Abstract

We investigate in detail the focusing properties of the composite vector beam (CVB) composed of two orthogonally linearly polarized beams with inhomogeneous polarization modulation. By optimizing the modulation factor, a multifocus with excellent quality is obtained, where the sizes of each focus are fairly smaller than that of the focusing spot of a radially polarized beam, the uniformity in the intensity of the focal spots is as high as 1, and the distributions of each focal spot have nearly circular symmetry. In order to decrease the power loss of the incident beam, the CVB formed by an annular beam is demonstrated as the substitute for the optimized CVB formed by a Gaussian beam. This work is important for high-resolution and high-speed imaging in biology and micro- nanofabrication.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, Nat. Meth. 8, 139 (2011).
    [CrossRef]
  2. X. Dong, Z. Zhao, and X. Duan, Appl. Phys. Lett. 91, 124103 (2007).
    [CrossRef]
  3. H. Guo, J. Chen, and S. Zhuang, J. Opt. Soc. Am. A 23, 2756 (2006).
    [CrossRef]
  4. Y. J. Yoon, W. C. Kim, N. C. Park, K. S. Park, and Y. P. Park, Opt. Lett. 34, 1961 (2009).
    [CrossRef] [PubMed]
  5. G. Terakado, K. Watanabe, and H. Kano, Appl. Opt. 48, 1114 (2009).
    [CrossRef]
  6. H. Dehez, M. Piché, and Y. De Koninck, Opt. Lett. 34, 3601 (2009).
    [CrossRef] [PubMed]
  7. L. Sacconi, E. Froner, and R. Antolini, M. R. Taghizadeh, A. Choudhury, and F. S. Pavone, Opt. Lett. 28, 1918 (2003).
    [CrossRef] [PubMed]
  8. K. Obata, J. Koch, U. Hinze, and B. N. Chichkov, Opt. Express 18, 17193 (2010).
    [CrossRef] [PubMed]
  9. J. Bewersdorf, R. Pick, and S. W. Hell, Opt. Lett. 23, 655 (1998).
    [CrossRef]
  10. J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, Appl. Phys. Lett. 86, 044102 (2005).
    [CrossRef]
  11. T. Minamikawa, M. Hashimoto, K. Fujita, S. Kawata, and T. Araki1, Opt. Express 17, 9526 (2009).
    [CrossRef] [PubMed]
  12. Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, Appl. Phys. B 99, 633 (2010).
    [CrossRef]
  13. C. J. R. Sheppard, S. Rehman, N. K. Balla, E. Y. S. Yew, and T. W. Teng, Opt. Commun. 282, 4647 (2009).
    [CrossRef]
  14. R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
    [CrossRef]
  15. B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
    [CrossRef]
  16. P. Török and P. Varga, Appl. Opt. 36, 2305 (1997).
    [CrossRef] [PubMed]
  17. G. M. Philip and N. K. Viswanathan, J. Opt. Soc. Am. A 27, 2394 (2010).
    [CrossRef]

2011 (1)

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, Nat. Meth. 8, 139 (2011).
[CrossRef]

2010 (3)

2009 (5)

2007 (1)

X. Dong, Z. Zhao, and X. Duan, Appl. Phys. Lett. 91, 124103 (2007).
[CrossRef]

2006 (1)

2005 (1)

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, Appl. Phys. Lett. 86, 044102 (2005).
[CrossRef]

2003 (1)

2000 (1)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

1998 (1)

1997 (1)

1959 (1)

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

Adachi, Y.

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, Appl. Phys. Lett. 86, 044102 (2005).
[CrossRef]

Antolini, R.

Araki1, T.

Arisaka, K.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, Nat. Meth. 8, 139 (2011).
[CrossRef]

Balla, N. K.

C. J. R. Sheppard, S. Rehman, N. K. Balla, E. Y. S. Yew, and T. W. Teng, Opt. Commun. 282, 4647 (2009).
[CrossRef]

Bewersdorf, J.

Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Bomzon, Z.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Chen, J.

Cheng, A.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, Nat. Meth. 8, 139 (2011).
[CrossRef]

Chichkov, B. N.

Choudhury, A.

Davidson, N.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Dehez, H.

Dong, X.

X. Dong, Z. Zhao, and X. Duan, Appl. Phys. Lett. 91, 124103 (2007).
[CrossRef]

Duan, X.

X. Dong, Z. Zhao, and X. Duan, Appl. Phys. Lett. 91, 124103 (2007).
[CrossRef]

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Froner, E.

Fujita, K.

Golshani, P.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, Nat. Meth. 8, 139 (2011).
[CrossRef]

Gonçalves, J. T.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, Nat. Meth. 8, 139 (2011).
[CrossRef]

Guo, H.

Hashimoto, M.

Hasman, E.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Hell, S. W.

Hinze, U.

Kano, H.

Kato, J.

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, Appl. Phys. Lett. 86, 044102 (2005).
[CrossRef]

Kawata, S.

T. Minamikawa, M. Hashimoto, K. Fujita, S. Kawata, and T. Araki1, Opt. Express 17, 9526 (2009).
[CrossRef] [PubMed]

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, Appl. Phys. Lett. 86, 044102 (2005).
[CrossRef]

Kim, W. C.

Koch, J.

Koninck, Y. De

Li, H.

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, Appl. Phys. B 99, 633 (2010).
[CrossRef]

Minamikawa, T.

Niu, H.

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, Appl. Phys. B 99, 633 (2010).
[CrossRef]

Obata, K.

Oron, R.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Park, K. S.

