Abstract

We demonstrate an experimental scheme that allows the elucidation of the orbital angular momentum discrete spectrum of an arbitrary light signal. The orbital angular momentum spectrum is represented in a Laguerre–Gaussian mode base, and the spectral components are resolved in the frequency domain by exploiting the Doppler frequency shift that is imparted to rotating light beams.

© 2003 Optical Society of America

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References

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  2. S. M. Barnett, J. Opt. B Quantum Semiclass. Opt. 4, S7 (2002).
    [CrossRef]
  3. M. Vasnetsov and K. Staliunas, eds., Optical Vortices (Nova Science, Commack, N.Y., 1999).
  4. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
    [CrossRef] [PubMed]
  5. K. T. Gahagan and G. A. Swartzlander, Opt. Lett. 21, 827 (1996).
    [CrossRef] [PubMed]
  6. N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
    [CrossRef] [PubMed]
  7. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
    [CrossRef] [PubMed]
  8. G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
    [CrossRef]
  9. M. V. Vasnetsov, V. V. Slyusar, and M. S. Soskin, Quantum Electron. 31, 464 (2001).
    [CrossRef]
  10. X. Xue, H. Wei, and A. G. Kirk, Opt. Lett. 26, 1746 (2001).
    [CrossRef]
  11. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
    [CrossRef]
  12. G. Nienhuis, Optics Commun. 132, 8 (1996).
    [CrossRef]
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    [CrossRef]
  14. J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
    [CrossRef]
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  17. A. Vaziri, G. Weihs, and A. Zeilinger, J. Opt. B Quantum Semiclass. Opt. 4, S47 (2002).
    [CrossRef]

2003 (1)

2002 (4)

A. Vaziri, G. Weihs, and A. Zeilinger, J. Opt. B Quantum Semiclass. Opt. 4, S47 (2002).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

S. M. Barnett, J. Opt. B Quantum Semiclass. Opt. 4, S7 (2002).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

2001 (3)

M. V. Vasnetsov, V. V. Slyusar, and M. S. Soskin, Quantum Electron. 31, 464 (2001).
[CrossRef]

X. Xue, H. Wei, and A. G. Kirk, Opt. Lett. 26, 1746 (2001).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

1998 (2)

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

1997 (2)

I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. Lett. 78, 2539 (1997).
[CrossRef]

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

1996 (2)

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

1992 (1)

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

Allen, L.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

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

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

Barnett, S. M.

S. M. Barnett, J. Opt. B Quantum Semiclass. Opt. 4, S7 (2002).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Basisty, I. V.

Beijersbergen, M. W.

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

Bekshaev, A. Ya.

Bialynicka-Birula, Z.

I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. Lett. 78, 2539 (1997).
[CrossRef]

Bialynicki-Birula, I.

I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. Lett. 78, 2539 (1997).
[CrossRef]

Courtial, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

Dholakia, K.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

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

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Gahagan, K. T.

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Kirk, A. G.

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

Nienhuis, G.

G. Nienhuis, Optics Commun. 132, 8 (1996).
[CrossRef]

Padgett, M. J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

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

Robertson, D. A.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Simpson, N. B.

Slyusar, V. V.

Soskin, M. S.

Spreeuw, R. J. C.

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

Swartzlander, G. A.

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

Vasnetsov, M. V.

Vaziri, A.

A. Vaziri, G. Weihs, and A. Zeilinger, J. Opt. B Quantum Semiclass. Opt. 4, S47 (2002).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Wei, H.

Weihs, G.

A. Vaziri, G. Weihs, and A. Zeilinger, J. Opt. B Quantum Semiclass. Opt. 4, S47 (2002).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Woerdman, J. P.

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

Xue, X.

Zeilinger, A.

A. Vaziri, G. Weihs, and A. Zeilinger, J. Opt. B Quantum Semiclass. Opt. 4, S47 (2002).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

J. Opt. B Quantum Semiclass. Opt. (1)

A. Vaziri, G. Weihs, and A. Zeilinger, J. Opt. B Quantum Semiclass. Opt. 4, S47 (2002).
[CrossRef]

J. Opt. B Quantum Semiclass. Opt. (1)

S. M. Barnett, J. Opt. B Quantum Semiclass. Opt. 4, S7 (2002).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Opt. Lett. (4)

Optics Commun. (1)

G. Nienhuis, Optics Commun. 132, 8 (1996).
[CrossRef]

Phys. Rev. A (1)

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

Phys. Rev. Lett. (6)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. Lett. 78, 2539 (1997).
[CrossRef]

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Quantum Electron. (1)

M. V. Vasnetsov, V. V. Slyusar, and M. S. Soskin, Quantum Electron. 31, 464 (2001).
[CrossRef]

Other (1)

M. Vasnetsov and K. Staliunas, eds., Optical Vortices (Nova Science, Commack, N.Y., 1999).

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Figures (3)

Fig. 1
Fig. 1

(a) Experimental setup: M1, M2, mirrors. BS1, BS2, beam splitters; PM, piezo-driven mirror; GP, glass plate. See text for full details and other abbreviations. (b) Spiraling fringe pattern produced by coaxial interference of the LG01 mode and a Gaussian, seen by a CCD camera. (c) Oscilloscope trace of the signal.

Fig. 2
Fig. 2

(a) Spectrum of the signal in Fig. 1(c). The peak at 10 Hz corresponds to the frequency shift f in the reference wave. Inset, LG01 mode. (b) Rotation of the off-axis aperture results in the shift of the peak to the position f+Ω11.7 Hz. (c) Rotation of the aperture in the opposite direction results in the peak position f-Ω8.3 Hz. (d) Spectrum of the signal generated by beats between the frequency-shifted reference beam and the superposition of Gaussian and LG01 modes produced by the displaced grating (inset). (e) Rotation of the off-axis aperture results in the new spectral peak at 11.7 Hz and appearance of the peak at 1.7 Hz. (f) Rotation of the aperture in the opposite direction results in the LG01 mode related peak at 8.3 Hz.

Fig. 3
Fig. 3

Ratio of the measured amplitudes of the spectral peaks, corresponding to the LG00 and LG01 components of the signal beam as a function of the hologram relative displacement. The dashed line is a fit to the linear dependence.

Equations (2)

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Esρ,φ=12A-1u0-1ρexp-iφ+A0u00ρ+A1u01ρexpiφ+c.c.,
It,ρa=12I0+mnAmAnu0mρau0nρa×cosm-nΩt+Aru00ρamAmu0mρa×cosf+mΩt,

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