Abstract

Self-diffraction can be induced using a biased photorefractive crystal in the Fourier plane of an imaging system where the light beam intensity is naturally high due to the concentration effect of an optical lens. The spatial frequency spectrum of the output image is proportional to the optical power density distribution in the Fourier plane. A photorefractive crystal with small size can be used and hence an reduced amount of biased voltage is needed to obtain significant diffraction effect in the image plane. When the input image is an overlay of a signal and a noise pattern, theoretic model reveals that the induced diffraction in the Fourier plane may be preferably applied on the noise pattern. In order to illustrate the effect experimentally, a signal from a weakly illuminated object is coupled with an overwhelming noise pattern and then the hidden signal is successfully recovered using a SBN61 crystal with an applied voltage of 800 V in the Fourier plane. Such technology can be employed in encrypted spatial communication systems for security purposes.

© 2015 Optical Society of America

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References

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  1. B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10(3), 446–453 (1993).
    [Crossref]
  2. G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, and E. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19(16), 1195–1197 (1994).
    [Crossref] [PubMed]
  3. D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12(9), 1628–1633 (1995).
    [Crossref]
  4. S. Gatz and J. Herrmann, “Anisotropy, nonlocality, and space-charge field displacement in (2 + 1)-dimensional self-trapping in biased photorefractive crystals,” Opt. Lett. 23(15), 1176–1178 (1998).
    [Crossref] [PubMed]
  5. M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
    [Crossref] [PubMed]
  6. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78(4), 646–649 (1997).
    [Crossref]
  7. M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature 387(26), 880–883 (1997).
  8. Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280(5365), 889–892 (1998).
    [Crossref] [PubMed]
  9. T. H. Coskun, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, “Coherence enhancement of spatially incoherent light beams through soliton interactions,” Opt. Lett. 25(11), 826–828 (2000).
    [Crossref] [PubMed]
  10. T. H. Coskun, D. N. Christodoulides, Y.-R. Kim, Z. Chen, M. Soljacic, and M. Segev, “Bright spatial solitons on a partially incoherent background,” Phys. Rev. Lett. 84(11), 2374–2377 (2000).
    [Crossref] [PubMed]
  11. C. Sun, D. V. Dylov, and J. W. Fleischer, “Nonlinear focusing and defocusing of partially coherent spatial beams,” Opt. Lett. 34(19), 3003–3005 (2009).
    [Crossref] [PubMed]
  12. M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84(3), 467–470 (2000).
    [Crossref] [PubMed]
  13. D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19(3), 502–512 (2002).
    [Crossref]
  14. D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290(5491), 495–498 (2000).
    [Crossref] [PubMed]
  15. Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” Proc. Natl. Acad. Sci. U.S.A. 99(8), 5223–5227 (2002).
    [Crossref] [PubMed]
  16. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
    [Crossref] [PubMed]
  17. D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4(5), 323–328 (2010).
    [Crossref]
  18. W. Wan, D. V. Dylov, C. Barsi, and J. W. Fleischer, “Diffraction from an edge in a self-focusing medium,” Opt. Lett. 35(16), 2819–2821 (2010).
    [Crossref] [PubMed]
  19. D. V. Dylov and J. W. Fleischer, “Modulation instability of a coherent-incoherent mixture,” Opt. Lett. 35(13), 2149–2151 (2010).
    [Crossref] [PubMed]
  20. D. V. Dylov, L. Waller, and J. W. Fleischer, “Instability-driven recovery of diffused images,” Opt. Lett. 36(18), 3711–3713 (2011).
    [Crossref] [PubMed]
  21. C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
    [Crossref]
  22. A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83(3), 031802 (2011).
    [Crossref]
  23. A. Goy and D. Psaltis, “Imaging in focusing Kerr media using reverse propagation,” Photon. Res. 1(2), 96–101 (2013).
    [Crossref]
  24. Y. Wu, J. Xu, S. Liu, G. Zhang, and D. Guan, “Automatic low-frequency spatial filter that uses light-induced scattering in LiNbO3:Fe crystal,” Appl. Opt. 31(17), 3210–3212 (1992).
    [PubMed]
  25. J. Liu, J. Xu, G. Zhang, and S. Liu, “Phase contrast using photorefractive LiNbO3:Fe crystals,” Appl. Opt. 34(22), 4972–4975 (1995).
    [Crossref] [PubMed]
  26. H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
    [Crossref]

2014 (1)

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

2013 (1)

2011 (2)

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83(3), 031802 (2011).
[Crossref]

