Abstract

We consider classical second-order ghost imaging with uniformly partially polarized electromagnetic beams and examine the effect of the degree of polarization of the incident light on the visibility of the image. Closed- form expressions for two previously proposed definitions of visibility are derived. Both results are physically similar and show that the visibility increases with the degree of polarization. Hence, a polarized beam is superior to an unpolarized one to obtain a high-visibility ghost image. Some related issues in recent literature are also addressed.

© 2011 Optical Society of America

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  1. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, in Quantum Imaging, M.I.Kolobov, ed. (Springer, 2007), pp. 79–111.
    [CrossRef]
  2. B. I. Erkmen and J. H. Shapiro, Adv. Opt. Photon. 2, 405(2010).
    [CrossRef]
  3. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
    [CrossRef] [PubMed]
  4. R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
    [CrossRef] [PubMed]
  5. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
    [CrossRef]
  6. Y. Cai and S. Y. Zhu, Phys. Rev. E 71, 056607 (2005).
    [CrossRef]
  7. A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
    [CrossRef]
  8. B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
    [CrossRef]
  9. V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, Phys. Rev. A 77, 043811 (2008).
    [CrossRef]
  10. T. Setälä, T. Shirai, and A. T. Friberg, Phys. Rev. A 82, 043813 (2010).
    [CrossRef]
  11. T. Shirai, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. B 27, 2549 (2010).
    [CrossRef]
  12. Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
    [CrossRef]
  13. B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 79, 023833(2009).
    [CrossRef]
  14. O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
    [CrossRef]
  15. F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
    [CrossRef] [PubMed]
  16. J. Cheng and S.-S. Han, Chin. Phys. Lett. 22, 1676 (2005).
    [CrossRef]
  17. H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, Opt. Commun. 283, 405 (2010).
    [CrossRef]
  18. Z. Tong, Y. Cai, and O. Korotkova, Opt. Commun. 283, 3838 (2010).
    [CrossRef]
  19. D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
    [CrossRef]
  20. M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. A 73, 053802 (2006).
    [CrossRef]
  21. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  22. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  23. J. Tervo, T. Setälä, and A. T. Friberg, Opt. Express 11, 1137 (2003).
    [CrossRef] [PubMed]
  24. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 31, 2669(2006).
    [CrossRef] [PubMed]

2010 (6)

B. I. Erkmen and J. H. Shapiro, Adv. Opt. Photon. 2, 405(2010).
[CrossRef]

T. Setälä, T. Shirai, and A. T. Friberg, Phys. Rev. A 82, 043813 (2010).
[CrossRef]

T. Shirai, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. B 27, 2549 (2010).
[CrossRef]

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, Opt. Commun. 283, 405 (2010).
[CrossRef]

Z. Tong, Y. Cai, and O. Korotkova, Opt. Commun. 283, 3838 (2010).
[CrossRef]

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef] [PubMed]

2009 (3)

Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 79, 023833(2009).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

2008 (3)

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
[CrossRef]

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, Phys. Rev. A 77, 043811 (2008).
[CrossRef]

2006 (3)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. A 73, 053802 (2006).
[CrossRef]

T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 31, 2669(2006).
[CrossRef] [PubMed]

2005 (2)

J. Cheng and S.-S. Han, Chin. Phys. Lett. 22, 1676 (2005).
[CrossRef]

Y. Cai and S. Y. Zhu, Phys. Rev. E 71, 056607 (2005).
[CrossRef]

2004 (1)

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

2003 (2)

2002 (1)

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

1995 (1)

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

Bache, M.

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. A 73, 053802 (2006).
[CrossRef]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

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

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, in Quantum Imaging, M.I.Kolobov, ed. (Springer, 2007), pp. 79–111.
[CrossRef]

Bennink, R. S.

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

Bentley, S. J.

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

Boyd, R. W.

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

Brambilla, E.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. A 73, 053802 (2006).
[CrossRef]

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

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, in Quantum Imaging, M.I.Kolobov, ed. (Springer, 2007), pp. 79–111.
[CrossRef]

Bromberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Cai, Y.

Z. Tong, Y. Cai, and O. Korotkova, Opt. Commun. 283, 3838 (2010).
[CrossRef]

Y. Cai and S. Y. Zhu, Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Cao, D.-Z.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Cheng, J.

J. Cheng and S.-S. Han, Chin. Phys. Lett. 22, 1676 (2005).
[CrossRef]

Erkmen, B. I.

B. I. Erkmen and J. H. Shapiro, Adv. Opt. Photon. 2, 405(2010).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 79, 023833(2009).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
[CrossRef]

Ferri, F.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef] [PubMed]

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. A 73, 053802 (2006).
[CrossRef]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

Friberg, A. T.

Gao, L.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Gatti, A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef] [PubMed]

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. A 73, 053802 (2006).
[CrossRef]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

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

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, in Quantum Imaging, M.I.Kolobov, ed. (Springer, 2007), pp. 79–111.
[CrossRef]

Guan, D.-S.

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, Opt. Commun. 283, 405 (2010).
[CrossRef]

Han, S.-S.

J. Cheng and S.-S. Han, Chin. Phys. Lett. 22, 1676 (2005).
[CrossRef]

Katz, O.

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

Korotkova, O.

