Abstract

By experimental measurements and theoretical analyses, we demonstrate the control of modulation instability in photorefractive crystals though the intensity ratio of coherent background to signal fields. Appearance, suppression, and disappearance of modulated stripes are observed in a series of spontaneous optical pattern formations, as the intensity of input coherent beam increases. Theoretical curves based on the band transport model give good agreement to experimental data, both for different bias voltages and different intensity ratios.

© 2015 Optical Society of America

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References

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  1. T. Shinbrot and F. J. Muzzio, “Noise to order,” Nature 410, 251 (2001).
    [Crossref] [PubMed]
  2. V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exper. Theor. Phys. Lett. 3, 307 (1966).
  3. V. I. Karpman, “Self-modulation of nonlinear plane waves in dispersive media,” J. Exper. Theor. Phys. Lett. 6, 277 (1967).
  4. T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water,” J. Fluid Mech. 27, 417 (1967).
    [Crossref]
  5. A. Hasegawa, Plasma Instabilities and Nonlinear Effects, (Springer-Verlag1975).
    [Crossref]
  6. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  7. M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals,” Opt. Commun. 126, 167 (1996).
    [Crossref]
  8. C. C. Jeng, Y. Y. Lin, R. C. Hong, and R.-K. Lee, “Optical Pattern Transitions from Modulation to Transverse Instabilities in Photorefractive Crystals,” Phys. Rev. Lett. 102, 153905(2009).
    [Crossref] [PubMed]
  9. M. Shen, Y. Su, R.-C. Hong, Y. Y. Lin, C.-C. Jeng, M.-F. Shih, and R.-K. Lee, “Observation of phase boundaries in spontaneous optical pattern formation,” Phys. Rev. A 91, 023810 (2015)
    [Crossref]
  10. D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nature Photon. 6, 463 (2012).
    [Crossref]
  11. A. M. Rubenchik, S. K. Turitsyn, and M. P. Fedoruk, “Modulation instability in high power laser amplifiers,” Opt. Express 18, 1380 (2010).
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    [Crossref] [PubMed]
  13. K. Nithyanandan, R. Vasantha Jayakantha Raja, and K. Porsezian, “Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion,” Phys. Rev. A 87, 043805 (2013).
    [Crossref]
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    [Crossref] [PubMed]
  15. M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467 (2000).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  21. D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 9 (1995).
    [Crossref]
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    [Crossref]

2015 (1)

M. Shen, Y. Su, R.-C. Hong, Y. Y. Lin, C.-C. Jeng, M.-F. Shih, and R.-K. Lee, “Observation of phase boundaries in spontaneous optical pattern formation,” Phys. Rev. A 91, 023810 (2015)
[Crossref]

2013 (1)

K. Nithyanandan, R. Vasantha Jayakantha Raja, and K. Porsezian, “Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion,” Phys. Rev. A 87, 043805 (2013).
[Crossref]

2012 (2)

A. Armaroli and F. Biancalana, “Tunable modulational instability sidebands via parametric resonance in periodically tapered optical fibers,” Opt. Express 20, 25096 (2012).
[Crossref] [PubMed]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nature Photon. 6, 463 (2012).
[Crossref]

2011 (1)

2010 (2)

2009 (1)

C. C. Jeng, Y. Y. Lin, R. C. Hong, and R.-K. Lee, “Optical Pattern Transitions from Modulation to Transverse Instabilities in Photorefractive Crystals,” Phys. Rev. Lett. 102, 153905(2009).
[Crossref] [PubMed]

2002 (1)

M. F. Shih, C. C. Jeng, F. W. Sheu, and C. Y. Lin, “Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 88, 133902 (2002).
[Crossref] [PubMed]

2001 (2)

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[Crossref]

T. Shinbrot and F. J. Muzzio, “Noise to order,” Nature 410, 251 (2001).
[Crossref] [PubMed]

2000 (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, 495 (2000).
[Crossref] [PubMed]

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

1996 (1)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals,” Opt. Commun. 126, 167 (1996).
[Crossref]

1995 (1)

1979 (1)

N.V. Kuktharev, V.B. Markov, S.G. Odulov, M.S. Soskin, and L. Vinetskii, “Holographic storage in electrooptic crystals I,” Ferroelectrics 22, 949 (1979).
[Crossref]

1967 (2)

V. I. Karpman, “Self-modulation of nonlinear plane waves in dispersive media,” J. Exper. Theor. Phys. Lett. 6, 277 (1967).

