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在近轴光束近似条件下,采用交叉谱密度传输公式推导了 部分相干涡旋光束传输一段距离后观测平面上交叉谱密度矩阵元的解析表达式, 在此基础上对观测平面上的光强分布进行了分析.研究表明, 和完全相干涡旋光束不同,部分相干涡旋光束传输后光斑中心点的光强会逐渐凸现出来, 随着传输距离的增加,观测平面上的光强会逐渐演变为类似高斯型分布的特性. 这种演变规律与源平面上光源的拓扑电荷数和相干长度有关, 在其他参数不变的情况下,拓扑电荷数越小,相干长度越短, 演变为高斯型光斑的速度越快.最后针对一阶部分相干高斯涡旋光束, 通过观测平面上光强极值研究,对光斑随传输距离演变的过程进行了详细的分析, 在理论上对这种演变规律给出了严格的证明.The propagation law of the cross spectrum density is employed to derive the analytical expression of the elements of the cross spectrum density matrix in the observation plane for partially coherent vortex beam after propagation under the condition of paraxial approximation. Based on the derived result, the intensity distribution in the observation plane is analyzed. It is shown that different from the completely coherent vortex beam, the partially coherent votex beam has an intensity of the center-point in the observation plane, which gradually becomes prominent after propagation, and the intensity distribution in the observation plane tends to the distribution of Gaussian-like type with the increase of propagation length. The evolution of intensity distribution depends on the topological charge and correlation length of the source beam. On the condition that other parameters of the source beam are invariable, the beam will evolve fast if the topological charge is small and the correlation length is short. Finally, for the first-order partially coherent vortex beam, the detail of the evolution of the beam shape is investigated by studying the extremum of the intensity in the observation plane. And the theoretical proof is presented for the rule of the evolution of the beam.
[1] Chen K, Zhang H R, Lü B D 2010 Acta Phys. Sin. 59 246 (in Chinese) [程科, 张洪润, 吕百达 2010 59 246]
[2] Li Y Y, Chen Z Y, Liu H, Pu J X 2010 Acta Phys. Sin. 59 1740 (in Chinese) [李阳月, 陈子阳, 刘辉, 蒲继雄 2010 59 1740]
[3] Xie Q S, Zhao D M 2008 Opt. Commun. 281 7
[4] Georgi M, Dragomir N N, Alexander D 2009 Phys. Rev. A 80 053828
[5] Babiker M, Bennett C R, Andrews D L, Davila Romero L C 2002 Phys. Rev. Lett. 89 143601
[6] Lu X H, Huang H Q, Zhao C L, Wang J F, Chen H 2008 Laser & Optoelectronics Progress 45 50 (in Chinese) [陆璇辉, 黄慧琴, 赵承良, 王将峰, 陈和 2008 激光与光电子学进展 45 50]
[7] Rao L Z, Pu J X 2004 J. Opt. Soc. Am. A 24 2242
[8] Chen Z Y, Pu J X 2008 Phys. Lett. A 372 2734
[9] Wolf E 2003 Phys. Lett. A 312 263
[10] Roychowdhury H, Korotkova O 2005 Opt. Commun. 249 379
[11] Pu J X, Korotkova O, Wolf E 2006 Opt. Lett. 31 2097
[12] Korotkova O, Salem M, Wolf E 2004 Opt. Lett. 29 11735
[13] Korotkova O, Wolf E 2005 Opt. Lett. 30 198
[14] Chen B S, Chen Z Y, Pu J X 2008 Opt. Laser Technol. 28 820
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[1] Chen K, Zhang H R, Lü B D 2010 Acta Phys. Sin. 59 246 (in Chinese) [程科, 张洪润, 吕百达 2010 59 246]
[2] Li Y Y, Chen Z Y, Liu H, Pu J X 2010 Acta Phys. Sin. 59 1740 (in Chinese) [李阳月, 陈子阳, 刘辉, 蒲继雄 2010 59 1740]
[3] Xie Q S, Zhao D M 2008 Opt. Commun. 281 7
[4] Georgi M, Dragomir N N, Alexander D 2009 Phys. Rev. A 80 053828
[5] Babiker M, Bennett C R, Andrews D L, Davila Romero L C 2002 Phys. Rev. Lett. 89 143601
[6] Lu X H, Huang H Q, Zhao C L, Wang J F, Chen H 2008 Laser & Optoelectronics Progress 45 50 (in Chinese) [陆璇辉, 黄慧琴, 赵承良, 王将峰, 陈和 2008 激光与光电子学进展 45 50]
[7] Rao L Z, Pu J X 2004 J. Opt. Soc. Am. A 24 2242
[8] Chen Z Y, Pu J X 2008 Phys. Lett. A 372 2734
[9] Wolf E 2003 Phys. Lett. A 312 263
[10] Roychowdhury H, Korotkova O 2005 Opt. Commun. 249 379
[11] Pu J X, Korotkova O, Wolf E 2006 Opt. Lett. 31 2097
[12] Korotkova O, Salem M, Wolf E 2004 Opt. Lett. 29 11735
[13] Korotkova O, Wolf E 2005 Opt. Lett. 30 198
[14] Chen B S, Chen Z Y, Pu J X 2008 Opt. Laser Technol. 28 820
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