部分相干厄米–高斯光束通过非Kolmogorov大气湍流传输的束宽扩展和方向性
The Beam-Width Spread and Directionality of Partially Coherent Hermite-Ganssian Beams Propagating through Non-Kolmogorov Atmospheric Turbulence*
摘要: 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。
Abstract: 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.

文章引用：彭艳艳, 李晋红, 魏计林, 王伟伟. 部分相干厄米–高斯光束通过非Kolmogorov大气湍流传输的束宽扩展和方向性[J]. 应用物理, 2013, 3(3): 61-67. http://dx.doi.org/10.12677/APP.2013.33012

参考文献

[1] V. I. Tatarskii. Wave propagation in a turbulent medium. New York: McGraw-Hill, 1961.
[2] L. C. Andrews, R. L. Phillips. Laser beam propagation through random media. Bellingham: SPIE Press, 1998.
[3] G. Gbur, E. Wolf. Spreading of partially coherent beams in random media. Journal of the Optical Society of America A-Optics Image Science and Vision, 2002, 19(8): 1592-1598.
[4] T. Shirai, A. Dogariu and E. Wolf. Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence. Journal of the Optical Society of America A-Optics Image Science and Vision, 2003, 20(6): 1094-1102.
[5] T. Shirai, A. Dogariu and E. Wolf. Directional-ity of Gaussian Schell-model beams propagating in atmospheric turbu-lence. Optics Letters, 2003, 28(8): 610-612.
[6] Y. J. Cai, S. L. He. Average intensity and spreading of an elliptical Gaussian beam propa-gating in a turbulent atmosphere. Optics Letters, 2006, 31(5): 568-570.
[7] J. Li, A. Yang and B. Lü. Comparative study of the beam-width spreading of partially coherent Hermite-sinh-Gaussian beams in atmospheric turbulence. Journal of the Optical Society of America a-Optics Image Science and Vision, 2008, 25(1): 2670-2679.
[8] J. Li, A. Yang and B. Lü. The angular spread and directionality of general partially coherent beams in atmospheric tur-bulence. Journal of Optics A: Pure and Applied Optics, 2008, 10(9): Article ID: 095003.
[9] T. Wang, J. Pu and Z. Chen. Beam-spreading and topological charge of vortex beams propagating in a turbulent atmosphere. Optics Communications, 2009, 282(7): 1255-1259.
[10] L. Dou, X. Ji and W. Zhu. Near-field and far-field spreading of partially coherent annular beams propagating through atmospheric turbulence. Applied Physics B: Lasers and Optics, 2012, 108(1): 217-229.
[11] 郑宇龙, 季小玲. 大气湍流对多色高斯–谢尔模型光束扩展的影响[J]. 强激光与粒子束, 2012, 24: 276-280.
[12] A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt and Y. Shtemler. Lidar study of aerosol turbulence char-acteristics in the troposphere: Kolmogorov and non-Kol- mogorov turbulence. Atmospheric Research, 2008, 88: 66-77.
[13] I. Toselli, L. C. Andrews, R. L. Phillips and V. Ferrero. Free space optical system performance for laser beam propagation through non Kolmogorov turbulence for uplink and downlink paths. Proceedings of the SPIE, 2007, 6708: Article ID: 670803.
[14] O. Korotkova, E. Shchepakina. Color changes in stochastic light fields propagating in non-Kolmogorov turbulence. Optics Letters, 2010, 35(22): 3772-3774.
[15] H. Xu, Z. Cui and J. Qu. Propagation of elegant Laguerre- Gaussian beam in non-Kolmogorov turbulence. Optics Ex-press, 2011, 19(22): 21163-21173.
[16] M. Zahid, M. S. Zubairy. Directionality of partially coherent Bessel-Gauss beams. Optics Com-munications, 1989, 70(5): 361- 364.
[17] P. Zhou, X. Wang, Y. Ma, R. Tao and Z. Liu. Average spreading and directionality of broadband partially coherent beam in non- Kolmogorov turbulence. Applied Physics B: Lasers and Optics, 2011, 104(4): 1013-1017.
[18] I. S. Gradysteyn, I. M. Ryzhik. Table of integrals, series, and products. New York: Academic Press, 2007: 803-804.
[19] M. Salem, T. Shirai, A. Dogariu and E. Wolf. Long-distance propagation of partially coherent beams through atmospheric turbulence. Optics Communications, 2003, 216(4-6): 261-265.

为你推荐