Abstract

The vectorial Debye integral shows that tightly focused Laguerre–Gaussian (LG) beams have a residual intensity at the focal point for linear polarization, for a topological charge of m=1 and 2. We measured the shapes of linearly and circularly polarized LG beams and found that a central intensity appeared at m=1 and 2 for linear and right-handed circular polarization, however, it is completely canceled for left-handed circular polarization. In general, when the orbital angular momentum of the LG beam is parallel to the spin angular momentum of the photons, zero intensity is always achieved at the focus.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Allen, M. V. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  2. S. Furhapter, A. Esacher, S. Bernet, and M. Ritsch-Marte, Opt. Express 13, 689 (2005).
    [CrossRef] [PubMed]
  3. Y. Iketaki, T. Watanabe, N. Bokor, T. Omatsu, T. Hiraga, K. Yamamoto, and M. Fujii, Appl. Spectrosc. 61, 6 (2007).
    [CrossRef] [PubMed]
  4. P. Török and P. R. T. Munro, Opt. Express 12, 3605 (2004).
    [CrossRef] [PubMed]
  5. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
    [CrossRef]
  6. J. Yin and Y. Zhu, J. Appl. Phys. 85, 2473 (1999).
    [CrossRef]
  7. H. He, N. Hechenberg, C. Smith, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
    [CrossRef]
  8. B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
    [CrossRef]
  9. N. Bokor, Y. Iketaki, T. Watanabe, and M. Fujii, Opt. Express 13, 10440 (2005).
    [CrossRef] [PubMed]
  10. G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. Friesem, Opt. Commun. 209, 265 (2002).
    [CrossRef]

2007 (1)

2005 (2)

2004 (1)

2002 (1)

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. Friesem, Opt. Commun. 209, 265 (2002).
[CrossRef]

1999 (1)

J. Yin and Y. Zhu, J. Appl. Phys. 85, 2473 (1999).
[CrossRef]

1997 (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

1995 (1)

H. He, N. Hechenberg, C. Smith, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

1992 (1)

L. Allen, M. V. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

1959 (1)

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

Allen, L.

L. Allen, M. V. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Beijersbergen, M. V.

L. Allen, M. V. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Bernet, S.

Blit, S.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. Friesem, Opt. Commun. 209, 265 (2002).
[CrossRef]

Bokor, N.

Davidson, N.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. Friesem, Opt. Commun. 209, 265 (2002).
[CrossRef]

Esacher, A.

Friesem, A.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. Friesem, Opt. Commun. 209, 265 (2002).
[CrossRef]

Fujii, M.

Furhapter, S.

Hasman, E.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. Friesem, Opt. Commun. 209, 265 (2002).
[CrossRef]

He, H.

H. He, N. Hechenberg, C. Smith, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Hechenberg, N.

H. He, N. Hechenberg, C. Smith, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Hiraga, T.

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Iketaki, Y.

Ishaaya, A. A.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. Friesem, Opt. Commun. 209, 265 (2002).
[CrossRef]

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Machavariani, G.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. Friesem, Opt. Commun. 209, 265 (2002).
[CrossRef]

Munro, P. R. T.

Omatsu, T.

Richards, B.

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

Ritsch-Marte, M.

Rubinsztein-Dunlop, H.

H. He, N. Hechenberg, C. Smith, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Smith, C.

H. He, N. Hechenberg, C. Smith, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. V. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Török, P.

Watanabe, T.

Woerdman, J. P.

L. Allen, M. V. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Wolf, E.

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

Yamamoto, K.

Yin, J.

J. Yin and Y. Zhu, J. Appl. Phys. 85, 2473 (1999).
[CrossRef]

Zhu, Y.

J. Yin and Y. Zhu, J. Appl. Phys. 85, 2473 (1999).
[CrossRef]

Appl. Spectrosc. (1)

J. Appl. Phys. (1)

J. Yin and Y. Zhu, J. Appl. Phys. 85, 2473 (1999).
[CrossRef]

J. Mod. Opt. (1)

H. He, N. Hechenberg, C. Smith, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Opt. Commun. (1)

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. Friesem, Opt. Commun. 209, 265 (2002).
[CrossRef]

Opt. Express (3)

Phys. Rev. A (1)

L. Allen, M. V. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

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

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Experimental setup for measuring the profile of the focused LG beam in the focal plane. PMT, photomultiplier tube; PC, personal computer; QWP, quarter-wave plate. The geometry of the fabricated SPP is shown for the (b) 1st-order and (c) 2nd-order LG beam. The surfaces of the quartz plates are divided into eight areas spokewise around the center. Each area is etched so that the optical path length changes stepwise from 0 to m λ at a wavelength of 599 nm , with (b) m = 1 and (c) m = 2 .

Fig. 2
Fig. 2

Calculated intensity contour maps and profiles of the focused 1st-order LG beam for (a) LC polarization, (b) linear polarization, and (c) RC polarization.

Fig. 3
Fig. 3

Calculated intensity contour maps and profiles of the focused 2nd-order beam for (a) LC polarization, (b) linear polarization, and (c) RC polarization.

Fig. 4
Fig. 4

Measured intensity contour maps and profiles of the focused 1st- and 2nd-order LG beams: (a)–(c) 1st-order LG beam, (d)–(f) 2nd-order LG beam. The polarizations are (a) and (d) LC, (b) and (e) linear, (c) and (f) RC.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

E = ( E x E y E z ) = E 1 + e i φ E 2 ,
E 1 = ( E 1 x E 1 y E 1 z ) = 0 α d θ E 0 ( θ ) cos θ sin θ 0 2 π d ϕ e i m ϕ ( cos θ cos 2 ϕ sin 2 ϕ ( 1 cos θ ) sin ϕ cos ϕ sin θ cos ϕ ) ,
E 2 = ( E 2 x E 2 y E 2 z ) = 0 α d θ E 0 ( θ ) cos θ sin θ 0 2 π d ϕ e i m ϕ ( ( 1 cos θ ) sin ϕ cos ϕ cos θ sin 2 ϕ cos 2 ϕ sin θ sin ϕ ) ,
m = 1 : E 1 = ( 0 0 π C ) , m = 2 : E 1 = ( π ( A B ) 2 i π ( A B ) 2 0 ) ,
m = 1 : E 2 = ( 0 0 i π C ) , m = 2 : E 2 = ( i π ( A B ) 2 π ( A B ) 2 0 ) .
A = 0 α E 0 ( θ ) cos θ sin θ cos θ d θ ,
B = 0 α E 0 ( θ ) cos θ sin θ d θ ,
C = 0 α E 0 ( θ ) cos θ sin 2 θ d θ .
m = 1 : E R = ( 0 0 2 π C ) ,
m = 2 : E R = ( π ( A B ) i π ( A B ) 0 ) ,
m 3 : E R = ( 0 0 0 ) ,

Metrics