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Based on the vector angular spectrum representation of the Maxwell equations and the method of stationary phase, only with the far field approximation, the analytical expressions of energy flux density of a hollow Gaussian beam diffracted by a circular phase aperture is presented. It is shown that the total energy flux of the beam can be expressed as the sum of the unapertured term and the additional term, where the additional term is the effect of the phase aperture on the beam; the total energy flux, the unapertured one and the additional one each can be expressed as the sum of TE term and TM term. The distributions of the total energy flux, the unapertuered one, the additional one, and their TE terms and TM terms are depicted in the far field. The influences of truncation parameter and the phase delay on the longitudinal total energy flux distributions are discussed.
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Keywords:
- hollow Gaussian beam /
- vectorial structure /
- phase aperture
[1] Ito H, Nakata T, Sakaki K, Ohtsu M 1996 Phys. Rev. Lett. 76 4500
[2] Yan M, Yin J P, Zhu Y F 2000 J. Opt. Soc. Am. B 17 1817
[3] Wang Z L, Dai M, Yin J P 2005 Opt. Express 13 8406
[4] Luo Y M, Lü B D 2009 Acta Phys. Sin. 58 3915 (in Chinese) [罗亚梅, 吕百达 2009 58 3915]
[5] Kuga T, Torii Y, Shiokawa N, Hirano T, Shimizu Y, Sasa H 1997 Phys. Rev. Lett. 78 4713
[6] Arlt J, Dholakia K 2000 Opt. Commun. 177 297
[7] Cai Y J, Lu X H, Lin Q 2003 Opt. Lett. 28 1084
[8] Zhang L, Cai Y J, Lu X H 2004 Acta Phys. Sin. 53 1777 (in Chinese) [张蕾, 蔡阳健, 陆璇辉 2004 53 1777]
[9] Liu Z J, Zhao H F, Liu J L, Lin J, Ahmad M A, Liu S T 2007 Opt. Lett. 32 2076
[10] Zheng C W 2006 Phys. Lett. A 355 156
[11] Zhao C L, Wang L G, Lu X H 2008 Opt. Laser Technol. 40 58
[12] Zhang H F, Wu G H, Guo H 2008 Opt. Commun. 281 4169
[13] Alkelly A A, Al-Nadarya H, Alhijrya I A 2011 Opt. Commun. 284 322
[14] Zhou G Q, Chu X X, Zheng J 2008 Opt. Commun. 281 5653
[15] Wu G H, Lou Q H, Zhou J 2008 Opt. Express 16 6417
[16] Zhang Y L, Wang B, Li X Y, Zhu J Q 2010 Optik 121 652
[17] Cai Y J, He S L 2006 J. Opt. Soc. Am. A 23 1410
[18] Deng D G, Yu H, Xu S Q, Tian G L, Fan Z X 2008 J. Opt. Soc. Am. B 25 83
[19] Zhou G Q 2009 Opt. Laser Technol. 41 562
[20] Jiang Z P, Lu Q S, Liu Z J 1997 Appl. Opt. 36 772
[21] Zhou G Q 2011 Opt. Commun. 284 8
[22] Martinez-Herrero R, Mejias P M, Bosch S, Carnicer A 2001 J. Opt. Soc. Am. A 18 1678
[23] Zhou G Q 2006 Opt. Lett. 31 2616
[24] Luo H L, Wen S C, Shu W X, Fan D Y 2010 Phys. Rev. A 81 053826
[25] Luo H L, Wen S C, Shu W X, Fan D Y 2012 Opt. Commun. 285 864
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[1] Ito H, Nakata T, Sakaki K, Ohtsu M 1996 Phys. Rev. Lett. 76 4500
[2] Yan M, Yin J P, Zhu Y F 2000 J. Opt. Soc. Am. B 17 1817
[3] Wang Z L, Dai M, Yin J P 2005 Opt. Express 13 8406
[4] Luo Y M, Lü B D 2009 Acta Phys. Sin. 58 3915 (in Chinese) [罗亚梅, 吕百达 2009 58 3915]
[5] Kuga T, Torii Y, Shiokawa N, Hirano T, Shimizu Y, Sasa H 1997 Phys. Rev. Lett. 78 4713
[6] Arlt J, Dholakia K 2000 Opt. Commun. 177 297
[7] Cai Y J, Lu X H, Lin Q 2003 Opt. Lett. 28 1084
[8] Zhang L, Cai Y J, Lu X H 2004 Acta Phys. Sin. 53 1777 (in Chinese) [张蕾, 蔡阳健, 陆璇辉 2004 53 1777]
[9] Liu Z J, Zhao H F, Liu J L, Lin J, Ahmad M A, Liu S T 2007 Opt. Lett. 32 2076
[10] Zheng C W 2006 Phys. Lett. A 355 156
[11] Zhao C L, Wang L G, Lu X H 2008 Opt. Laser Technol. 40 58
[12] Zhang H F, Wu G H, Guo H 2008 Opt. Commun. 281 4169
[13] Alkelly A A, Al-Nadarya H, Alhijrya I A 2011 Opt. Commun. 284 322
[14] Zhou G Q, Chu X X, Zheng J 2008 Opt. Commun. 281 5653
[15] Wu G H, Lou Q H, Zhou J 2008 Opt. Express 16 6417
[16] Zhang Y L, Wang B, Li X Y, Zhu J Q 2010 Optik 121 652
[17] Cai Y J, He S L 2006 J. Opt. Soc. Am. A 23 1410
[18] Deng D G, Yu H, Xu S Q, Tian G L, Fan Z X 2008 J. Opt. Soc. Am. B 25 83
[19] Zhou G Q 2009 Opt. Laser Technol. 41 562
[20] Jiang Z P, Lu Q S, Liu Z J 1997 Appl. Opt. 36 772
[21] Zhou G Q 2011 Opt. Commun. 284 8
[22] Martinez-Herrero R, Mejias P M, Bosch S, Carnicer A 2001 J. Opt. Soc. Am. A 18 1678
[23] Zhou G Q 2006 Opt. Lett. 31 2616
[24] Luo H L, Wen S C, Shu W X, Fan D Y 2010 Phys. Rev. A 81 053826
[25] Luo H L, Wen S C, Shu W X, Fan D Y 2012 Opt. Commun. 285 864
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