T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water,” J. Fluid Mech. 27, 417 (1967).
[Crossref]

1966 (1)

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exper. Theor. Phys. Lett. 3, 307 (1966).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Armaroli, A.

Bang, O.

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[Crossref]

Barviau, B.

Benjamin, T. B.

T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water,” J. Fluid Mech. 27, 417 (1967).
[Crossref]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exper. Theor. Phys. Lett. 3, 307 (1966).

Biancalana, F.

Boucon, A.

Carvalho, M. I.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals,” Opt. Commun. 126, 167 (1996).
[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 (1995).
[Crossref]

Christodoulides, D. N.

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

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

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals,” Opt. Commun. 126, 167 (1996).
[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 (1995).
[Crossref]

Coskun, T. H.

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

Denz, C.

C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics, (Springer-Verlag, 2003).
[Crossref]

Droques, M.

Dylov, D. V.

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, 495 (2000).
[Crossref] [PubMed]

Fedoruk, M. P.

Feir, J. E.

T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water,” J. Fluid Mech. 27, 417 (1967).
[Crossref]

Fleischer, J. W.

Hasegawa, A.

A. Hasegawa, Plasma Instabilities and Nonlinear Effects, (Springer-Verlag1975).
[Crossref]

Herink, G.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nature Photon. 6, 463 (2012).
[Crossref]

Hong, R. C.

C. C. Jeng, Y. Y. Lin, R. C. Hong, and R.-K. Lee, “Optical Pattern Transitions from Modulation to Transverse Instabilities in Photorefractive Crystals,” Phys. Rev. Lett. 102, 153905(2009).
[Crossref] [PubMed]

Hong, R.-C.

M. Shen, Y. Su, R.-C. Hong, Y. Y. Lin, C.-C. Jeng, M.-F. Shih, and R.-K. Lee, “Observation of phase boundaries in spontaneous optical pattern formation,” Phys. Rev. A 91, 023810 (2015)
[Crossref]

Jalali, B.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nature Photon. 6, 463 (2012).
[Crossref]

Jeng, C. C.

C. C. Jeng, Y. Y. Lin, R. C. Hong, and R.-K. Lee, “Optical Pattern Transitions from Modulation to Transverse Instabilities in Photorefractive Crystals,” Phys. Rev. Lett. 102, 153905(2009).
[Crossref] [PubMed]

M. F. Shih, C. C. Jeng, F. W. Sheu, and C. Y. Lin, “Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 88, 133902 (2002).
[Crossref] [PubMed]

Jeng, C.-C.

M. Shen, Y. Su, R.-C. Hong, Y. Y. Lin, C.-C. Jeng, M.-F. Shih, and R.-K. Lee, “Observation of phase boundaries in spontaneous optical pattern formation,” Phys. Rev. A 91, 023810 (2015)
[Crossref]

Karpman, V. I.

V. I. Karpman, “Self-modulation of nonlinear plane waves in dispersive media,” J. Exper. Theor. Phys. Lett. 6, 277 (1967).

Kip, D.

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

Krolikowski, W.

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[Crossref]

Kudlinski, A.

Kuktharev, N.V.

N.V. Kuktharev, V.B. Markov, S.G. Odulov, M.S. Soskin, and L. Vinetskii, “Holographic storage in electrooptic crystals I,” Ferroelectrics 22, 949 (1979).
[Crossref]

Lee, R.-K.

M. Shen, Y. Su, R.-C. Hong, Y. Y. Lin, C.-C. Jeng, M.-F. Shih, and R.-K. Lee, “Observation of phase boundaries in spontaneous optical pattern formation,” Phys. Rev. A 91, 023810 (2015)
[Crossref]

C. C. Jeng, Y. Y. Lin, R. C. Hong, and R.-K. Lee, “Optical Pattern Transitions from Modulation to Transverse Instabilities in Photorefractive Crystals,” Phys. Rev. Lett. 102, 153905(2009).
[Crossref] [PubMed]

Lin, C. Y.

M. F. Shih, C. C. Jeng, F. W. Sheu, and C. Y. Lin, “Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 88, 133902 (2002).
[Crossref] [PubMed]

Lin, Y. Y.

