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The properties of off-center Gaussian vortex beams focused by a high numerical aperture are investigated on the basis of vector Debye integral. A complex amplitude of off-center Gaussian vortex beams through a high numerical aperture objective is derived and numerical calculation is performed to analyze the intensity and phase distributions of the beams in the focal plane. It is shown that the intensity and phase distributions change significantly with the variation of off-axial distance; the intensity distribution in the focal plane is different in the direction of y-axis which is enhanced with the increase of off-axial distances; the sign of off-axial distance determines the direction in which the intensity is concentrated. On the other hand, different from the 1st order off-axial vortex beam, high-order off-axial vortex will split in the tightly focused field. Multiple phase singularities will appear and the number of singularities is equal to the topological charge of the original beam. Besides, the split singularities are symmetric, obviously. It is found that the splitting of high-order vortex is due to the tight focusing.
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Keywords:
- tight focusing /
- split of singularity /
- vector Debye integral /
- off-center Gaussian vortex beams
[1] Liu Y D, Gao C Q, Gao M W, L F 2007 Acta Phys. Sin. 56 854
[2] Bokor N, Davidson N 2007 Opt. Commun. 279 229
[3] Grosjean T, Courjon D 2007 Opt. Commun. 272 314
[4] Li X, Cao Y, Gu M 2011 Opt. Lett. 36 2510
[5] Chen Z Y, Pu J X, Zhao D M 2011 Phys. Lett. A 375 2958
[6] Kim W, Park N 2007 Opt. Rev. 14 236
[7] Shimizu Y, Sasad A H 1997 Phys. Rev. Lett. 78 4713
[8] Zhan Q 2006 Opt. Lett. 31 867
[9] Chen B, Pu J, Korotkova O 2010 Opt. Express 18 10822
[10] Hua M, Chen Z, Chen B, Pu J 2010 Chin. Phys. B 19 014202
[11] Yan H W, Cheng K, L D 2008 Acta Phys. Sin. 57 5542 (in Chinese) [闫红卫, 程科, 吕百达 2008 57 5542]
[12] 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]
[13] Richards B, Wolf E 1959 Proc. R. Soc. A 253 358
[14] Chon J W M, Gan X S, Gu M 2002 Phys. Lett. 81 1576
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[1] Liu Y D, Gao C Q, Gao M W, L F 2007 Acta Phys. Sin. 56 854
[2] Bokor N, Davidson N 2007 Opt. Commun. 279 229
[3] Grosjean T, Courjon D 2007 Opt. Commun. 272 314
[4] Li X, Cao Y, Gu M 2011 Opt. Lett. 36 2510
[5] Chen Z Y, Pu J X, Zhao D M 2011 Phys. Lett. A 375 2958
[6] Kim W, Park N 2007 Opt. Rev. 14 236
[7] Shimizu Y, Sasad A H 1997 Phys. Rev. Lett. 78 4713
[8] Zhan Q 2006 Opt. Lett. 31 867
[9] Chen B, Pu J, Korotkova O 2010 Opt. Express 18 10822
[10] Hua M, Chen Z, Chen B, Pu J 2010 Chin. Phys. B 19 014202
[11] Yan H W, Cheng K, L D 2008 Acta Phys. Sin. 57 5542 (in Chinese) [闫红卫, 程科, 吕百达 2008 57 5542]
[12] 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]
[13] Richards B, Wolf E 1959 Proc. R. Soc. A 253 358
[14] Chon J W M, Gan X S, Gu M 2002 Phys. Lett. 81 1576
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