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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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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