Abstract

We propose a method for generating focal beams with special intensity distributions using radially polarized vortex beams in a 4Pi configuration. A spherical dark-hollow beam and hollow beam array can be obtained by vortex beams with topological charge of m=1. A dark channel can be generated using vortex beams with topological charge of m=2. The length of the well-defined hollow beam array and the dark channel is about 30λ. These interesting beams are useful in optical trapping and manipulation.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef]
  2. H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
    [CrossRef]
  3. X. Hao, C. Kuang, T. Wang, and X. Liu, Opt. Lett. 35, 3928 (2010).
    [CrossRef]
  4. S. Hell and E. H. K. Stelzer, J. Opt. Soc. Am. A 9, 2159 (1992).
    [CrossRef]
  5. S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
    [CrossRef]
  6. K. S. Youngworth and T. G. Brown, Opt. Express 7, 77 (2000).
    [CrossRef]
  7. H. P. Urbach and S. F. Pereira, Phys. Rev. Lett. 100, 123904 (2008).
    [CrossRef]
  8. H. Lin, B. Jia, and M. Gu, Opt. Lett. 36, 2471 (2011).
    [CrossRef]
  9. Q. Zhan, Opt. Express 12, 3377 (2004).
    [CrossRef]
  10. Y. Zhang, T. Suyama, and B. Ding, Opt. Lett. 35, 1281 (2010).
    [CrossRef]
  11. N. Bokor and N. Davidson, Opt. Lett. 29, 1968 (2004).
    [CrossRef]
  12. W. Chen and Q. Zhan, Opt. Lett. 34, 2444 (2009).
    [CrossRef]
  13. S. Yan, B. Yao, W. Zhao, and M. Lei, J. Opt. Soc. Am. A 27, 2033 (2010).
    [CrossRef]
  14. S. Yan, B. Yao, and R. Rupp, Opt. Express 19, 673 (2011).
    [CrossRef]
  15. N. Bokor and N. Davidson, Opt. Lett. 31, 149 (2006).
    [CrossRef]
  16. M. Gu, Advanced Optical Imaging Theory (Springer, 1999).
  17. S. W. Hell, S. Lindek, and E. H. K. Stelzer, J. Mod. Opt. 41, 675 (1994).
    [CrossRef]
  18. Y. Zhao, Q. Zhan, Y. Zhang, and Y. Li, Opt. Lett. 30, 848 (2005).
    [CrossRef]
  19. B. Tian and J. Pu, Opt. Lett. 36, 2014 (2011).
    [CrossRef]
  20. Y. Iketaki, T. Watanabe, N. Bokor, and M. Fujii, Opt. Lett. 32, 2357 (2007).
    [CrossRef]

2011

2010

2009

2008

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

H. P. Urbach and S. F. Pereira, Phys. Rev. Lett. 100, 123904 (2008).
[CrossRef]

2007

2006

2005

2004

2003

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

2000

1994

S. W. Hell, S. Lindek, and E. H. K. Stelzer, J. Mod. Opt. 41, 675 (1994).
[CrossRef]

S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
[CrossRef]

1992

Bokor, N.

Brown, T. G.

Chen, W.

Chong, C. T.

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

Cremer, C.

S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
[CrossRef]

Davidson, N.

Ding, B.

Dorn, R.

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

Fujii, M.

Gu, M.

H. Lin, B. Jia, and M. Gu, Opt. Lett. 36, 2471 (2011).
[CrossRef]

M. Gu, Advanced Optical Imaging Theory (Springer, 1999).

Hao, X.

Hell, S.

Hell, S. W.

S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
[CrossRef]

S. W. Hell, S. Lindek, and E. H. K. Stelzer, J. Mod. Opt. 41, 675 (1994).
[CrossRef]

Iketaki, Y.

Jia, B.

Kuang, C.

Lei, M.

Leuchs, G.

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

Li, Y.

Lin, H.

Lindek, S.

S. W. Hell, S. Lindek, and E. H. K. Stelzer, J. Mod. Opt. 41, 675 (1994).
[CrossRef]

S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
[CrossRef]

Liu, X.

Lukyanchuk, B.

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

Pereira, S. F.

H. P. Urbach and S. F. Pereira, Phys. Rev. Lett. 100, 123904 (2008).
[CrossRef]

Pu, J.

Quabis, S.

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

Rupp, R.

Sheppard, C.

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

Shi, L.

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

Stelzer, E. H. K.