Z. Tong, Y. Cai, and O. Korotkova, Opt. Commun. 283, 3838 (2010).
[CrossRef]

Lajunen, H.

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, Phys. Rev. A 77, 043811 (2008).
[CrossRef]

Lancis, J.

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, Phys. Rev. A 77, 043811 (2008).
[CrossRef]

Li, L.

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, Opt. Commun. 283, 405 (2010).
[CrossRef]

Lin, L.-F.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Liu, H.-C.

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, Opt. Commun. 283, 405 (2010).
[CrossRef]

Lugiato, L. A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef] [PubMed]

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. A 73, 053802 (2006).
[CrossRef]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

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

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, in Quantum Imaging, M.I.Kolobov, ed. (Springer, 2007), pp. 79–111.
[CrossRef]

Magatti, D.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef] [PubMed]

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. A 73, 053802 (2006).
[CrossRef]

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Pittman, T. B.

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

Sergienko, A. V.

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

Setälä, T.

Shapiro, J. H.

B. I. Erkmen and J. H. Shapiro, Adv. Opt. Photon. 2, 405(2010).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 79, 023833(2009).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
[CrossRef]

Shih, Y. H.

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

Shirai, T.

T. Setälä, T. Shirai, and A. T. Friberg, Phys. Rev. A 82, 043813 (2010).
[CrossRef]

T. Shirai, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. B 27, 2549 (2010).
[CrossRef]

Silberberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Strekalov, D. V.

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

Tervo, J.

Tong, Z.

Z. Tong, Y. Cai, and O. Korotkova, Opt. Commun. 283, 3838 (2010).
[CrossRef]

Torres-Company, V.

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, Phys. Rev. A 77, 043811 (2008).
[CrossRef]

Wang, K.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Wolf, E.

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Xiong, J.

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, Opt. Commun. 283, 405 (2010).
[CrossRef]

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Zhang, S.-H.

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, Opt. Commun. 283, 405 (2010).
[CrossRef]

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Zhu, S. Y.

Y. Cai and S. Y. Zhu, Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (2)

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Chin. Phys. Lett. (1)

J. Cheng and S.-S. Han, Chin. Phys. Lett. 22, 1676 (2005).
[CrossRef]

J. Mod. Opt. (1)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, J. Mod. Opt. 53, 739 (2006).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

H.-C. Liu, D.-S. Guan, L. Li, S.-H. Zhang, and J. Xiong, Opt. Commun. 283, 405 (2010).
[CrossRef]

Z. Tong, Y. Cai, and O. Korotkova, Opt. Commun. 283, 3838 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Lett. A (1)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

Phys. Rev. A (8)

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, Phys. Rev. A 73, 053802 (2006).
[CrossRef]

Y. Bromberg, O. Katz, and Y. Silberberg, Phys. Rev. A 79, 053840 (2009).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 79, 023833(2009).
[CrossRef]

B. I. Erkmen and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
[CrossRef]

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, Phys. Rev. A 77, 043811 (2008).
[CrossRef]

T. Setälä, T. Shirai, and A. T. Friberg, Phys. Rev. A 82, 043813 (2010).
[CrossRef]

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

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

Phys. Rev. E (1)

Y. Cai and S. Y. Zhu, Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

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

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef] [PubMed]

Other (2)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, in Quantum Imaging, M.I.Kolobov, ed. (Springer, 2007), pp. 79–111.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Ghost imaging setup for analysis.

Fig. 2
Fig. 2

Visibility plotted against the degree of polarization of the incident beam, based on (a) Cao et al.’s definition [Eq. (11)] and (b) Gatti et al.’s definition [Eq. (12)].

Equations (14)

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

V C = [ I 1 I 2 ] max [ I 1 I 2 ] min [ I 1 I 2 ] max + [ I 1 I 2 ] min ,
V G = [ I 1 I 2 I 1 I 2 ] max [ I 1 I 2 ] max ,
Γ i j = Γ ( r i , t i ; r j , t j ) = [ E α * ( r i , t i ) E β ( r j , t j ) ] ,
I i = tr Γ i i ,
I i I j = tr ( Γ i j Γ i j ) + tr Γ i i tr Γ j j ,
V C = [ tr ( Γ 12 Γ 12 ) ] max [ tr ( Γ 12 Γ 12 ) ] min [ tr ( Γ 12 Γ 12 ) ] max + [ tr ( Γ 12 Γ 12 ) ] min + 2 tr Γ 11 tr Γ 22 .
V G = [ tr ( Γ 12 Γ 12 ) ] max [ tr ( Γ 12 Γ 12 ) ] max + tr Γ 11 tr Γ 22
Γ i j = Γ 0 ( t 1 , t 2 ) K i * ( t i , t 1 ) K j ( t j , t 2 ) d t 1 d t 2 ,
Γ i j = J 0 Γ i j ,
Γ i j = K i * ( t i , t 1 ) K j ( t j , t 1 ) d t 1 .
V C = P 2 + 1 P 2 + 5 .
V G = P 2 + 1 P 2 + 3
V G = [ | Γ 12 | 2 ] max [ | Γ 12 | 2 ] max + Γ 11 Γ 22 ,
V G = [ | g 12 ( 1 ) | 2 ] max [ g 12 ( 2 ) ] max ,

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