Abstract

The interference of Laguerre–Gaussian beams carrying orbital angular momentum was demonstrated in Young’s double-slit geometry. Double-slit interference is shown to be affected by the azimuthal phase dependence of a Laguerre–Gaussian beam. This interference provides new insight into the helical phase structure of the Laguerre–Gaussian beam and has potential applications for measuring the orbital angular momentum of an arbitrary wavefront.

© 2006 Optical Society of America

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References

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  1. T. Young, Philos. Trans. R. Soc. London 12, 387 (1802).
  2. C. Jonsson, Z. Phys. 161, 454 (1961).
    [CrossRef]
  3. C. Jonsson, Am. J. Phys. 42, 4 (1974).
    [CrossRef]
  4. A. Zeilinger, R. Gahler, C. G. Shull, W. Treimer, and W. Mampe, Rev. Mod. Phys. 60, 10671073 (1988).
    [CrossRef]
  5. O. Carnal and J. Mlynek, Phys. Rev. Lett. 66, 26892692 (1991).
    [CrossRef]
  6. L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics Volume XXXIX (Elsevier, 1999), p. 291.
    [CrossRef]
  7. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  8. M. J. Padgett, J. Arlt, and N. Simpson, Am. J. Phys. 64, 7782 (1996).
    [CrossRef]
  9. J. M. Vaughan and D. V. Willetts, Opt. Commun. 30, 263 (1979).
    [CrossRef]
  10. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
    [CrossRef] [PubMed]
  11. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
    [CrossRef]
  12. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Chap. 7.
  13. E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, Phys. Rev. Lett. 90, 203901 (2003).
    [CrossRef] [PubMed]
  14. A. Vaziri, G. Weihs, and A. Zeilinger, J. Opt. B Quantum Semiclassical Opt. 4, S47 (2002).
    [CrossRef]

2003

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

2002

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

1996

M. J. Padgett, J. Arlt, and N. Simpson, Am. J. Phys. 64, 7782 (1996).
[CrossRef]

1992

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

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

1991

O. Carnal and J. Mlynek, Phys. Rev. Lett. 66, 26892692 (1991).
[CrossRef]

1988

A. Zeilinger, R. Gahler, C. G. Shull, W. Treimer, and W. Mampe, Rev. Mod. Phys. 60, 10671073 (1988).
[CrossRef]

1979

J. M. Vaughan and D. V. Willetts, Opt. Commun. 30, 263 (1979).
[CrossRef]

1974

C. Jonsson, Am. J. Phys. 42, 4 (1974).
[CrossRef]

1961

C. Jonsson, Z. Phys. 161, 454 (1961).
[CrossRef]

1802

T. Young, Philos. Trans. R. Soc. London 12, 387 (1802).

Allen, L.

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

L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics Volume XXXIX (Elsevier, 1999), p. 291.
[CrossRef]

Arlt, J.

M. J. Padgett, J. Arlt, and N. Simpson, Am. J. Phys. 64, 7782 (1996).
[CrossRef]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics Volume XXXIX (Elsevier, 1999), p. 291.
[CrossRef]

Beijersbergen, M. W.

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

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Chap. 7.

Carnal, O.

O. Carnal and J. Mlynek, Phys. Rev. Lett. 66, 26892692 (1991).
[CrossRef]

Crawford, P. R.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

Gahler, R.

A. Zeilinger, R. Gahler, C. G. Shull, W. Treimer, and W. Mampe, Rev. Mod. Phys. 60, 10671073 (1988).
[CrossRef]

Galvez, E. J.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

Haglin, P. J.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

Heckenberg, N. R.

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Jonsson, C.

C. Jonsson, Am. J. Phys. 42, 4 (1974).
[CrossRef]

C. Jonsson, Z. Phys. 161, 454 (1961).
[CrossRef]

Mampe, W.

A. Zeilinger, R. Gahler, C. G. Shull, W. Treimer, and W. Mampe, Rev. Mod. Phys. 60, 10671073 (1988).
[CrossRef]

McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Mlynek, J.

O. Carnal and J. Mlynek, Phys. Rev. Lett. 66, 26892692 (1991).
[CrossRef]

Padgett, M. J.

M. J. Padgett, J. Arlt, and N. Simpson, Am. J. Phys. 64, 7782 (1996).
[CrossRef]

L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics Volume XXXIX (Elsevier, 1999), p. 291.
[CrossRef]

Pysher, M. J.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Shull, C. G.

