Abstract

We analyze and recover, by means of spatial intensity correlations, the image obtained by a seeded frequency-downconversion process in which the seed field is chaotic and an intensity modulation is encoded in the pump field. Although the field generated is as chaotic as the seed field and does not carry any information about the modulation of the pump, one can extract an image of the pump by measuring the spatial intensity correlations between the generated field and one Fourier component of the seed.

© 2005 Optical Society of America

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  1. M. I. Kolobov, Rev. Mod. Phys. 71, 1539–1589 (1999).
    [CrossRef]
  2. B. E. A. Saleh, A. F. Abbouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
    [CrossRef]
  3. A. V. Belinskii and D. N. Klyshko, JETP 105, 259–262 (1994).
  4. P. H. S. Ribeiro, S. Padua, J. C. Machado da Silva, and G. A. Barbosa, Phys. Rev. A 49, 4176–4179 (1994).
    [CrossRef] [PubMed]
  5. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600–3603 (1995).
    [CrossRef] [PubMed]
  6. G. A. Barbosa, Phys. Rev. A 54, 4473 (1994).
    [CrossRef]
  7. R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
    [CrossRef]
  8. R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 92, 033601 (2004).
    [CrossRef]
  9. A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 90, 133603 (2003).
    [CrossRef]
  10. J. Cheng and S. Han, Phys. Rev. Lett. 92, 093903 (2004).
    [CrossRef]
  11. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
    [CrossRef]
  12. D. Magatti, F. Ferri, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “Experimental evidence of high-resolution ghost imaging and ghost diffraction with classical thermal light,” quant-ph/0408021.
  13. A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, J. Opt. Soc. Am. B 19, 1174 (2002).
    [CrossRef]
  14. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
    [CrossRef]
  15. C. H. Monken, P. H. S. Ribeiro, and S. Padua, Phys. Rev. A 57, 3123 (1998).
    [CrossRef]
  16. D. P. Caetano, P. H. S. Ribeiro, J. T. C. Pardal, and A. Z. Khoury, Phys. Rev. A 68, 023805 (2003).
    [CrossRef]
  17. A. Andreoni, M. Bondani, Yu. N. Denisyuk, and M. A. C. Potenza, J. Opt. Soc. Am. B 17, 966 (2000).
    [CrossRef]
  18. M. Bondani and A. Andreoni, Phys. Rev. A 66, 033805 (2002).
    [CrossRef]
  19. M. Bondani, A. Allevi, A. Brega, E. Puddu, and A. Andreoni, J. Opt. Soc. Am. B 21, 280–288 (2004).
    [CrossRef]
  20. M. Bondani, E. Puddu, and A. Andreoni, “Image transfer through a chaotic channel by intensity correlations,” J. Mod. Opt. (to be published).

2004 (4)

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

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

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

M. Bondani, A. Allevi, A. Brega, E. Puddu, and A. Andreoni, J. Opt. Soc. Am. B 21, 280–288 (2004).
[CrossRef]

2003 (2)

D. P. Caetano, P. H. S. Ribeiro, J. T. C. Pardal, and A. Z. Khoury, Phys. Rev. A 68, 023805 (2003).
[CrossRef]

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

2002 (3)

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

M. Bondani and A. Andreoni, Phys. Rev. A 66, 033805 (2002).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, J. Opt. Soc. Am. B 19, 1174 (2002).
[CrossRef]

2000 (2)

A. Andreoni, M. Bondani, Yu. N. Denisyuk, and M. A. C. Potenza, J. Opt. Soc. Am. B 17, 966 (2000).
[CrossRef]

B. E. A. Saleh, A. F. Abbouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

1999 (1)

M. I. Kolobov, Rev. Mod. Phys. 71, 1539–1589 (1999).
[CrossRef]

1998 (1)

C. H. Monken, P. H. S. Ribeiro, and S. Padua, Phys. Rev. A 57, 3123 (1998).
[CrossRef]

1995 (2)

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, 3600–3603 (1995).
[CrossRef] [PubMed]

1994 (3)

G. A. Barbosa, Phys. Rev. A 54, 4473 (1994).
[CrossRef]

A. V. Belinskii and D. N. Klyshko, JETP 105, 259–262 (1994).

P. H. S. Ribeiro, S. Padua, J. C. Machado da Silva, and G. A. Barbosa, Phys. Rev. A 49, 4176–4179 (1994).
[CrossRef] [PubMed]

Abbouraddy, A. F.

B. E. A. Saleh, A. F. Abbouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Abouraddy, A. F.

Allevi, A.

Andreoni, A.