M. Shen, Y. Su, R.-C. Hong, Y. Y. Lin, C.-C. Jeng, M.-F. Shih, and R.-K. Lee, “Observation of phase boundaries in spontaneous optical pattern formation,” Phys. Rev. A 91, 023810 (2015)
[Crossref]

C. C. Jeng, Y. Y. Lin, R. C. Hong, and R.-K. Lee, “Optical Pattern Transitions from Modulation to Transverse Instabilities in Photorefractive Crystals,” Phys. Rev. Lett. 102, 153905(2009).
[Crossref] [PubMed]

Markov, V.B.

N.V. Kuktharev, V.B. Markov, S.G. Odulov, M.S. Soskin, and L. Vinetskii, “Holographic storage in electrooptic crystals I,” Ferroelectrics 22, 949 (1979).
[Crossref]

Mussot, A.

Muzzio, F. J.

T. Shinbrot and F. J. Muzzio, “Noise to order,” Nature 410, 251 (2001).
[Crossref] [PubMed]

Nithyanandan, K.

K. Nithyanandan, R. Vasantha Jayakantha Raja, and K. Porsezian, “Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion,” Phys. Rev. A 87, 043805 (2013).
[Crossref]

Odulov, S.G.

N.V. Kuktharev, V.B. Markov, S.G. Odulov, M.S. Soskin, and L. Vinetskii, “Holographic storage in electrooptic crystals I,” Ferroelectrics 22, 949 (1979).
[Crossref]

Porsezian, K.

K. Nithyanandan, R. Vasantha Jayakantha Raja, and K. Porsezian, “Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion,” Phys. Rev. A 87, 043805 (2013).
[Crossref]

Rasmussen, J. J.

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[Crossref]

Ropers, C.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nature Photon. 6, 463 (2012).
[Crossref]

Rubenchik, A. M.

Schwab, M.

C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics, (Springer-Verlag, 2003).
[Crossref]

Segev, M.

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

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

Shen, M.

M. Shen, Y. Su, R.-C. Hong, Y. Y. Lin, C.-C. Jeng, M.-F. Shih, and R.-K. Lee, “Observation of phase boundaries in spontaneous optical pattern formation,” Phys. Rev. A 91, 023810 (2015)
[Crossref]

Sheu, F. W.

M. F. Shih, C. C. Jeng, F. W. Sheu, and C. Y. Lin, “Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 88, 133902 (2002).
[Crossref] [PubMed]

Shih, M. F.

M. F. Shih, C. C. Jeng, F. W. Sheu, and C. Y. Lin, “Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 88, 133902 (2002).
[Crossref] [PubMed]

Shih, M.-F.

M. Shen, Y. Su, R.-C. Hong, Y. Y. Lin, C.-C. Jeng, M.-F. Shih, and R.-K. Lee, “Observation of phase boundaries in spontaneous optical pattern formation,” Phys. Rev. A 91, 023810 (2015)
[Crossref]

Shinbrot, T.

T. Shinbrot and F. J. Muzzio, “Noise to order,” Nature 410, 251 (2001).
[Crossref] [PubMed]

Singh, S. R.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals,” Opt. Commun. 126, 167 (1996).
[Crossref]

Soljacic, M.

M. Soljacic, M. Segev, T. H. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467 (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, 495 (2000).
[Crossref] [PubMed]

Solli, D. R.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nature Photon. 6, 463 (2012).
[Crossref]

Soskin, M.S.

N.V. Kuktharev, V.B. Markov, S.G. Odulov, M.S. Soskin, and L. Vinetskii, “Holographic storage in electrooptic crystals I,” Ferroelectrics 22, 949 (1979).
[Crossref]

Su, Y.

M. Shen, Y. Su, R.-C. Hong, Y. Y. Lin, C.-C. Jeng, M.-F. Shih, and R.-K. Lee, “Observation of phase boundaries in spontaneous optical pattern formation,” Phys. Rev. A 91, 023810 (2015)
[Crossref]

Sylvestre, T.

Taki, M.

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exper. Theor. Phys. Lett. 3, 307 (1966).

Turitsyn, S. K.

Vasantha Jayakantha Raja, R.

K. Nithyanandan, R. Vasantha Jayakantha Raja, and K. Porsezian, “Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion,” Phys. Rev. A 87, 043805 (2013).
[Crossref]

Vinetskii, L.

N.V. Kuktharev, V.B. Markov, S.G. Odulov, M.S. Soskin, and L. Vinetskii, “Holographic storage in electrooptic crystals I,” Ferroelectrics 22, 949 (1979).
[Crossref]

Vishwanath, A.

