Abstract

We experimentally generate optical vortices in the output beam of a 20-fs Ti:sapphire laser. Screw phase dislocations are imposed on the spectral components of the short pulses by aligning a computer-generated hologram in a dispersionless 4f setup.

© 2004 Optical Society of America

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  1. J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 190 (1974).
    [CrossRef]
  2. N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
    [CrossRef] [PubMed]
  3. G. Pretzler, A. Kasper, and K. J. Witte, Appl. Phys. B 70, 1 (2000).
    [CrossRef]
  4. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
    [CrossRef]
  5. D. V. Petrov, F. Canal, and L. Torner, Opt. Commun. 143, 265 (1997).
    [CrossRef]
  6. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
    [CrossRef]
  7. D. Ganic, X. Gan, M. Gu, M. Hain, S. Somalingam, S. Stankovic, and T. Tschudi, Opt. Lett. 27, 1351 (2002).
    [CrossRef]
  8. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
    [CrossRef]
  9. M. B. Danailov and I. P. Christov, J. Mod. Opt. 36, 725 (1989).
    [CrossRef]
  10. W.-H. Lee, in Progress in Optics XVI, E. Wolf, ed. (ElsevierNorth-Holland, Amsterdam, 1978), p. 119.
    [CrossRef]
  11. F. Lindner, G. G. Paulus, F. Grasbon, A. Dreischuh, and H. Walther, IEEE J. Quantum Electron. 38, 1465 (2002).
    [CrossRef]
  12. J. Leach and M. J. Padgett, New J. Phys. 5, 154.1 (2003).
    [CrossRef]
  13. M. V. Berry, New J. Phys. 4, 66.1 (2002).

2003 (1)

J. Leach and M. J. Padgett, New J. Phys. 5, 154.1 (2003).
[CrossRef]

2002 (3)

M. V. Berry, New J. Phys. 4, 66.1 (2002).

F. Lindner, G. G. Paulus, F. Grasbon, A. Dreischuh, and H. Walther, IEEE J. Quantum Electron. 38, 1465 (2002).
[CrossRef]

D. Ganic, X. Gan, M. Gu, M. Hain, S. Somalingam, S. Stankovic, and T. Tschudi, Opt. Lett. 27, 1351 (2002).
[CrossRef]

2000 (1)

G. Pretzler, A. Kasper, and K. J. Witte, Appl. Phys. B 70, 1 (2000).
[CrossRef]

1997 (2)

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

1992 (1)

1989 (1)

M. B. Danailov and I. P. Christov, J. Mod. Opt. 36, 725 (1989).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 190 (1974).
[CrossRef]

Allen, L.

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[CrossRef] [PubMed]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Berry, M. V.

M. V. Berry, New J. Phys. 4, 66.1 (2002).

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 190 (1974).
[CrossRef]

Canal, F.

D. V. Petrov, F. Canal, and L. Torner, Opt. Commun. 143, 265 (1997).
[CrossRef]

Christov, I. P.

M. B. Danailov and I. P. Christov, J. Mod. Opt. 36, 725 (1989).
[CrossRef]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Danailov, M. B.

M. B. Danailov and I. P. Christov, J. Mod. Opt. 36, 725 (1989).
[CrossRef]

Dholakia, K.

Dreischuh, A.

F. Lindner, G. G. Paulus, F. Grasbon, A. Dreischuh, and H. Walther, IEEE J. Quantum Electron. 38, 1465 (2002).
[CrossRef]

Gan, X.

Ganic, D.

Grasbon, F.

F. Lindner, G. G. Paulus, F. Grasbon, A. Dreischuh, and H. Walther, IEEE J. Quantum Electron. 38, 1465 (2002).
[CrossRef]

Gu, M.

Hain, M.

Heckenberg, N. R.

Kasper, A.

G. Pretzler, A. Kasper, and K. J. Witte, Appl. Phys. B 70, 1 (2000).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Leach, J.

J. Leach and M. J. Padgett, New J. Phys. 5, 154.1 (2003).
[CrossRef]

Lee, W.-H.