M. Bondani, A. Allevi, A. Brega, E. Puddu, and A. Andreoni, J. Opt. Soc. Am. B 21, 280–288 (2004).
[CrossRef]

M. Bondani and A. Andreoni, Phys. Rev. A 66, 033805 (2002).
[CrossRef]

A. Andreoni, M. Bondani, Yu. N. Denisyuk, and M. A. C. Potenza, J. Opt. Soc. Am. B 17, 966 (2000).
[CrossRef]

M. Bondani, E. Puddu, and A. Andreoni, “Image transfer through a chaotic channel by intensity correlations,” J. Mod. Opt. (to be published).

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, S. Padua, J. C. Machado da Silva, and G. A. Barbosa, Phys. Rev. A 49, 4176–4179 (1994).
[CrossRef] [PubMed]

G. A. Barbosa, Phys. Rev. A 54, 4473 (1994).
[CrossRef]

Belinskii, A. V.

A. V. Belinskii and D. N. Klyshko, JETP 105, 259–262 (1994).

Bennink, R. S.

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

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

Bondani, M.

M. Bondani, A. Allevi, A. Brega, E. Puddu, and A. Andreoni, J. Opt. Soc. Am. B 21, 280–288 (2004).
[CrossRef]

M. Bondani and A. Andreoni, Phys. Rev. A 66, 033805 (2002).
[CrossRef]

A. Andreoni, M. Bondani, Yu. N. Denisyuk, and M. A. C. Potenza, J. Opt. Soc. Am. B 17, 966 (2000).
[CrossRef]

M. Bondani, E. Puddu, and A. Andreoni, “Image transfer through a chaotic channel by intensity correlations,” J. Mod. Opt. (to be published).

Boyd, R. W.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, 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]

Brega, A.

Caetano, D. P.

D. P. Caetano, P. H. S. Ribeiro, J. T. C. Pardal, and A. Z. Khoury, Phys. Rev. A 68, 023805 (2003).
[CrossRef]

Cheng, J.

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

Denisyuk, Yu. N.

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]

Han, S.

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

Khoury, A. Z.

D. P. Caetano, P. H. S. Ribeiro, J. T. C. Pardal, and A. Z. Khoury, Phys. Rev. A 68, 023805 (2003).
[CrossRef]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

A. V. Belinskii and D. N. Klyshko, JETP 105, 259–262 (1994).

Kolobov, M. I.

M. I. Kolobov, Rev. Mod. Phys. 71, 1539–1589 (1999).
[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]

Machado da Silva, J. C.

P. H. S. Ribeiro, S. Padua, J. C. Machado da Silva, and G. A. Barbosa, Phys. Rev. A 49, 4176–4179 (1994).
[CrossRef] [PubMed]

Monken, C. H.

C. H. Monken, P. H. S. Ribeiro, and S. Padua, Phys. Rev. A 57, 3123 (1998).
[CrossRef]

Padua, S.

C. H. Monken, P. H. S. Ribeiro, and S. Padua, Phys. Rev. A 57, 3123 (1998).
[CrossRef]

P. H. S. Ribeiro, S. Padua, J. C. Machado da Silva, and G. A. Barbosa, Phys. Rev. A 49, 4176–4179 (1994).
[CrossRef] [PubMed]

Pardal, J. T. C.

D. P. Caetano, P. H. S. Ribeiro, J. T. C. Pardal, and A. Z. Khoury, Phys. Rev. A 68, 023805 (2003).
[CrossRef]

Pittman, T. B.

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

Potenza, M. A. C.

Puddu, E.

M. Bondani, A. Allevi, A. Brega, E. Puddu, and A. Andreoni, J. Opt. Soc. Am. B 21, 280–288 (2004).
[CrossRef]

M. Bondani, E. Puddu, and A. Andreoni, “Image transfer through a chaotic channel by intensity correlations,” J. Mod. Opt. (to be published).

Ribeiro, P. H. S.

D. P. Caetano, P. H. S. Ribeiro, J. T. C. Pardal, and A. Z. Khoury, Phys. Rev. A 68, 023805 (2003).
[CrossRef]

C. H. Monken, P. H. S. Ribeiro, and S. Padua, Phys. Rev. A 57, 3123 (1998).
[CrossRef]

P. H. S. Ribeiro, S. Padua, J. C. Machado da Silva, and G. A. Barbosa, Phys. Rev. A 49, 4176–4179 (1994).
[CrossRef] [PubMed]

Saleh, B. E. A.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, J. Opt. Soc. Am. B 19, 1174 (2002).
[CrossRef]

B. E. A. Saleh, A. F. Abbouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Sergienko, A. V.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, J. Opt. Soc. Am. B 19, 1174 (2002).
[CrossRef]

B. E. A. Saleh, A. F. Abbouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

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

Shih, Y. H.