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

Weilnau, C.

C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics, (Springer-Verlag, 2003).
[Crossref]

Wyller, J.

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[Crossref]

Ferroelectrics (1)

N.V. Kuktharev, V.B. Markov, S.G. Odulov, M.S. Soskin, and L. Vinetskii, “Holographic storage in electrooptic crystals I,” Ferroelectrics 22, 949 (1979).
[Crossref]

J. Exper. Theor. Phys. Lett. (2)

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exper. Theor. Phys. Lett. 3, 307 (1966).

V. I. Karpman, “Self-modulation of nonlinear plane waves in dispersive media,” J. Exper. Theor. Phys. Lett. 6, 277 (1967).

J. Fluid Mech. (1)

T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water,” J. Fluid Mech. 27, 417 (1967).
[Crossref]

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

Nature (1)

T. Shinbrot and F. J. Muzzio, “Noise to order,” Nature 410, 251 (2001).
[Crossref] [PubMed]

Nature Photon. (1)

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nature Photon. 6, 463 (2012).
[Crossref]

Opt. Commun. (1)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Modulational instability of quasi-plane-wave optical beams biased in photorefractive crystals,” Opt. Commun. 126, 167 (1996).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (2)

K. Nithyanandan, R. Vasantha Jayakantha Raja, and K. Porsezian, “Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion,” Phys. Rev. A 87, 043805 (2013).
[Crossref]

M. Shen, Y. Su, R.-C. Hong, Y. Y. Lin, C.-C. Jeng, M.-F. Shih, and R.-K. Lee, “Observation of phase boundaries in spontaneous optical pattern formation,” Phys. Rev. A 91, 023810 (2015)
[Crossref]

Phys. Rev. E (1)

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[Crossref]

Phys. Rev. Lett. (3)

C. C. Jeng, Y. Y. Lin, R. C. Hong, and R.-K. Lee, “Optical Pattern Transitions from Modulation to Transverse Instabilities in Photorefractive Crystals,” Phys. Rev. Lett. 102, 153905(2009).
[Crossref] [PubMed]

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

M. F. Shih, C. C. Jeng, F. W. Sheu, and C. Y. Lin, “Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 88, 133902 (2002).
[Crossref] [PubMed]

Science (1)

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

Other (3)

A. Hasegawa, Plasma Instabilities and Nonlinear Effects, (Springer-Verlag1975).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

C. Denz, M. Schwab, and C. Weilnau, Transverse-Pattern Formation in Photorefractive Optics, (Springer-Verlag, 2003).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 Illustration of our experimental setup, where PBS is the polarization beam splitter, SBN:60 is the photorefractive crystal, HWP is a half-wave plate, L1 and L2 are two planoconvex lenses used for beam collimation, M1 and M2 are two reflecting mirrors, and L3 is an imaging lens to collect pattern images into the CCD camera.
Fig. 2
Fig. 2 Upper-panel: Optical intensity patterns of a coherent beam at the output plane through a nonlinear crystal at different bias voltages (shown in the left column) and different signal intensities (increase from left to right). Lower-panel: MI spectra for the instability growth rate h2 versus the normalized signal intensity I/Ith. Theoretical curves for different bias voltages are depicted in solid-curves; while the labeled markers correspond to the experimental data shown in the Upper-panel. Here, the intensity ratio of background to signal beams is rBS = 0.
Fig. 3
Fig. 3 Upper-panel: Optical intensity patterns measured at different intensity ratios (shown in the left column) and different signal intensities (increase from left to right). Lower-panel: MI spectra for the instability growth rate h2 versus the normalized signal intensity I/Ith. Theoretical curves are depicted in solid-curves; while the labeled markers correspond to the experimental data shown in the Upper-panel. Here, unlabeled markers (with empty shapes) are additional measured data points not shown in the Upper-panel.

Equations (3)

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i A z + 1 2 A x x γ ( V ) 2 t F ( | A ( t ) | 2 ) e ( t t ) / τ τ d t A = 0 ,
F ( | A | 2 ) = 1 1 + ( 1 + r BS ) | A | 2 ,
h 2 = ± Re { γ 2 ( 1 + i Ω τ ) ( 1 + r BS ) I [ 1 + ( 1 + r BS ) I ] 2 k 2 k 4 4 } ,

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