Abstract

The properties of circularly polarized vortex beams in cylindrical polarization bases are studied. A circularly polarized vortex beam is decomposed into radial and azimuthal polarization. With the proper combination of vortex charge and the handedness of the circular polarization, a focal field with an extremely strong longitudinal component as well as a flat-topped profile can be obtained. The cylindrical decomposition also sheds light on the connections between orbital angular momentum and the spin of the light beams.

© 2006 Optical Society of America

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References

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  1. L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol. XXXIX, pp. 291-372.
  2. J. F. Nye, Proc. R. Soc. London Ser. A 387, 105 (1983).
    [Crossref]
  3. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 27, 285 (2002).
    [Crossref]
  4. R. Dorn, S. Qubis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
    [Crossref] [PubMed]
  5. C. Sun and C. Liu, Opt. Lett. 28, 99 (2003).
    [Crossref] [PubMed]
  6. Q. Zhan and J. R. Leger, Opt. Express 10, 324 (2002).
    [PubMed]
  7. Y. Q. Zhao, Q. Zhan, Y. L. Zhang, and Y.-P. Li, Opt. Lett. 30, 848 (2005).
    [Crossref] [PubMed]
  8. E. Wolf, Proc. R. Soc. London Ser. A 253, 349 (1959).
    [Crossref]
  9. B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
    [Crossref]
  10. K. S. Youngworth and T. G. Brown, Opt. Express 7, 77 (2000).
    [Crossref] [PubMed]
  11. M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, 2000).
  12. A. T. O'Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
    [Crossref] [PubMed]
  13. E. J. Sanchez, L. Novotny, and X. S. Xie, Phys. Rev. Lett. 82, 4014 (1999).
    [Crossref]
  14. Q. Zhan, Opt. Express 12, 3377 (2004).
    [Crossref] [PubMed]

2005 (1)

2004 (1)

2003 (2)

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

C. Sun and C. Liu, Opt. Lett. 28, 99 (2003).
[Crossref] [PubMed]

2002 (3)

2000 (1)

1999 (1)

E. J. Sanchez, L. Novotny, and X. S. Xie, Phys. Rev. Lett. 82, 4014 (1999).
[Crossref]

1983 (1)

J. F. Nye, Proc. R. Soc. London Ser. A 387, 105 (1983).
[Crossref]

1959 (2)

E. Wolf, Proc. R. Soc. London Ser. A 253, 349 (1959).
[Crossref]

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

Allen, L.

A. T. O'Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[Crossref] [PubMed]

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol. XXXIX, pp. 291-372.

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol. XXXIX, pp. 291-372.

Biener, G.

Bomzon, Z.

Brown, T. G.

Dorn, R.

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

Gu, M.

M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, 2000).

Hasman, E.

Kleiner, V.

Leger, J. R.

Leuchs, G.

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

Li, Y.-P.

Liu, C.

Mac Vicar, I.

A. T. O'Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[Crossref] [PubMed]

Novotny, L.

E. J. Sanchez, L. Novotny, and X. S. Xie, Phys. Rev. Lett. 82, 4014 (1999).
[Crossref]

Nye, J. F.

J. F. Nye, Proc. R. Soc. London Ser. A 387, 105 (1983).
[Crossref]

O'Neil, A. T.

A. T. O'Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[Crossref] [PubMed]

Padgett, M. J.

A. T. O'Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[Crossref] [PubMed]

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol. XXXIX, pp. 291-372.

Qubis, S.

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

Richards, B.

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

Sanchez, E. J.

E. J. Sanchez, L. Novotny, and X. S. Xie, Phys. Rev. Lett. 82, 4014 (1999).
[Crossref]

Sun, C.

Wolf, E.

E. Wolf, Proc. R. Soc. London Ser. A 253, 349 (1959).
[Crossref]

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

Xie, X. S.

E. J. Sanchez, L. Novotny, and X. S. Xie, Phys. Rev. Lett. 82, 4014 (1999).
[Crossref]

Youngworth, K. S.

Zhan, Q.

Zhang, Y. L.

Zhao, Y. Q.

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. Lett. (3)

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

A. T. O'Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[Crossref] [PubMed]

E. J. Sanchez, L. Novotny, and X. S. Xie, Phys. Rev. Lett. 82, 4014 (1999).
[Crossref]

Proc. R. Soc. London Ser. A (2)

J. F. Nye, Proc. R. Soc. London Ser. A 387, 105 (1983).
[Crossref]

E. Wolf, Proc. R. Soc. London Ser. A 253, 349 (1959).
[Crossref]

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

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

Other (2)

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol. XXXIX, pp. 291-372.

M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, 2000).

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Figures (4)

Fig. 1
Fig. 1

Calculated two-dimensional distribution of E 2 for a highly focused LHC polarized vortex beam with charge m = 0 : (a) total field, (b) longitudinal component E z 2 , (c) transversal component E t 2 , (d) line scan of the focus. The focus is dominated by the transversal field.

Fig. 2
Fig. 2

Calculated two-dimensional distribution of E 2 for a highly focused LHC polarized vortex beam with charge m = 1 : (a) total field, (b) longitudinal component E z 2 , (c) transversal component E t 2 , (d) line scan of the focus. A strong longitudinal field is generated by the radial component of the vortex beam.

Fig. 3
Fig. 3

Flat-topped focusing with a highly focused LHC polarized vortex beam with charge m = 1 : (a) total field, (b) longitudinal component E z 2 , (c) transversal component E t 2 , (d) line scan of the focus, showing that flat-topped focus can be obtained.

Fig. 4
Fig. 4

Calculated two-dimensional distribution of E 2 for a highly focused LHC polarized vortex beam with charge m = 2 : (a) total field, (b) longitudinal component E z 2 , (c) transversal component E t 2 , (d) line scan of the focus. It can be seen that the field strength distribution is identical to that of Fig. 1.

Equations (5)

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E LHC = P ( r ) ( e x + j e y ) 2 = P ( r ) [ ( cos φ e r sin φ e φ ) + j ( sin φ e r + cos φ e φ ) ] 2 = P ( r ) e j φ ( e r + j e φ ) 2 ,
E ρ ( ρ s , ϕ s , z ) = A exp [ j ( m + 1 ) ϕ s ] j m + 1 0 α cos 1 2 ( θ ) sin θ cos θ P 0 ( θ ) [ J m + 2 ( k ρ s sin θ ) + j 2 ( m + 1 ) J m ( k ρ s sin θ ) ] exp ( j k z s cos θ ) d θ ,
E z ( ρ s , ϕ s , z ) = A exp [ j ( m + 1 ) ϕ s ] j m 0 α cos 1 2 ( θ ) sin 2 θ P 0 ( θ ) [ J m + 1 ( k ρ s sin θ ) + j 2 ( m + 1 ) J ( m + 1 ) ( k ρ s sin θ ) ] exp ( i k z s cos θ ) d θ ,
E ϕ ( ρ s , ϕ s , z ) = A exp [ j ( m + 1 ) ϕ s ] j m 0 α cos 1 2 ( θ ) sin θ P 0 ( θ ) [ J m + 2 ( k ρ s sin θ ) + j 2 ( m + 1 ) J m ( k ρ s sin θ ) ] exp ( i k z s cos θ ) d θ ,
J z = [ 1 2 ( l p , r + l p , a ) ] ω .

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