D. V. Dylov, L. Waller, and J. W. Fleischer, “Instability-driven recovery of diffused images,” Opt. Lett. 36(18), 3711–3713 (2011).
[Crossref] [PubMed]

2010 (3)

2009 (2)

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
[Crossref]

C. Sun, D. V. Dylov, and J. W. Fleischer, “Nonlinear focusing and defocusing of partially coherent spatial beams,” Opt. Lett. 34(19), 3003–3005 (2009).
[Crossref] [PubMed]

2003 (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[Crossref] [PubMed]

2002 (2)

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” Proc. Natl. Acad. Sci. U.S.A. 99(8), 5223–5227 (2002).
[Crossref] [PubMed]

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19(3), 502–512 (2002).
[Crossref]

2000 (4)

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290(5491), 495–498 (2000).
[Crossref] [PubMed]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84(3), 467–470 (2000).
[Crossref] [PubMed]

T. H. Coskun, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, “Coherence enhancement of spatially incoherent light beams through soliton interactions,” Opt. Lett. 25(11), 826–828 (2000).
[Crossref] [PubMed]

T. H. Coskun, D. N. Christodoulides, Y.-R. Kim, Z. Chen, M. Soljacic, and M. Segev, “Bright spatial solitons on a partially incoherent background,” Phys. Rev. Lett. 84(11), 2374–2377 (2000).
[Crossref] [PubMed]

1998 (2)

S. Gatz and J. Herrmann, “Anisotropy, nonlocality, and space-charge field displacement in (2 + 1)-dimensional self-trapping in biased photorefractive crystals,” Opt. Lett. 23(15), 1176–1178 (1998).
[Crossref] [PubMed]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280(5365), 889–892 (1998).
[Crossref] [PubMed]

1997 (2)

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78(4), 646–649 (1997).
[Crossref]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature 387(26), 880–883 (1997).

1996 (1)

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
[Crossref] [PubMed]

1995 (2)

1994 (1)

1993 (1)

1992 (1)

Barsi, C.

W. Wan, D. V. Dylov, C. Barsi, and J. W. Fleischer, “Diffraction from an edge in a self-focusing medium,” Opt. Lett. 35(16), 2819–2821 (2010).
[Crossref] [PubMed]

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
[Crossref]

Carvalho, M. I.

Chen, Z.

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” Proc. Natl. Acad. Sci. U.S.A. 99(8), 5223–5227 (2002).
[Crossref] [PubMed]

T. H. Coskun, D. N. Christodoulides, Y.-R. Kim, Z. Chen, M. Soljacic, and M. Segev, “Bright spatial solitons on a partially incoherent background,” Phys. Rev. Lett. 84(11), 2374–2377 (2000).
[Crossref] [PubMed]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280(5365), 889–892 (1998).
[Crossref] [PubMed]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
[Crossref] [PubMed]

Christodoulides, D. N.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[Crossref] [PubMed]

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” Proc. Natl. Acad. Sci. U.S.A. 99(8), 5223–5227 (2002).
[Crossref] [PubMed]

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19(3), 502–512 (2002).
[Crossref]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290(5491), 495–498 (2000).
[Crossref] [PubMed]

T. H. Coskun, D. N. Christodoulides, Y.-R. Kim, Z. Chen, M. Soljacic, and M. Segev, “Bright spatial solitons on a partially incoherent background,” Phys. Rev. Lett. 84(11), 2374–2377 (2000).
[Crossref] [PubMed]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84(3), 467–470 (2000).
[Crossref] [PubMed]

T. H. Coskun, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, “Coherence enhancement of spatially incoherent light beams through soliton interactions,” Opt. Lett. 25(11), 826–828 (2000).
[Crossref] [PubMed]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280(5365), 889–892 (1998).
[Crossref] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78(4), 646–649 (1997).
[Crossref]

D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12(9), 1628–1633 (1995).
[Crossref]

Coskun, T.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84(3), 467–470 (2000).
[Crossref] [PubMed]

Coskun, T. H.

T. H. Coskun, D. N. Christodoulides, Y.-R. Kim, Z. Chen, M. Soljacic, and M. Segev, “Bright spatial solitons on a partially incoherent background,” Phys. Rev. Lett. 84(11), 2374–2377 (2000).
[Crossref] [PubMed]

T. H. Coskun, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, “Coherence enhancement of spatially incoherent light beams through soliton interactions,” Opt. Lett. 25(11), 826–828 (2000).
[Crossref] [PubMed]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280(5365), 889–892 (1998).
[Crossref] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78(4), 646–649 (1997).
[Crossref]

Crosignani, B.

