent Gaussian laser beam in free space and in non-Kolmogorov atmospheric turbulence. The results are interpreted physically.