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, 3600–3603 (1995).
[CrossRef] [PubMed]

Strekalov, D. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Phys. Rev. Lett. 74, 3600–3603 (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, J. Opt. Soc. Am. B 19, 1174 (2002).
[CrossRef]

B. E. A. Saleh, A. F. Abbouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

J. Opt. Soc. Am. B (3)

JETP (1)

A. V. Belinskii and D. N. Klyshko, JETP 105, 259–262 (1994).

Phys. Rev. A (8)

P. H. S. Ribeiro, S. Padua, J. C. Machado da Silva, and G. A. Barbosa, Phys. Rev. A 49, 4176–4179 (1994).
[CrossRef] [PubMed]

B. E. A. Saleh, A. F. Abbouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

G. A. Barbosa, Phys. Rev. A 54, 4473 (1994).
[CrossRef]

M. Bondani and A. Andreoni, Phys. Rev. A 66, 033805 (2002).
[CrossRef]

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]

C. H. Monken, P. H. S. Ribeiro, and S. Padua, Phys. Rev. A 57, 3123 (1998).
[CrossRef]

D. P. Caetano, P. H. S. Ribeiro, J. T. C. Pardal, and A. Z. Khoury, Phys. Rev. A 68, 023805 (2003).
[CrossRef]

Phys. Rev. Lett. (5)

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

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

A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. Lett. 90, 133603 (2003).
[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, 3600–3603 (1995).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

M. I. Kolobov, Rev. Mod. Phys. 71, 1539–1589 (1999).
[CrossRef]

Other (2)

D. Magatti, F. Ferri, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “Experimental evidence of high-resolution ghost imaging and ghost diffraction with classical thermal light,” quant-ph/0408021.

M. Bondani, E. Puddu, and A. Andreoni, “Image transfer through a chaotic channel by intensity correlations,” J. Mod. Opt. (to be published).

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of the propagation experiment. (b) Interaction inside the crystal; the optical axis is on the shaded plane.

Fig. 2
Fig. 2

Experimental setup: HS, harmonic separator; D, diffusing plate; M 1 M 5 , mirrors; L 1 , L 2 , lenses; other abbreviations defined in text. L 1 images O into O through a 2 f 2 f system. Distances are in centimeters. Inset, logarithmic plot of P r , t ( I 1 ) .

Fig. 3
Fig. 3

(a) Map of G [ I 1 , j , I 2 ( x 2 , y 2 ) ] evaluated for 1000 shots. (b) Plane-wave image. Chaotic images: (c) single-shot and (d) average over 1000 shots.

Equations (7)

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

U F ( x F , y F ) = k 3 2 π i d exp [ i k 3 2 d ( x F 2 + y F 2 ) ] d x O d y O U O ( x O , y O ) exp [ i k 3 2 d d F f f ( x O 2 + y O 2 ) + i k 3 d ( x F x O + y F y O ) ] .
a 1 ( L ) = a 1 ( 0 ) cosh [ f ( ϑ , β ) a 3 ( 0 ) L ] a 1 ( 0 ) ,
a 2 ( L ) = i g eff L a 1 * ( 0 ) a 3 ( 0 ) a 3 ( 0 ) sinh [ f ( ϑ , β ) a 3 ( 0 ) L ] i g eff L f ( ϑ , β ) a 1 * ( 0 ) a 3 ( 0 ) ,
a 3 ( L ) = a 3 ( 0 ) = U F ( x F , y F ) ,
E 2 ( r out ) n = 1 N i g eff L f ( ϑ , β ) a 1 , n * ( 0 ) a 3 ( 0 ) exp ( i k 2 , n r out ) ,
I 2 ( r 2 ) E 2 [ x 2 , y 2 , ( k 2 k 3 ) d ] 2 = n = 1 N c n a 1 , n U O ( x 2 , n x 2 , y 2 , n y 2 ) 2 = n = 1 N c n 2 a 1 , n 2 U O ( x 2 , n x 2 , y 2 , n y 2 ) 2 ,
G ( I 1 , j , I 2 ) = I 1 , j I 2 I 1 , j I 2 = n = 1 N c n 2 U O ( x 2 , n x 2 , y 2 , n y 2 ) 2 ( a 1 , j 2 a 1 , n 2 a 1 , j 2 a 1 , n 2 ) = n = 1 N c n 2 U O ( x 2 , n x 2 , y 2 , n y 2 ) 2 σ 2 ( a 1 , n 2 ) δ j , n = c j 2 σ 2 ( I 1 , j ) U O ( x 2 , j x 2 , y 2 , j y 2 ) 2 ,

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