Abstract

We demonstrate that a sharper focal spot area can be generated (0.147λ2) by using an azimuthally polarized beam propagating through a vortex 02π phase plate than for radial polarization (0.17λ2) or for linear polarization (0.26λ2) under the same condition. Further research illustrates that such optimistic results can still be expected when condition limitations are liberalized. This will facilitate new approaches to get superresolution in confocal systems.

© 2010 Optical Society of America

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References

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

2007

2004

2003

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

2000

K. S. Youngworth and T. G. 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]

1996

1959

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

Bokor, N.

Brown, T. G.

Chong, C. T.

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

Davidson, N.

Dorn, R.

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

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]

Hell, S. W.

S. W. Hell, Cytom. Part A 71A, 742 (2007).

Jacket, S.

Leuchs, G.

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

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

Lukyanchuk, B.

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

Lumer, Y.

Machavariani, G.

Meir, A.

Moshe, I.

Qiu, L. R.

Quabis, S.

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

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. Roy. Soc. Lond. Ser. A 253, 358 (1959).
[CrossRef]

Schadt, M.

Sheppard, C.

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

Shi, L. P.

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

Stalder, M.

Tan, J. B.

Wang, H. F.

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

Wolf, E.

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

Youngworth, K. S.

Zhan, Q.

Zhao, W. Q.

Adv. Opt. Photon.

Cytom. Part A

S. W. Hell, Cytom. Part A 71A, 742 (2007).

Nat. Photon.

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

Opt. Commun.

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

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

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

Proc. Roy. Soc. Lond. Ser. A

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

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Figures (4)

Fig. 1
Fig. 1

Schematic of the focus system. A classic structure, including the phase plate and the AL, is shown.

Fig. 2
Fig. 2

Normalized intensity at cross sections at the focal plane along the radial direction for apertures with different annular factors: (a) 0, (b) 0.5, (c) 0.92, and (d) 0.95.

Fig. 3
Fig. 3

Relationship between the annular factor and focal spot size with different beam shapes of the incidence light under NA = 1.4 .

Fig. 4
Fig. 4

Bars of areas of the focal spot size by various polarized beams: azimuthally polarized beam encoded by the vortex 0 2 π phase plate ( 0.147 λ 2 ), radially polarized beam ( 0.17 λ 2 ), circularly polarized beam ( 0.229 λ 2 ), and linearly polarized beam ( 0.26 λ 2 ) under NA = 0.9 and ξ = 0.92 , respectively. The radial and linear polarization mentioned above correspond to the Dorn result in [1].

Equations (7)

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E = E · e i Δ α ( r , φ ) = E · e i φ ,
E ( r 2 , φ 2 , z 2 ) = i C Ω sin ( θ ) A 1 ( θ , φ ) A 2 ( θ , φ ) [ p x p y p z ] e i Δ α ( θ , φ ) e i k n ( z 2 cos θ + r 2 sin θ cos ( φ φ 2 ) ) d θ d φ ,
A 1 ( θ , φ ) = exp [ β 0 2 ( sin θ sin α ) 2 ] J 1 ( 2 β 0 sin θ sin α ) ,
A 2 ( θ , φ ) = a ( θ ) V ( θ , φ ) ,
a ( θ ) = cos θ ,
V ( θ , φ ) = [ 1 + ( cos θ 1 ) cos 2 φ ( cos θ 1 ) cos φ sin φ sin θ cos φ ( cos θ 1 ) cos φ sin φ 1 + ( cos θ 1 ) sin 2 φ sin θ sin φ sin θ cos φ sin θ sin φ cos θ ] .
ξ = r inner r outer .

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