Abstract

Ghost interference with partially coherent radiation sources is studied using optical coherence theory. The visibility of the ghost interference fringes is strongly influenced by the transverse size and transverse coherence width of the source. An increase of the transverse source size leads to a decrease of the fringes’ visibility. An increase of the transverse coherence results in an increase of the visibility. The difference between ghost interference formed with entangled photon pairs and with partially coherent light is discussed.

© 2004 Optical Society of America

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  1. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
    [CrossRef] [PubMed]
  2. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
    [CrossRef]
  3. P. H. S. Ribeiro and G. A. Barbosa, Phys. Rev. A 54, 3489 (1996).
    [CrossRef]
  4. A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 83, 1763 (1999).
    [CrossRef]
  5. P. H. S. Ribeiro, S. Padua, and C. H. Monken, Phys. Rev. A 60, 5074 (1999).
    [CrossRef]
  6. A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 90, 133603 (2003).
    [CrossRef]
  7. V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. A 65, 022309 (2002).
    [CrossRef]
  8. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
    [CrossRef] [PubMed]
  9. M. D. Angelo, M. V. Chekhova, and Y. H. Shih, Phys. Rev. Lett. 87, 013602 (2001).
    [CrossRef]
  10. A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Opt. Express 9, 498 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  11. A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001).
    [CrossRef]
  12. R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
    [CrossRef]
  13. R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
    [CrossRef]
  14. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
    [CrossRef]
  15. J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
    [CrossRef]
  16. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, New York, 1995).
    [CrossRef]
  17. S. A. Collins, J. Opt. Soc. Am. 60, 1168 (1970).
  18. J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1976).
    [CrossRef]

2004

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef]

2003

A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 90, 133603 (2003).
[CrossRef]

2002

V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. A 65, 022309 (2002).
[CrossRef]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

2001

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Opt. Express 9, 498 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef]

2000

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

1999

A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 83, 1763 (1999).
[CrossRef]

P. H. S. Ribeiro, S. Padua, and C. H. Monken, Phys. Rev. A 60, 5074 (1999).
[CrossRef]

1996

P. H. S. Ribeiro and G. A. Barbosa, Phys. Rev. A 54, 3489 (1996).
[CrossRef]

1995

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef] [PubMed]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

1976

J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1976).
[CrossRef]

1970

Abouraddy, A. F.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Opt. Express 9, 498 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Angelo, M. D.

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

Bache, M.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Barbosa, G. A.

P. H. S. Ribeiro and G. A. Barbosa, Phys. Rev. A 54, 3489 (1996).
[CrossRef]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Boyd, R. W.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

Brambilla, E.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 90, 133603 (2003).
[CrossRef]

A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 83, 1763 (1999).
[CrossRef]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Chekhova, M. V.

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

Cheng, J.

J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef]

Collins, S. A.

Dowling, J. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Foley, J. T.

J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1976).
[CrossRef]

Gatti, A.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 90, 133603 (2003).
[CrossRef]

A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 83, 1763 (1999).
[CrossRef]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. A 65, 022309 (2002).
[CrossRef]

Han, S.

J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef]

Howell, J. C.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef] [PubMed]

Kok, P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. A 65, 022309 (2002).
[CrossRef]

Lugiato, L. A.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 90, 133603 (2003).
[CrossRef]

A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 83, 1763 (1999).
[CrossRef]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. A 65, 022309 (2002).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, New York, 1995).
[CrossRef]

Monken, C. H.

P. H. S. Ribeiro, S. Padua, and C. H. Monken, Phys. Rev. A 60, 5074 (1999).
[CrossRef]

Padua, S.

P. H. S. Ribeiro, S. Padua, and C. H. Monken, Phys. Rev. A 60, 5074 (1999).
[CrossRef]

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Ribeiro, P. H. S.

P. H. S. Ribeiro, S. Padua, and C. H. Monken, Phys. Rev. A 60, 5074 (1999).
[CrossRef]

P. H. S. Ribeiro and G. A. Barbosa, Phys. Rev. A 54, 3489 (1996).
[CrossRef]

Saleh, B. E. A.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Opt. Express 9, 498 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef]

Sergienko, A. V.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Opt. Express 9, 498 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef] [PubMed]

Shih, Y. H.

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef] [PubMed]

Strekalov, D. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef] [PubMed]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Teich, M. C.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Opt. Express 9, 498 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Williams, C. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, New York, 1995).
[CrossRef]

Zubairy, M. S.

J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1976).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1976).
[CrossRef]

Opt. Express

Phys. Rev. A

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

P. H. S. Ribeiro and G. A. Barbosa, Phys. Rev. A 54, 3489 (1996).
[CrossRef]

P. H. S. Ribeiro, S. Padua, and C. H. Monken, Phys. Rev. A 60, 5074 (1999).
[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. A 65, 022309 (2002).
[CrossRef]

Phys. Rev. Lett.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef]

A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 90, 133603 (2003).
[CrossRef]

A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 83, 1763 (1999).
[CrossRef]

J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
[CrossRef]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600 (1995).
[CrossRef] [PubMed]

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, New York, 1995).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Scheme for ghost interference with partially coherent radiation.

Fig. 2
Fig. 2

Ghost interference fringes of double slits with partially coherent GSM radiation for different transverse sizes with σg=0.000001 mm.

Fig. 3
Fig. 3

Ghost interference fringes of double slits with partially coherent GSM radiation for different transverse coherence widths with σI=5 mm.

Fig. 4
Fig. 4

Dependence of the visibility of the ghost interference fringes of double slits on the normalized transverse coherence width σg/d for different σI.

Equations (12)

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

G2u1,u2=Eu1Eu2E*u2E*u1=Iu1Iu2+Γu1,u22,
Iui=--hix1,uihi*x2,ui×Esx1Es*x2dx1dx2, i=1,2,
Γu1,u2=--Esx1Es*x2×h1x1,u1h2*x2,u2dx1dx2,
h1u1,x1=-1λ2z1z21/2-exp-iπλz1x12-2x1v1+v12Hv1exp-iπλz2v12-2v1u1+u12dv1,
h2u2,x2=-iλz1/2exp-iπλzx22-2x2u2+u22,
Esx1Es*x2=G0 exp-x12+x224σI2-x1-x222σg2,
Iu1=0=πλ2z1z2A1A2--Hv1H*v2×exp2iπλz1v1-iπA1σg2λz1v224A2×exp-π2A1λ2z12v22×exp-iπλz1v12-iπλz2v12×expiπλz1v22+iπλz2v22dv1dv2,
Iu2=πλzB1B2×exp2iπλzu2-iπλzσg2B1u224B2×exp-π2u22B1λ2z2,
Γu1=0,u22=π2λ3z1z2zC1C2-Hv1×exp2iπλz1v1-iπC1σg2λzu224C2×exp-π2C1λ2z2u22×exp-iπλz1v12-iπλz2v12dv12,
A1=14σI2+12σg2-iπλz1,A2=14σI2+12σg2+iπλz1-14A1σg4,B1=14σI2+12σg2-iπλz,B2=14σI2+12σg2+iπλz-14B1σg4,C1=14σI2+12σg2-iπλz,C2=14σI2+12σg2+iπλz1-14C1σg4.
1λ2z-z12sin c2u2aπλz-z1cos2u2dπλz-z1.
1l1-z1+1l2=1f

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