S. W. Hell, S. Lindek, and E. H. K. Stelzer, J. Mod. Opt. 41, 675 (1994).
[CrossRef]

S. Hell and E. H. K. Stelzer, J. Opt. Soc. Am. A 9, 2159 (1992).
[CrossRef]

Stelzer, E. K.

S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
[CrossRef]

Suyama, T.

Tian, B.

Urbach, H. P.

H. P. Urbach and S. F. Pereira, Phys. Rev. Lett. 100, 123904 (2008).
[CrossRef]

Wang, H.

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

Wang, T.

Watanabe, T.

Yan, S.

Yao, B.

Youngworth, K. S.

Zhan, Q.

Zhang, Y.

Zhao, W.

Zhao, Y.

Appl. Phys. Lett.

S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
[CrossRef]

J. Mod. Opt.

S. W. Hell, S. Lindek, and E. H. K. Stelzer, J. Mod. Opt. 41, 675 (1994).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photon.

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

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

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

H. P. Urbach and S. F. Pereira, Phys. Rev. Lett. 100, 123904 (2008).
[CrossRef]

Other

M. Gu, Advanced Optical Imaging Theory (Springer, 1999).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Illustration of a 4Pi focusing system illuminated by two counterpropagating, radially polarized beams. The dash array denotes the direction of the polarization of illumination. The spatial modulation of the beam can be achieved by AMF.

Fig. 2.
Fig. 2.

Spherical focal spot formed by radially polarized LG beam with m = 0 . (a) Intensity distribution in r z plane, (b) intensity distribution in the focal plane, (c) intensity profile along the z or r axis. The other parameters are E 0 = 1 , w = 0.01 m , f = 0.01 m , NA = 0.9 .

Fig. 3.
Fig. 3.

Dark-hollow beam formed by radially polarized LG beam of topological charge m = 1 . (a) Intensity distribution in r z plane, (b) intensity distribution in the focal plane, (c) intensity profile along the z or r axis.

Fig. 4.
Fig. 4.

Dark-hollow beam array in the vicinity of focal axis generated using radially polarized LG beam with m = 1 .

Fig. 5.
Fig. 5.

Dark channel produced by radially polarized LG beam with topological charge m = 2 . Two counterpropagating incident beams have (a) the same topological charge but opposite radial polarization direction and (b) opposite topological charge but same radial polarization direction.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

E ( ρ , ϕ ) = E 0 exp ( ρ 2 w 2 ) ( ρ w ) m exp ( i m ϕ ) ,
[ E x ( r , φ , z ) E y ( r , φ , z ) E z ( r , φ , z ) ] = i π 0 α 0 2 π sin θ cos θ E 0 ( θ , ϕ ) T ( θ ) × exp { i k [ z cos θ + r sin θ cos ( ϕ φ ) ] } [ cos θ cos ϕ cos θ sin ϕ sin θ ] d ϕ d θ ,
E r ( r , φ , z ) = E x ( r , φ , z ) cos φ + E y ( r , φ , z ) sin φ ,
E φ ( r , φ , z ) = E y ( r , φ , z ) cos φ E x ( r , φ , z ) sin φ .
E r ( r , φ , z ) = i 0 α E 0 exp ( f 2 sin 2 θ w 2 ) ( f sin θ w ) m exp ( i m φ ) × sin θ cos 3 / 2 θ T ( θ ) exp ( i k z cos θ ) [ i m + 1 J m + 1 ( k r sin θ ) + i m 1 J m 1 ( k r sin θ ) ] d θ ,
E φ ( r , φ , z ) = 0 α E 0 exp ( f 2 sin 2 θ w 2 ) ( f sin θ w ) m × exp ( i m φ ) sin θ cos 3 / 2 θ T ( θ ) exp ( i k z cos θ ) × [ i m + 1 J m + 1 ( k r sin θ ) i m 1 J m 1 ( k r sin θ ) ] d θ ,
E z ( r , φ , z ) = 2 i m + 1 0 α E 0 exp ( f 2 sin 2 θ w 2 ) ( f sin θ w ) m exp ( i m φ ) × sin 2 θ cos θ T ( θ ) exp ( i k z cos θ ) J m ( k r sin θ ) d θ .
E ( r , φ , z ) = E 1 ( r , φ , z ) + E 2 ( r , φ , z ) ,
T ( θ ) = { 1 , ( 0 θ 0.37 and 0.94 θ α ) 0 , ( 0.37 < θ < 0.94 ) .

Metrics