Park, N. C.

Park, Y. P.

Pavone, F. S.

Philip, G. M.

Piché, M.

Pick, R.

Portera-Cailliau, C.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, Nat. Meth. 8, 139 (2011).
[CrossRef]

Qi, J.

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, Appl. Phys. B 99, 633 (2010).
[CrossRef]

Qu, J.

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, Appl. Phys. B 99, 633 (2010).
[CrossRef]

Rehman, S.

C. J. R. Sheppard, S. Rehman, N. K. Balla, E. Y. S. Yew, and T. W. Teng, Opt. Commun. 282, 4647 (2009).
[CrossRef]

Richards, B.

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

Sacconi, L.

Shao, Y.

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, Appl. Phys. B 99, 633 (2010).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, S. Rehman, N. K. Balla, E. Y. S. Yew, and T. W. Teng, Opt. Commun. 282, 4647 (2009).
[CrossRef]

Sun, H.-B.

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, Appl. Phys. Lett. 86, 044102 (2005).
[CrossRef]

Taghizadeh, M. R.

Takeyasu, N.

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, Appl. Phys. Lett. 86, 044102 (2005).
[CrossRef]

Teng, T. W.

C. J. R. Sheppard, S. Rehman, N. K. Balla, E. Y. S. Yew, and T. W. Teng, Opt. Commun. 282, 4647 (2009).
[CrossRef]

Terakado, G.

Török, P.

Varga, P.

Viswanathan, N. K.

Wang, Y.

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, Appl. Phys. B 99, 633 (2010).
[CrossRef]

Watanabe, K.

Wolf, E.

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

Xu, G.

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, Appl. Phys. B 99, 633 (2010).
[CrossRef]

Yew, E. Y. S.

C. J. R. Sheppard, S. Rehman, N. K. Balla, E. Y. S. Yew, and T. W. Teng, Opt. Commun. 282, 4647 (2009).
[CrossRef]

Yoon, Y. J.

Zhao, Z.

X. Dong, Z. Zhao, and X. Duan, Appl. Phys. Lett. 91, 124103 (2007).
[CrossRef]

Zhuang, S.

Appl. Opt. (2)

Appl. Phys. B (1)

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, Appl. Phys. B 99, 633 (2010).
[CrossRef]

Appl. Phys. Lett. (3)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

X. Dong, Z. Zhao, and X. Duan, Appl. Phys. Lett. 91, 124103 (2007).
[CrossRef]

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, Appl. Phys. Lett. 86, 044102 (2005).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nat. Meth. (1)

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, Nat. Meth. 8, 139 (2011).
[CrossRef]

Opt. Commun. (1)

C. J. R. Sheppard, S. Rehman, N. K. Balla, E. Y. S. Yew, and T. W. Teng, Opt. Commun. 282, 4647 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Proc. R. Soc. London Ser. A (1)

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

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 (6)

Fig. 1
Fig. 1

Geometry of imaging of an aplanatic system.

Fig. 2
Fig. 2

Light intensities of the (a) transverse and (b) axial components and (c) the total light intensity at the focal plane for the case of n = 5 and n 1 = n 2 = 1 .

Fig. 3
Fig. 3

Normalized intensities of the left focus in the second row of Fig. 2c (dashed and solid curves) and the focus of the radially polarized beam (dotted curve) along the x and y axes.

Fig. 4
Fig. 4

Variation of I z / I t with Δ n for (a) a fixed n = 5 with various n 1 and (b) a fixed n 1 = 1.33 with various n.

Fig. 5
Fig. 5

Light intensities and polarizations of (a) the CVB used in Fig. 2 and (b) the annular beam at the entrance pupil.

Fig. 6
Fig. 6

Light intensities of the (a) transverse and (b) axial components and (c) the total light intensity at the focal plane for the annular beam.

Equations (9)

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

E o = [ x cos n ( φ + φ 0 ) + y p sin n ( φ + φ 0 ) ] h n A o ( h ) ,
cos n ( φ + φ 0 ) = 1 2 2 m k = 0 m C n k cos [ ( 2 m 2 k + 1 ) ( φ + φ 0 ) ] ,
sin n ( φ + φ 0 ) = 1 2 2 m k = 0 m ( 1 ) m + k C n k sin [ ( 2 m 2 k + 1 ) ( φ + φ 0 ) ] ,
E x ( P ) = A k = 0 m C n k [ ( 1 ) m k ( D + 2 cos Θ 2 + + D 2 cos Θ 2 + 2 A cos Θ 0 + ) p ( D + 2 cos Θ 2 + D 2 cos Θ 2 ) ] ,
E y ( P ) = A k = 0 m C n k [ ( 1 ) m k ( D + 1 sin Θ 2 + D 2 sin Θ 2 ) + p ( 2 A sin Θ 0 + D + 2 sin Θ 2 + D 2 sin Θ 2 ) ] ,
E z ( P ) = j 2 A k = 0 m C n k [ ( 1 ) m k ( B + 1 cos Θ 1 + B 1 cos Θ 1 ) p ( B + 1 cos Θ 1 + + B 1 cos Θ 1 ) ] ,
A = 0 Φ cos 1 2 θ 1 sin θ 1 ( T + T cos θ 1 ) R d θ 1 ,
B = 0 Φ cos 3 2 θ 1 sin θ 1 cos 1 θ 2 sin θ 2 T R d θ 1 ,
D = 0 Φ cos 1 2 θ 1 sin θ 1 ( T T cos θ 1 ) R d θ 1 ,

Metrics