Abstract

A needle of strong longitudinally polarized field with homogeneous intensity along the optical axis, long depth of focus, and subdiffraction beam size can be generated by focusing a radially polarized light with a high-NA lens and a diffractive optical element (DOE) with belts. A method combining the global-search-optimization algorithm and the tight focusing properties of the radially polarized light is proposed to design the DOE. Based on the tight focusing properties, the light incident on the lens is divided into two parts: areas A and B. We discover that the longitudinal field in the focal region is mainly dependent on the number of belts in area B but not the total number of belts in the DOE.

© 2010 Optical Society of America

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

G. M. Lerman and U. Levy, Opt. Express 16, 4567 (2008).
[CrossRef] [PubMed]

2007

E. Y. S. Yew and C. J. R. Sheppard, Opt. Commun. 275, 453 (2007).
[CrossRef]

2006

W. Chen and Q. Zhan, Opt. Commun. 265, 411 (2006).
[CrossRef]

2004

N. Hayazawa, Y. Saito, and S. Kawata, Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

2003

2001

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

2000

K. Youngworth and T. Brown, Opt. Express 7, 77 (2000).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

1999

1997

1996

1994

1990

L. Cicchitelli, H. Hora, and R. Postle, Phys. Rev. A 41, 3727 (1990).
[CrossRef] [PubMed]

1959

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

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

Biss, D. P.

Brown, T.

Brown, T. G.

D. P. Biss and T. G. Brown, Opt. Lett. 28, 923 (2003).
[CrossRef] [PubMed]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

Chen, W.

W. Chen and Q. Zhan, Opt. Commun. 265, 411 (2006).
[CrossRef]

Chong, C. T.

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

Cicchitelli, L.

L. Cicchitelli, H. Hora, and R. Postle, Phys. Rev. A 41, 3727 (1990).
[CrossRef] [PubMed]

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Glockl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Hall, D. G.

Hayazawa, N.

N. Hayazawa, Y. Saito, and S. Kawata, Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

Hora, H.

L. Cicchitelli, H. Hora, and R. Postle, Phys. Rev. A 41, 3727 (1990).
[CrossRef] [PubMed]

Jordan, R. H.

Kawata, S.

N. Hayazawa, Y. Saito, and S. Kawata, Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

Lerman, G. M.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Levy, U.

Liu, C.

Lukyanchuk, B.

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

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

Postle, R.

L. Cicchitelli, H. Hora, and R. Postle, Phys. Rev. A 41, 3727 (1990).
[CrossRef] [PubMed]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Richards, B.

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

Saito, Y.

N. Hayazawa, Y. Saito, and S. Kawata, Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

Sheppard, C.

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

Sheppard, C. J. R.

E. Y. S. Yew and C. J. R. Sheppard, Opt. Commun. 275, 453 (2007).
[CrossRef]

C. J. R. Sheppard, Opt. Lett. 24, 505 (1999).
[CrossRef]

Shi, L.

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

Sun, C.

Wang, H.

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

Wolf, E.

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

Xiao, M.

Yew, E. Y. S.

E. Y. S. Yew and C. J. R. Sheppard, Opt. Commun. 275, 453 (2007).
[CrossRef]

Youngworth, K.

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

Zhan, Q.

W. Chen and Q. Zhan, Opt. Commun. 265, 411 (2006).
[CrossRef]

Appl. Phys. Lett.

N. Hayazawa, Y. Saito, and S. Kawata, Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

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

Opt. Commun.

E. Y. S. Yew and C. J. R. Sheppard, Opt. Commun. 275, 453 (2007).
[CrossRef]

W. Chen and Q. Zhan, Opt. Commun. 265, 411 (2006).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

L. Cicchitelli, H. Hora, and R. Postle, Phys. Rev. A 41, 3727 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

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 (4)

Fig. 1
Fig. 1

The ratio of the peak intensity of the longitudinal and radial component field in the focal plane of a 0.95 NA lens illuminated by a radially polarized BG beam (solid curve). The dotted line means | E z | max 2 = | E r | max 2 . For a radially polarized BG beam, | E z | max 2 equals | E r | max 2 at R = R 0 ( R 0 = 0.5293 for a 0.95 NA lens). The boundary of areas A and B is the vertical dotted-dashed line R = R 0 .

Fig. 2
Fig. 2

(a) Schematic of focusing of a radially polarized BG beam with a DOE and high NA lens. The focal plane of the focusing lens is at z = 0 . (b) Phase of a four-belt DOE in the x y plane. Phases in the white and gray areas are 0 and π, respectively. The dashed circle with radius R 0 divides the DOE into two parts: areas A and B.

Fig. 3
Fig. 3

The electric density distributions in the y z plane after the phase modulation of DOE. (a) Radial component. (b) Longitudinal component. (c) Total electric energy distribution. (d) The radial (dashed curve), longitudinal (dotted-dashed curve), and total (solid curve) electric fields in the focal plane.

Fig. 4
Fig. 4

Phase of DOE with belts. Phases in the white and gray areas are 0 and π, respectively. The dashed circle with radius R 0 is the boundary of area A ( R < R 0 ) and area B ( R > R 0 ) . (a) A three-belt DOE with R 1 = 0.4635 and R 2 = 0.6966 . (b) A five-belt DOE with R 1 = 0.2042 , R 2 = 0.3252 , R 3 = 0.5084 , and R 4 = 0.7111 . (c) A four-belt DOE with R 1 = 0.3904 , R 2 = 0.5923 , and R 3 = 0.7682 . The belt ( R 1 < R < R 2 ) is divided into two belts by the dashed circle, resulting two belts in area A and three in area B.

Equations (2)

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l 0 ( θ ) = J 1 ( 2 β 1   sin   θ sin   α ) exp [ ( β 2   sin   θ sin   α ) 2 ] ,
R 1 = 0.3420 ,     R 2 = 0.7205 ,     with   fixed   R 0 = 0.5293.

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