Abstract

We have experimentally demonstrated the measurement of a tighter focal spot generated by a radially polarized narrow-width annular beam with the double-knife-edge method. The reconstructed spot profiles indicate that sharper focus cannot be achieved by shrinking the annular aperture further. The smallest focal spot (0.0711λ2) is obtained in experiment with an annular factor of 0.91. An apodization function has been introduced with the consideration of the diffraction effect, which achieves good agreement with the experimental data. Our result shows that the diffraction effect should be considered with small topography structures of the incident beam.

© 2013 Optical Society of America

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References

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2013 (1)

X. S. Xie, L. Li, S. C. Wang, Z. X. Wang, and J. Y. Zhou, AIP Adv. 3, 022110 (2013).
[CrossRef]

2011 (1)

A. Ambrosio and P. Maddalena, Appl. Phys. Lett. 98, 091108 (2011).
[CrossRef]

2010 (4)

2008 (2)

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

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

2007 (2)

2006 (2)

2005 (1)

2004 (1)

2003 (1)

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

2000 (2)

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

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

1959 (1)

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

Ambrosio, A.

A. Ambrosio and P. Maddalena, Appl. Phys. Lett. 98, 091108 (2011).
[CrossRef]

Brown, T. G.

Cheng, Y.

Chong, C. T.

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

Choudhury, A.

Deng, S. H.

DePaola, B. D.

Dorn, R.

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

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]

Gan, X. S.

Glockl, O.

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

Gu, M.

Hao, B.

Hao, X.

Hecht, B.

L. Novotny and B. Hecht, The Principle of Nano Optics (Cambridge University, 2003).

Jia, B. H.

Kang, H.

Kitamura, K.

Kozawa, Y.

Kuang, C. F.

Leger, J.

Lerman, G. M.

Leuchs, G.

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

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

Levy, U.

Li, L.

X. S. Xie, L. Li, S. C. Wang, Z. X. Wang, and J. Y. Zhou, AIP Adv. 3, 022110 (2013).
[CrossRef]

Li, R. X.

Liu, L.

Liu, X.

Lukyanchuk, B.

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

Maddalena, P.

A. Ambrosio and P. Maddalena, Appl. Phys. Lett. 98, 091108 (2011).
[CrossRef]

Noda, S.

Novotny, L.

L. Novotny and B. Hecht, The Principle of Nano Optics (Cambridge University, 2003).

Quabis, S.

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

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. A 253, 358 (1959).
[CrossRef]

Sakai, K.

Sato, S.

Shah, M. H.

Sheppard, C.

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

Sheppard, C. J. R.

Shi, L. P.

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

Trachy, M. L.

Veshapidze, G.

Wang, H. F.

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

Wang, S. C.

X. S. Xie, L. Li, S. C. Wang, Z. X. Wang, and J. Y. Zhou, AIP Adv. 3, 022110 (2013).
[CrossRef]

Wang, T. T.

Wang, Z. X.

X. S. Xie, L. Li, S. C. Wang, Z. X. Wang, and J. Y. Zhou, AIP Adv. 3, 022110 (2013).
[CrossRef]

Wolf, E.

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

Xie, X. S.

X. S. Xie, L. Li, S. C. Wang, Z. X. Wang, and J. Y. Zhou, AIP Adv. 3, 022110 (2013).
[CrossRef]

Xu, Z. Z.

Yew, E. Y. S.

Youngworth, K. S.

Zhou, J. Y.

X. S. Xie, L. Li, S. C. Wang, Z. X. Wang, and J. Y. Zhou, AIP Adv. 3, 022110 (2013).
[CrossRef]

AIP Adv. (1)

X. S. Xie, L. Li, S. C. Wang, Z. X. Wang, and J. Y. Zhou, AIP Adv. 3, 022110 (2013).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

A. Ambrosio and P. Maddalena, Appl. Phys. Lett. 98, 091108 (2011).
[CrossRef]

Nat. Photonics (1)

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

Opt. Commun. (1)

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

Opt. Express (7)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

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

Proc. R. Soc. A (1)

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

Other (1)

L. Novotny and B. Hecht, The Principle of Nano Optics (Cambridge University, 2003).

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup of the focused light beam measurement.

Fig. 2.
Fig. 2.

Transmitting images (left column), reconstructed profiles (center column), and simulation profiles (right column) of the focal spots. The annular factor are (a) 0, (b) 0.45, (c) 0.91, and (d) 0.98, respectively. The insets in (a1), (b1), (c1), and (d1) are the corresponding apodization function Pd(θ).

Fig. 3.
Fig. 3.

Calculated spot sizes for three types of RP beams compared with the experimental result.

Equations (5)

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Eρ(ρ,z)=A0α2Pd(θ)cos1/2θsin2θJ1(kρsinθ)exp(2ikzsinθ)dθEz(ρ,z)=2iA0α2Pd(θ)cos1/2θsin2θJ0(kρsinθ)exp(2ikzsinθ)dθ,
P(x,y)=P(θ)=P0(θ)T(θ)=exp[(βsinθsinα2)2]T(θ),
T(θ)={0(0θα1)1(α1<θα2),
(kx,ky;0)=14π2+P(x,y)exp[i(kxx+kyy)]dxdy.
Pd(θ)=Pd(x,y,z)=+(kx,ky;0)exp[i(kxx+kyy)]dkxdky.

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