Abstract

The focal electric fields for a 4π high numerical aperture (NA) focusing system with both the doughnut and higher-order Laguerre–Gaussian (LG) radially polarized (RP) beams are investigated in the case of NA=1, and the full width at half-maximum values of the focal spots are calculated. Compared with the single-lens high NA focusing configuration, a sharper spot, whose size is reduced efficiently in the transverse as well as the axial direction, can be formed. Such size reduction is attributed to not only the destruction interference of the longitudinal component caused by the π phase shift between any two adjacent rings of the incident higher-order LG RP beam coming from one particular direction but also the perfect destruction interference of the radial component formed by the two counter-propagating incident beams.

© 2013 Optical Society of America

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  1. Y. Zhang and J. Bai, Opt. Express 17, 3698 (2009).
    [CrossRef]
  2. K. Lou, S. X. Qian, X. L. Wang, Y. Li, B. Gu, C. Tu, and H. T. Wang, Opt. Express 20, 120 (2012).
    [CrossRef]
  3. P. L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
    [CrossRef]
  4. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef]
  5. Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, Opt. Express 19, 15947 (2011).
    [CrossRef]
  6. Y. Zhang, T. Suyama, and B. Ding, Opt. Lett. 35, 1281 (2010).
    [CrossRef]
  7. B. Richards and E. Wolf, Proc. R. Soc. A 253, 358 (1959).
    [CrossRef]
  8. K. S. Youngworth and T. G. Brown, Opt. Express 7, 77 (2000).
    [CrossRef]
  9. K. Kitamura, K. Sakai, and S. Noda, Opt. Express 18, 4518 (2010).
    [CrossRef]
  10. H. Dehez, A. April, and M. Piché, Opt. Express 20, 14891 (2012).
    [CrossRef]
  11. L. Yang, X. Xie, S. Wang, and J. Zhou, Opt. Lett. 38, 1331 (2013).
    [CrossRef]
  12. H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
    [CrossRef]
  13. H. Guo, X. Weng, M. Jiang, Y. Zhao, G. Sui, Q. Hu, Y. Wang, and S. Zhuang, Opt. Express 21, 5363 (2013).
    [CrossRef]
  14. C. C. Sun and C. K. Liu, Opt. Lett. 28, 99 (2003).
    [CrossRef]
  15. Y. Kozawa and S. Sato, J. Opt. Soc. Am. A 24, 1793 (2007).
    [CrossRef]
  16. S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
    [CrossRef]
  17. N. Bokor and N. Davidson, Opt. Lett. 29, 1968 (2004).
    [CrossRef]
  18. J. Stadler, C. Stanciu, C. Stupperich, and J. A. Meixner, Opt. Lett. 33, 681 (2008).
    [CrossRef]
  19. Z. Chen and D. Zhao, Opt. Lett. 37, 1286 (2012).
    [CrossRef]
  20. S. W. Hell, S. Lindek, and E. H. K. Stelzer, J. Mod. Opt. 41, 675 (1994).
    [CrossRef]
  21. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
    [CrossRef]
  22. Y. Kozawa and S. Sato, J. Opt. Soc. Am. A 27, 399 (2010).
    [CrossRef]

2013 (2)

2012 (3)

2011 (1)

2010 (4)

2009 (1)

2008 (2)

J. Stadler, C. Stanciu, C. Stupperich, and J. A. Meixner, Opt. Lett. 33, 681 (2008).
[CrossRef]

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

2007 (1)

2004 (1)

2003 (2)

C. C. Sun and C. K. Liu, Opt. Lett. 28, 99 (2003).
[CrossRef]

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]

1994 (2)

S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
[CrossRef]

S. W. Hell, S. Lindek, and E. H. K. Stelzer, J. Mod. Opt. 41, 675 (1994).
[CrossRef]

1959 (1)

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

April, A.

Bai, J.

Bokor, N.

Brown, T. G.

Chen, Z.

Chong, C. T.

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

Cremer, C.

S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
[CrossRef]

Davidson, N.

Dehez, H.

Ding, B.

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]

Fortin, P. L.

P. L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
[CrossRef]

Glockl, O.

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

Gu, B.

Guo, H.

Hashimoto, N.

Hell, S. W.

S. W. Hell, S. Lindek, and E. H. K. Stelzer, J. Mod. Opt. 41, 675 (1994).
[CrossRef]

S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
[CrossRef]

Hibi, T.