A. Zeilinger, R. Gahler, C. G. Shull, W. Treimer, and W. Mampe, Rev. Mod. Phys. 60, 10671073 (1988).
[CrossRef]

Simpson, N.

M. J. Padgett, J. Arlt, and N. Simpson, Am. J. Phys. 64, 7782 (1996).
[CrossRef]

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef] [PubMed]

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]

Sztul, H. I.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

Treimer, W.

A. Zeilinger, R. Gahler, C. G. Shull, W. Treimer, and W. Mampe, Rev. Mod. Phys. 60, 10671073 (1988).
[CrossRef]

Vaughan, J. M.

J. M. Vaughan and D. V. Willetts, Opt. Commun. 30, 263 (1979).
[CrossRef]

Vaziri, A.

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

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Weihs, G.

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

White, A. G.

Willetts, D. V.

J. M. Vaughan and D. V. Willetts, Opt. Commun. 30, 263 (1979).
[CrossRef]

Williams, R. E.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, Phys. Rev. Lett. 90, 203901 (2003).
[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]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Chap. 7.

Young, T.

T. Young, Philos. Trans. R. Soc. London 12, 387 (1802).

Zeilinger, A.

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

A. Zeilinger, R. Gahler, C. G. Shull, W. Treimer, and W. Mampe, Rev. Mod. Phys. 60, 10671073 (1988).
[CrossRef]

Am. J. Phys.

C. Jonsson, Am. J. Phys. 42, 4 (1974).
[CrossRef]

M. J. Padgett, J. Arlt, and N. Simpson, Am. J. Phys. 64, 7782 (1996).
[CrossRef]

J. Opt. B Quantum Semiclassical Opt.

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

Opt. Commun.

J. M. Vaughan and D. V. Willetts, Opt. Commun. 30, 263 (1979).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Philos. Trans. R. Soc. London

T. Young, Philos. Trans. R. Soc. London 12, 387 (1802).

Phys. Rev. A

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

Phys. Rev. Lett.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

O. Carnal and J. Mlynek, Phys. Rev. Lett. 66, 26892692 (1991).
[CrossRef]

Rev. Mod. Phys.

A. Zeilinger, R. Gahler, C. G. Shull, W. Treimer, and W. Mampe, Rev. Mod. Phys. 60, 10671073 (1988).
[CrossRef]

Z. Phys.

C. Jonsson, Z. Phys. 161, 454 (1961).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Chap. 7.

L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics Volume XXXIX (Elsevier, 1999), p. 291.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental diffraction setup. M, mirror; S, slits; B.T., beam telescope; N.D., neutral-density filters. Inset, (a) forked diffraction grating used to create LG beams of charge l = 0 , ± 1 , ± 2 , ; (b) LG mode selected with l = + 1 ; (c) helical wavefront of the LG beam.

Fig. 2
Fig. 2

(Color online) (a) Phase structure of a LG wavefront, where equal lines of shade represent equal values of phase (black is 0, white is 2 π ) (b) The same wavefront lies on two slits with its singularity between the slits. (c) Phase difference between the left and the right slit. (d) Pixel values along the y direction at the center of the slit in (c). These values are Δ ϕ ( y ) .

Fig. 3
Fig. 3

(a) Interference pattern from a LG wavefront incident on two slits, calculated from relation (6). (b) Interference pattern from a plane wave incident on two slits, calculated from relation (3). (c) Interference pattern from a LG wavefront incident on two slits, calculated with Δ ϕ ( y ) . (d)–(f) Experimental far-field interference patterns obtained from (d) the l = + 1 beam, (e) l = 0 beam, and (f) l = 1 beam passing through two slits.

Fig. 4
Fig. 4

(Color online) Observed interference along one fixed vertical interference fringe of Fig. 3d.

Equations (6)

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u ( r , ϕ , z ) p , l r l L p l ( 2 r 2 w 2 ) exp ( r 2 w 2 ) exp ( i l ϕ ) ,
I ( x ) cos 2 ( δ 2 ) ,
cos 2 ( π a x λ d ) ,
Δ ϕ ( y ) = ϕ 2 ( y ) ϕ 1 ( y ) .
I ( x , y ) cos 2 ( δ 2 + Δ ϕ ( y ) 2 )
cos 2 ( π a x λ d + Δ ϕ ( y ) 2 ) .

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