Di Porto, P.

Duree, G.

Dylov, D. V.

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[Crossref] [PubMed]

Engin, D.

Eugenieva, E.

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290(5491), 495–498 (2000).
[Crossref] [PubMed]

Fleischer, J. W.

D. V. Dylov, L. Waller, and J. W. Fleischer, “Instability-driven recovery of diffused images,” Opt. Lett. 36(18), 3711–3713 (2011).
[Crossref] [PubMed]

D. V. Dylov and J. W. Fleischer, “Modulation instability of a coherent-incoherent mixture,” Opt. Lett. 35(13), 2149–2151 (2010).
[Crossref] [PubMed]

W. Wan, D. V. Dylov, C. Barsi, and J. W. Fleischer, “Diffraction from an edge in a self-focusing medium,” Opt. Lett. 35(16), 2819–2821 (2010).
[Crossref] [PubMed]

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4(5), 323–328 (2010).
[Crossref]

C. Sun, D. V. Dylov, and J. W. Fleischer, “Nonlinear focusing and defocusing of partially coherent spatial beams,” Opt. Lett. 34(19), 3003–3005 (2009).
[Crossref] [PubMed]

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
[Crossref]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[Crossref] [PubMed]

Gan, H.

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

Gatz, S.

Goy, A.

A. Goy and D. Psaltis, “Imaging in focusing Kerr media using reverse propagation,” Photon. Res. 1(2), 96–101 (2013).
[Crossref]

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83(3), 031802 (2011).
[Crossref]

Grandpierre, A. G.

Guan, D.

Herrmann, J.

Kim, Y.-R.

T. H. Coskun, D. N. Christodoulides, Y.-R. Kim, Z. Chen, M. Soljacic, and M. Segev, “Bright spatial solitons on a partially incoherent background,” Phys. Rev. Lett. 84(11), 2374–2377 (2000).
[Crossref] [PubMed]

Kip, D.

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19(3), 502–512 (2002).
[Crossref]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290(5491), 495–498 (2000).
[Crossref] [PubMed]

Li, J.

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

Li, L.

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

Liu, J.

Liu, S.

Ma, C.

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

Martin, H.

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” Proc. Natl. Acad. Sci. U.S.A. 99(8), 5223–5227 (2002).
[Crossref] [PubMed]

Mitchell, M.

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280(5365), 889–892 (1998).
[Crossref] [PubMed]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature 387(26), 880–883 (1997).

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78(4), 646–649 (1997).
[Crossref]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
[Crossref] [PubMed]

Porto, P. D.

Psaltis, D.

A. Goy and D. Psaltis, “Imaging in focusing Kerr media using reverse propagation,” Photon. Res. 1(2), 96–101 (2013).
[Crossref]

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83(3), 031802 (2011).
[Crossref]

Salamo, G.

Sears, S. M.

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19(3), 502–512 (2002).
[Crossref]

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” Proc. Natl. Acad. Sci. U.S.A. 99(8), 5223–5227 (2002).
[Crossref] [PubMed]

Segev, M.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[Crossref] [PubMed]

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19(3), 502–512 (2002).
[Crossref]

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” Proc. Natl. Acad. Sci. U.S.A. 99(8), 5223–5227 (2002).
[Crossref] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290(5491), 495–498 (2000).
[Crossref] [PubMed]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84(3), 467–470 (2000).
[Crossref] [PubMed]

T. H. Coskun, D. N. Christodoulides, Y.-R. Kim, Z. Chen, M. Soljacic, and M. Segev, “Bright spatial solitons on a partially incoherent background,” Phys. Rev. Lett. 84(11), 2374–2377 (2000).
[Crossref] [PubMed]

T. H. Coskun, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, “Coherence enhancement of spatially incoherent light beams through soliton interactions,” Opt. Lett. 25(11), 826–828 (2000).
[Crossref] [PubMed]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280(5365), 889–892 (1998).
[Crossref] [PubMed]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature 387(26), 880–883 (1997).

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78(4), 646–649 (1997).
[Crossref]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
[Crossref] [PubMed]

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, and E. Sharp, “Dimensionality and size of photorefractive spatial solitons,” Opt. Lett. 19(16), 1195–1197 (1994).
[Crossref] [PubMed]

B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10(3), 446–453 (1993).
[Crossref]

Sharp, E.

Sheng, C.

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

Shih, M.

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
[Crossref] [PubMed]

Soljacic, M.

