Abstract

We study the focusing properties of a double-ring-shaped azimuthally polarized beam through an annular high NA objective lens. It is shown that a subwavelength focal hole (0.5λ) with a quite long depth of focus (26λ) is achieved near the focus. This kind of nondiffracting focal hole is called dark channel, which may have applications in atom optical experiments, such as with atomic lenses, atom traps, and atom switches.

© 2011 Optical Society of America

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2011 (1)

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, Opt. Commun. 284, 1766 (2011).
[CrossRef]

2010 (4)

2009 (2)

Y. Zhang, X. Xu, and Y. Okuno, Opt. Commun. 282, 4481 (2009).
[CrossRef]

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

2008 (2)

2007 (1)

2006 (2)

2003 (1)

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, Appl. Phys. B 77, 11 (2003).
[CrossRef]

2002 (3)

2001 (2)

T. A. Klar, E. Engel, and S. W. Hell, Phys. Rev. E 64, 066613 (2001).
[CrossRef]

Y. Shin, K. Kim, J. Kim, H. Noh, and W. Jhe, Opt. Lett. 26, 119 (2001).
[CrossRef]

2000 (1)

1959 (1)

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

Ahmed, M. A.

Biener, G.

Bomzon, Z.

Brown, T. G.

Chen, B.

Chen, W.

Chizhik, A.

Chong, C. T.

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

Enderlein, J.

Engel, E.

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, Appl. Phys. B 77, 11 (2003).
[CrossRef]

T. A. Klar, E. Engel, and S. W. Hell, Phys. Rev. E 64, 066613 (2001).
[CrossRef]

Escamilla, B.

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

Graf, T.

Gutbrod, R.

Hao, X.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, Opt. Commun. 284, 1766 (2011).
[CrossRef]

X. Hao, C. Kuang, T. Wang, and X. Liu, Opt. Lett. 35, 3928 (2010).
[CrossRef] [PubMed]

Hasman, E.

Haus, J.

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

Hell, S. W.

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, Appl. Phys. B 77, 11 (2003).
[CrossRef]

T. A. Klar, E. Engel, and S. W. Hell, Phys. Rev. E 64, 066613 (2001).
[CrossRef]

Helseth, L. E.

L. E. Helseth, Opt. Commun. 257, 1 (2006).
[CrossRef]

L. E. Helseth, Opt. Commun. 212, 343 (2002).
[CrossRef]

Huang, K.

Huse, N.

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, Appl. Phys. B 77, 11 (2003).
[CrossRef]

Jhe, W.

Kang, X.

Khoptyar, D.

Kim, J.

Kim, K.

Klar, T. A.

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, Appl. Phys. B 77, 11 (2003).
[CrossRef]

T. A. Klar, E. Engel, and S. W. Hell, Phys. Rev. E 64, 066613 (2001).
[CrossRef]

Kleiner, V.

Korotkova, O.

Kozawa, Y.

Kraus, M.

Ku, Y.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, Opt. Commun. 284, 1766 (2011).
[CrossRef]

Kuang, C.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, Opt. Commun. 284, 1766 (2011).
[CrossRef]

X. Hao, C. Kuang, T. Wang, and X. Liu, Opt. Lett. 35, 3928 (2010).
[CrossRef] [PubMed]

Leger, J. R.

Li, Y.

Liu, X.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, Opt. Commun. 284, 1766 (2011).
[CrossRef]

X. Hao, C. Kuang, T. Wang, and X. Liu, Opt. Lett. 35, 3928 (2010).
[CrossRef] [PubMed]

Lukyanchuk, B.

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

Meixner, A. J.

Michalowski, A.

Noh, H.

Okuno, Y.

Y. Zhang, X. Xu, and Y. Okuno, Opt. Commun. 282, 4481 (2009).
[CrossRef]

Powers, P.

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

Pu, J.

Richards, B.

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

Sato, S.

Schleifenbaum, F.

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]

Shi, P.

Shin, Y.

Steiner, M.

Voll, A.

Wang, H.

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

Wang, T.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, Opt. Commun. 284, 1766 (2011).
[CrossRef]

X. Hao, C. Kuang, T. Wang, and X. Liu, Opt. Lett. 35, 3928 (2010).
[CrossRef] [PubMed]

Weber, R.

Wolf, E.

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

Xu, X.

Y. Zhang, X. Xu, and Y. Okuno, Opt. Commun. 282, 4481 (2009).
[CrossRef]

Youngworth, K. S.

Zhan, Q.

Zhang, X.

Zhang, Y.

Y. Zhang, X. Xu, and Y. Okuno, Opt. Commun. 282, 4481 (2009).
[CrossRef]

Zhou, R.

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

Appl. Phys. B (1)

E. Engel, N. Huse, T. A. Klar, and S. W. Hell, Appl. Phys. B 77, 11 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

R. Zhou, B. Escamilla, J. Haus, P. Powers, and Q. Zhan, Appl. Phys. Lett. 95, 191111 (2009).
[CrossRef]

Nat. Photon. (1)

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

Opt. Commun. (4)

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, Opt. Commun. 284, 1766 (2011).
[CrossRef]

L. E. Helseth, Opt. Commun. 257, 1 (2006).
[CrossRef]

L. E. Helseth, Opt. Commun. 212, 343 (2002).
[CrossRef]

Y. Zhang, X. Xu, and Y. Okuno, Opt. Commun. 282, 4481 (2009).
[CrossRef]

Opt. Express (6)

Opt. Lett. (5)

Phys. Rev. E (1)

T. A. Klar, E. Engel, and S. W. Hell, Phys. Rev. E 64, 066613 (2001).
[CrossRef]

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

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

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Figures (6)

Fig. 1
Fig. 1

Scheme for a double-ring-shaped azimuthally polarized beam focused by an annular high NA objective lens. The beam section of the incident beam is plotted in the left part of the figure, in which the arrows indicate the direction of the polarization.

Fig. 2
Fig. 2

Intensity distribution of the focused field near focus for the double-ring-shaped azimuthally polarized beam focused by a high NA annular lens. (a)  δ = 0 ; (b)  δ = 0.75 . The other parameters are β = 1.2 and NA = 0.6 .

Fig. 3
Fig. 3

Intensity distribution of the focal hole in the focal plane z = 0 . The orange-colored arrows in (a) and (b) indicate the polarization direction. (a)  δ = 0 ; (b)  δ = 0.75 ; (c) The intensity distribution for δ = 0 (solid curve) and δ = 0.75 (dashed curve). The other parameters are the same as in Fig. 2.

Fig. 4
Fig. 4

FWHM of the dark channel along the optical axis z. δ = 0 (solid curve), and δ = 0.75 (dashed curve). The other parameters are the same as in Fig. 2.

Fig. 5
Fig. 5

Intensity distribution in the x z plane. (a)  NA = 0.8 , (b)  NA = 0.9 . δ = 0.75 . The other parameters are the same as in Fig. 2.

Fig. 6
Fig. 6

(a) Depth of focus and (b) FWHM of the focal hole in the focal plane as a function of NA. δ = 0.75 , β = 1.2 (solid curve), and β = 1.3 (dashed curve). The other parameters are the same as Fig. 2.

Equations (2)

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E ( r , φ , z ) = [ E r E φ E Z ] = [ 0 2 A δ · α α cos 1 2 θ sin θ A ( θ ) J 1 ( k r sin θ ) e i k z cos θ d θ 0 ] ,
A ( θ ) = β 2 sin θ sin 2 α exp [ ( β sin θ sin α ) 2 ] L p 1 [ 2 ( β sin θ sin α ) 2 ] .

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