Abstract

We focus on a new kind of vector optical field with bipolar symmetry of linear polarization instead of cylindrical and elliptical symmetries, enriching members of family of vector optical fields. We design theoretically and generate experimentally the demanded vector optical fields and then explore some novel tightly focusing properties. The geometric configurations of states of polarization provide additional degrees of freedom assisting in engineering the field distribution at the focus to the specific applications such as lithography, optical trapping, and material processing.

© 2013 Optical Society of America

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2013

2012

2010

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, Phys. Rev. Lett. 105, 253602 (2010).
[CrossRef]

X. L. Wang, Y. N. Li, J. Chen, C. S. Guo, J. P. Ding, and H. T. Wang, Opt. Express 18, 10786 (2010).
[CrossRef]

2009

2008

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

2007

2006

2003

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

2002

2000

1959

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
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Alexeyev, C.

Anischenko, P.

Arlt, J.

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Biener, G.

Bokor, N.

Bomzon, Z.

Brown, T. G.

Chen, J.

X. L. Wang, Y. N. Li, J. Chen, C. S. Guo, J. P. Ding, and H. T. Wang, Opt. Express 18, 10786 (2010).
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X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, Phys. Rev. Lett. 105, 253602 (2010).
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Chong, C. T.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
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Davidson, N.

Ding, J. P.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
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Fadeyeva, T.

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Guo, C. S.

Hasman, E.

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Jiao, X. Y.

Kleiner, V.

Kozawa, Y.

Leger, J.

Lerman, G.

Lerman, G. M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
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Levy, U.

Li, P.

Li, Y. N.

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, Phys. Rev. Lett. 105, 253602 (2010).
[CrossRef]

X. L. Wang, Y. N. Li, J. Chen, C. S. Guo, J. P. Ding, and H. T. Wang, Opt. Express 18, 10786 (2010).
[CrossRef]

Lilach, Y.

Liu, S.

Lukyanchuk, B.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Ni, W. J.

Padgett, M. J.

Peng, T.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

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B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Sato, S.

Sheppard, C.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Shi, L. P.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Volyar, A.

Wang, H. F.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Wang, H. T.

Wang, S. C.

Wang, X. L.

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Xie, X. S.

Yang, L. X.

Youngworth, K. S.

Zhan, Q.

Zhang, W.

Zhao, J. L.

Zhou, J. Y.

Adv. Opt. Photon.

Appl. Opt.

Nat. Photonics

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

New J. Phys.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, Phys. Rev. Lett. 105, 253602 (2010).
[CrossRef]

Proc. R. Soc. London Ser. A

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of experimental setup for generating the vector fields with the bipolar symmetry of linear polarization. A linear polarizer may be inserted between G and CCD, to record the total or a certain polarized component intensity pattern by CCD.

Fig. 2.
Fig. 2.

Bipolar coordinate system (u,v), where F1 and F2 are two foci located at (a,0) and (a,0), respectively. (x,y) is the corresponding Cartesian coordinate system.

Fig. 3.
Fig. 3.

Generated vector fields with the polarization distribution being a function of u independent of v for different m when n0. The first and second rows are the simulated and measured intensity patterns of the x components behind an x-oriented polarizer.

Fig. 4.
Fig. 4.

Generated vector fields with the polarization distribution being a function of v independent of u for different n when m0. The first and second rows are the simulated and measured intensity patterns of the x components behind an x-oriented polarizer.

Fig. 5.
Fig. 5.

Generated vector fields with the polarization distribution being a function of both u and v for different m and n. The first and second rows are the simulated and measured intensity patterns of the x components behind an x-oriented polarizer.

Fig. 6.
Fig. 6.

Simulated tight focusing field on the interval 2a between the two foci for the vector field with its polarization distribution being a function of u independent of v with m=1 and n=0, by using a lens with NA=0.9. Any picture has a dimension of 4λ×4λ.

Fig. 7.
Fig. 7.

Intensity profiles of a sharp line formed by tightly focused vector field with the bipolar symmetry of linear polarization when 2a=1.84f in the case of m=1 and n=0. Top and bottom panels are the profiles along the x and y axes, respectively.

Equations (6)

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E(x,y)=12A0[ejδ(x,y)e^++ejδ(x,y)e^],
=A0[cosδ(x,y)e^x+sinδ(x,y)e^y].
x=asinhvcoshvcosu,y=asinucoshvcosu.
u=ππ[1+sgn(x2+y2a2)]sgn(y)/2+arctan2ayx2+y2a2,
v=arctanh2axx2+y2+a2.
δ(x,y)=δ(u,v)=mu+nv+δ0,

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