Horanai, H.

Hu, Q.

Jiang, M.

Kitamura, K.

Kozawa, Y.

Kurihara, 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]

Li, Y.

Lindek, S.

S. W. Hell, S. Lindek, and E. H. K. Stelzer, J. Mod. Opt. 41, 675 (1994).
[CrossRef]

S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
[CrossRef]

Liu, C. K.

Lou, K.

Lukyanchuk, B.

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

Meixner, J. A.

Nemoto, T.

Noda, S.

Piché, M.

H. Dehez, A. April, and M. Piché, Opt. Express 20, 14891 (2012).
[CrossRef]

P. L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
[CrossRef]

Qian, S. X.

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, A.

Sato, S.

Sheppard, C.

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

Shi, L.

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

Stadler, J.

Stanciu, C.

Stelzer, E. H. K.

S. W. Hell, S. Lindek, and E. H. K. Stelzer, J. Mod. Opt. 41, 675 (1994).
[CrossRef]

Stelzer, E. K.

S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
[CrossRef]

Stupperich, C.

Sui, G.

Sun, C. C.

Suyama, T.

Tu, C.

Varin, C.

P. L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
[CrossRef]

Wang, H.

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

Wang, H. T.

Wang, S.

Wang, X. L.

Wang, Y.

Weng, X.

Wolf, E.

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

Xie, X.

Yang, L.

Yokoyama, H.

Youngworth, K. S.

Zhang, Y.

Zhao, D.

Zhao, Y.

Zhou, J.

Zhuang, S.

Appl. Phys. Lett. (1)

S. W. Hell, S. Lindek, C. Cremer, and E. K. Stelzer, Appl. Phys. Lett. 64, 1335 (1994).
[CrossRef]

J. Mod. Opt. (1)

S. W. Hell, S. Lindek, and E. H. K. Stelzer, J. Mod. Opt. 41, 675 (1994).
[CrossRef]

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

J. Phys. B (1)

P. L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
[CrossRef]

Nat. Photonics (1)

H. Wang, L. 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. (6)

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]

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Figures (7)

Fig. 1.
Fig. 1.

Diagram of the 4π focusing system illuminated by two counter-propagating higher-order LG RP beams. The short arrows indicate the directions of the instantaneous radial polarization vectors of the incident beams.

Fig. 2.
Fig. 2.

Calculated intensity distributions of (a) the axial component, (b) the radial component, and (c) and the total in rz plane under single-lens tight focusing with NA=1 for the R-TEM01* beam.

Fig. 3.
Fig. 3.

Calculated intensity distributions of the (a) axial component, (b) the radial component, and (c) and the total in rz plane under single-lens tight focusing with NA=1 for the higher-order LG RP (R-TEM11*) beam.

Fig. 4.
Fig. 4.

Calculated intensity profiles in (a) the focal plane and (b) along the optical axis for the R-TEM01* (dotted curve), R-TEM11* (dashed–dotted curve), R-TEM31* (dashed curve), and R-TEM51* (solid curve) beams under single-lens tight focusing with NA=1. The peak intensity for each mode is normalized to 1.

Fig. 5.
Fig. 5.

Calculated intensity distributions of (a) the axial component, (b) the radial component, and (c) the total in rz plane under the 4π tight focusing with NA=1 for the R-TEM01* beam.

Fig. 6.
Fig. 6.

Calculated intensity distributions of (a) the axial component, (b) the radial component, and (c) the total in the rz plane under the 4π tight focusing with NA=1 for the higher-order LG RP (R-TEM11*) beam.

Fig. 7.
Fig. 7.

Calculated intensity profiles in (a) the focal plane and (b) along the optical axis for the R-TEM01* (dotted curve), R-TEM11* (dashed–dotted curve), R-TEM31* (dashed curve), and R-TEM51* (solid curve) beams under the 4π tight focusing with NA=1. The peak intensity for each mode is normalized to 1.

Equations (4)

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E(r,z)=Ere^r+Eze^z,
Er(r,z)=A0αcosθsin(2θ)l(θ)J1(krsinθ)exp(ikzcosθ)dθ,Ez(r,z)=2iA0αcosθsin2θl(θ)J0(krsinθ)exp(ikzcosθ)dθ,
l(θ)=β2sinθsin2αexp[(βsinθsinα)2]Lp1[2(βsinθsinα)2].
E(r,z)=E1(r,z)+E2(r,z),

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