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When a radially-polarized beam passes through a wave plate, the polarization distribution of the beam strongly depends on the retardation angle and the spatial position. When the retardation angle is changed from 0 to π, the polarization of the beam becomes the local elliptic polarization with non-uniform polarization distribution. The rotating direction of polarization in the first and third quadrants is opposite to that in the second and fourth quadrants. In this paper we have numerically simulated the transverse and longitudinal electric field intensity, the transverse energy flux and the longitudinal angular momentum of the tightly focused beam in the focal plane. Our results show that the sum of the longitudinal angular momentum in the focal plane is zero, but it is varying in different quadrants. The liquid crystal variable retarder (LCVR) is adopted as a real-time continuous tunable wave plate with its retardation angle δ changing from 0 to π by varying the applied voltage. In this case the phase retardation angle δ introduced by the LCVR can be used as a control over the longitudinal electric field intensity and the longitudinal angular momentum.
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Keywords:
- polarization /
- tight focusing /
- angular momentum /
- liquid crystal variable retarder (LCVR)
[1] Stalder M, Schadt M 1996 Opt. Lett. 21 1948
[2] Li C F 2007 Opt. Lett. 32 3543
[3] Tidwell S C, Ford D H, Kimura W D 1990 Appl. Opt. 29 2234
[4] Phua P B, Lai W J, Lim Y L, Tiaw K S, Lim B C, Teo H H, Hong M H 2007 Opt. Lett. 32 376
[5] Machavariani G, Lumer Y, Moshe I, Meir A, Jackel S 2007 Opt. Lett. 32 1468
[6] Machavariani G, Lumer Y, Moshe I, Meir A, Jackel S 2008 Opt. Commun. 281 732
[7] Zhuang J J, Zhao R Q, Ye G M, Dai L S 1985 Acta Phys. Sin. 34 752 ( in Chinese ) [庄杰佳、赵润乔、叶桂木、戴立胜 1985 物理学报 34 752 ]
[8] Wang X L, Ding J, Ni W J, Guo C S, Wang H T 2007 Opt. Lett. 32 3549
[9] Li J L, Ueda K, Musha M, Shirakawa A, Zhong L X 2006 Opt. Lett. 31 2969
[10] Oron R, Blit S, Davidson N, Friesem A A, Bomzon Z, Hasman E 2000 Appl. Phys. Lett. 77 3322
[11] Youngworth K S, Brown T G 2000 Opt. Express 7 77
[12] Dorn R, Quabis S, Leuchs G 2003 Phys. Rev. Lett. 91 233901
[13] Quabis S, Dorn R, Eberler M, Glckl O, Leuchs G 2000 Opt. Commun. 179 1
[14] Chen B S, Pu J X 2009 Appl. Opt. 48 1288
[15] Luo Y M, Lü B D 2009 Acta Phys. Sin. 58 3915 ( in Chinese ) [罗亚梅、吕百达 2009 物理学报 58 3915 ]
[16] Pan L Z, Ding C L 2007 Chin. Phys. 16 137
[17] Kozawa Y, Sato S 2006 Opt. Lett. 31 820
[18] Zhuang Y L, Zhao Y Q, Zhan Q W, Li Y P 2006 Acta Phys. Sin. 55 1258 ( in Chinese ) [张艳丽、赵逸琼、詹其文、李永平 2006 物理学报 55 1258 ]
[19] Ding H B, Pang W N, Liu Y B, Shang R C 2005 Acta Phys. Sin. 54 4097 ( in Chinese ) [丁海兵、庞文宁、刘义保、尚仁成 2005 物理学报 54 4097 ]
[20] Goldstein D 2003 Polarized light (2nd ed)(New York: Marcel Dekker) p219 and p22
[21] Wolf E 1959 Proc. Roy. Soc. A 253 349
[22] Richards B, Wolf E 1959 Proc. Roy. Soc. A 253 358
[23] Allen L, Padgett M J, Babiker M 1999 Progress in Optics, 39 291
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[1] Stalder M, Schadt M 1996 Opt. Lett. 21 1948
[2] Li C F 2007 Opt. Lett. 32 3543
[3] Tidwell S C, Ford D H, Kimura W D 1990 Appl. Opt. 29 2234
[4] Phua P B, Lai W J, Lim Y L, Tiaw K S, Lim B C, Teo H H, Hong M H 2007 Opt. Lett. 32 376
[5] Machavariani G, Lumer Y, Moshe I, Meir A, Jackel S 2007 Opt. Lett. 32 1468
[6] Machavariani G, Lumer Y, Moshe I, Meir A, Jackel S 2008 Opt. Commun. 281 732
[7] Zhuang J J, Zhao R Q, Ye G M, Dai L S 1985 Acta Phys. Sin. 34 752 ( in Chinese ) [庄杰佳、赵润乔、叶桂木、戴立胜 1985 物理学报 34 752 ]
[8] Wang X L, Ding J, Ni W J, Guo C S, Wang H T 2007 Opt. Lett. 32 3549
[9] Li J L, Ueda K, Musha M, Shirakawa A, Zhong L X 2006 Opt. Lett. 31 2969
[10] Oron R, Blit S, Davidson N, Friesem A A, Bomzon Z, Hasman E 2000 Appl. Phys. Lett. 77 3322
[11] Youngworth K S, Brown T G 2000 Opt. Express 7 77
[12] Dorn R, Quabis S, Leuchs G 2003 Phys. Rev. Lett. 91 233901
[13] Quabis S, Dorn R, Eberler M, Glckl O, Leuchs G 2000 Opt. Commun. 179 1
[14] Chen B S, Pu J X 2009 Appl. Opt. 48 1288
[15] Luo Y M, Lü B D 2009 Acta Phys. Sin. 58 3915 ( in Chinese ) [罗亚梅、吕百达 2009 物理学报 58 3915 ]
[16] Pan L Z, Ding C L 2007 Chin. Phys. 16 137
[17] Kozawa Y, Sato S 2006 Opt. Lett. 31 820
[18] Zhuang Y L, Zhao Y Q, Zhan Q W, Li Y P 2006 Acta Phys. Sin. 55 1258 ( in Chinese ) [张艳丽、赵逸琼、詹其文、李永平 2006 物理学报 55 1258 ]
[19] Ding H B, Pang W N, Liu Y B, Shang R C 2005 Acta Phys. Sin. 54 4097 ( in Chinese ) [丁海兵、庞文宁、刘义保、尚仁成 2005 物理学报 54 4097 ]
[20] Goldstein D 2003 Polarized light (2nd ed)(New York: Marcel Dekker) p219 and p22
[21] Wolf E 1959 Proc. Roy. Soc. A 253 349
[22] Richards B, Wolf E 1959 Proc. Roy. Soc. A 253 358
[23] Allen L, Padgett M J, Babiker M 1999 Progress in Optics, 39 291
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