W.-H. Lee, in Progress in Optics XVI, E. Wolf, ed. (ElsevierNorth-Holland, Amsterdam, 1978), p. 119.
[CrossRef]

Lindner, F.

F. Lindner, G. G. Paulus, F. Grasbon, A. Dreischuh, and H. Walther, IEEE J. Quantum Electron. 38, 1465 (2002).
[CrossRef]

McDuff, R.

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 190 (1974).
[CrossRef]

Padgett, M. J.

Paulus, G. G.

F. Lindner, G. G. Paulus, F. Grasbon, A. Dreischuh, and H. Walther, IEEE J. Quantum Electron. 38, 1465 (2002).
[CrossRef]

Petrov, D. V.

D. V. Petrov, F. Canal, and L. Torner, Opt. Commun. 143, 265 (1997).
[CrossRef]

Pretzler, G.

G. Pretzler, A. Kasper, and K. J. Witte, Appl. Phys. B 70, 1 (2000).
[CrossRef]

Simpson, N. B.

Smith, C. P.

Somalingam, S.

Stankovic, S.

Torner, L.

D. V. Petrov, F. Canal, and L. Torner, Opt. Commun. 143, 265 (1997).
[CrossRef]

Tschudi, T.

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Walther, H.

F. Lindner, G. G. Paulus, F. Grasbon, A. Dreischuh, and H. Walther, IEEE J. Quantum Electron. 38, 1465 (2002).
[CrossRef]

White, A. G.

Witte, K. J.

G. Pretzler, A. Kasper, and K. J. Witte, Appl. Phys. B 70, 1 (2000).
[CrossRef]

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Appl. Phys. B (1)

G. Pretzler, A. Kasper, and K. J. Witte, Appl. Phys. B 70, 1 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

F. Lindner, G. G. Paulus, F. Grasbon, A. Dreischuh, and H. Walther, IEEE J. Quantum Electron. 38, 1465 (2002).
[CrossRef]

J. Mod. Opt. (1)

M. B. Danailov and I. P. Christov, J. Mod. Opt. 36, 725 (1989).
[CrossRef]

New J. Phys. (2)

J. Leach and M. J. Padgett, New J. Phys. 5, 154.1 (2003).
[CrossRef]

M. V. Berry, New J. Phys. 4, 66.1 (2002).

Opt. Commun. (3)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

D. V. Petrov, F. Canal, and L. Torner, Opt. Commun. 143, 265 (1997).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Opt. Lett. (3)

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

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 190 (1974).
[CrossRef]

Other (1)

W.-H. Lee, in Progress in Optics XVI, E. Wolf, ed. (ElsevierNorth-Holland, Amsterdam, 1978), p. 119.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Illustration of the 4f setup that is analyzed theoretically. G, diffraction grating; CGH, computer-generated hologram with an encoded phase singularity; L1, L2, lenses of equal focal length f; D, iris diaphragm. The input, Fourier, and output planes are denoted by indices 0, f, and 1, respectively.

Fig. 2
Fig. 2

Top, gray-scale images of OV beams 35 cm behind the CGH, for cw and femtosecond (fs) laser beams. No 4f setup is used. Bottom, vertical cross sections.

Fig. 3
Fig. 3

Scheme of the 4f setup used in the experiment. L, quartz lens of focal length f=20 cm; M, folding mirror; m, diffraction orders.

Fig. 4
Fig. 4

Top, optical vortices recorded 35 cm after the 4f setup in the cw and the fs regimes. Bottom, vertical cross sections of the optical vortices in both regimes.

Equations (5)

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

Ex,y,s=expi2πλsiλsEin×expiπλsx-x02+y-y02dx0dy0.
Ex0,y0=1/πE0 exp-x02+y02σ02expi2πdx,
Exf,yf=σ02λfE0 exp-xf-λfd2+yf2λfπσ02.
Ex1,y1=1πλ2f2E0 exp-x12+y12βσ02expi2πβdx1.
E=1πλf2E0 exp-x12+y12βσ02expiφx1,y1×expi2πd1+1βx1,

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