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19(3), 502–512 (2002).
[Crossref]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84(3), 467–470 (2000).
[Crossref] [PubMed]

T. H. Coskun, D. N. Christodoulides, Y.-R. Kim, Z. Chen, M. Soljacic, and M. Segev, “Bright spatial solitons on a partially incoherent background,” Phys. Rev. Lett. 84(11), 2374–2377 (2000).
[Crossref] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290(5491), 495–498 (2000).
[Crossref] [PubMed]

Song, F.

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

Sun, C.

Sun, M.

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

Sun, Z.

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

Vishwanath, A.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84(3), 467–470 (2000).
[Crossref] [PubMed]

Waller, L.

Wan, W.

W. Wan, D. V. Dylov, C. Barsi, and J. W. Fleischer, “Diffraction from an edge in a self-focusing medium,” Opt. Lett. 35(16), 2819–2821 (2010).
[Crossref] [PubMed]

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
[Crossref]

Wang, J.

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

Wu, Y.

Xu, J.

Xu, N.

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

Xu, T.

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

Yariv, A.

Zhang, G.

Appl. Opt. (2)

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

Nat. Photonics (2)

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4(5), 323–328 (2010).
[Crossref]

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
[Crossref]

Nature (2)

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature 387(26), 880–883 (1997).

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003).
[Crossref] [PubMed]

Opt. Lett. (7)

Photon. Res. (1)

Phys. Rev. A (1)

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83(3), 031802 (2011).
[Crossref]

Phys. Rev. Lett. (4)

T. H. Coskun, D. N. Christodoulides, Y.-R. Kim, Z. Chen, M. Soljacic, and M. Segev, “Bright spatial solitons on a partially incoherent background,” Phys. Rev. Lett. 84(11), 2374–2377 (2000).
[Crossref] [PubMed]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84(3), 467–470 (2000).
[Crossref] [PubMed]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
[Crossref] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in biased photorefractive media,” Phys. Rev. Lett. 78(4), 646–649 (1997).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” Proc. Natl. Acad. Sci. U.S.A. 99(8), 5223–5227 (2002).
[Crossref] [PubMed]

Proc. SPIE (1)

H. Gan, C. Ma, Z. Sun, T. Xu, J. Li, N. Xu, J. Wang, F. Song, C. Sheng, M. Sun, and L. Li, “Image blurring and deblurring using two biased photorefractive crystals in the frequency domain,” Proc. SPIE 9269, 926910 (2014).
[Crossref]

Science (2)

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290(5491), 495–498 (2000).
[Crossref] [PubMed]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280(5365), 889–892 (1998).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 Self-focusing and self-defocusing experimental results of a weakly illuminated object with a biased photorefractive crystal applied in the Fourier plane of the imaging system. Di: the self-defocused output image with a bias voltage of -i × 100V; FFT(Di): the calculated spatial frequency spectrum of Di; Fi: the self-focused output image with a bias voltage of i × 100V; FFT(Fi): the calculated spatial frequency spectrum of Fi; i = 0, 1, ... 5. The spatial frequency spectra are in log scale and zero-centered.
Fig. 2
Fig. 2 Modeling results illustrate the hidden signal recovery process: (a) is the input image combining a weak signal and an overwhelming noise pattern; (b) and (c) are output images with increased bias voltage. The average noise grain sizes in (a-c) are 1.4 × 1.4, 0.9 × 1.2, and 0.5 × 1.1 pixels on the CCD camera, respectively.
Fig. 3
Fig. 3 Experimental scheme for hidden image recovery using a photorefractive crystal in the Fourier plane of the imaging system. BS: beam splitter; L: lens; D: diffuser; A: aperture; M: mirror; AF: adjustable ND filter; BD: beam dump.
Fig. 4
Fig. 4 The output images of the optical imaging system with a biased photorefractive crystal in the Fourier plane. Ni, Si, and Ti are output images for noise, signal, and noise plus signal, respectively. The bias voltage is i × 200V for i = 0, 1, ...4, respectively and N0, S0, and T0 are the linear output images with zero bias.
Fig. 5
Fig. 5 Hidden image recovery with bias voltage applied on photorefractive crystal. The system is nonlinear with applied voltage.

Equations (2)

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Δ n e,o = 1 2 n e,o 3 r 33,13 E o 1 1+I(x,z)/ I d ,
n e,o x,z = 1 2 n e,o 3 r 33,13 E o 1 (1+I(x,z)/ I d ) 2 I(x,z) x,z .

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