Abstract

A novel dynamic of stochastic resonance in spatiotemporal chaos is presented, which is based on modulation instability of perturbed partially coherent wave. The noise immunity of chaos can be reinforced through this effect and used to restore the coherent signal information buried in chaotic perturbation. A theoretical model with fluctuations term is derived from the complex Ginzburg-Landau equation via Wigner transform. It shows that through weakening the nonlinear threshold and triggering energy redistribution, the coherent component dominates the instability damped by incoherent component. The spatiotemporal output showing the properties of stochastic resonance may provide a potential application of signal encryption and restoration.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2016 (1)

2015 (2)

A. J. Goodman and W. A. Tisdale, “Enhancement of second-order nonlinear-optical signals by optical stimulation,” Phys. Rev. Lett. 114(18), 183902 (2015).
[Crossref] [PubMed]

S. Kumar, R. Herrero, M. Botey, and K. Staliunas, “Taming of modulation instability by spatio-temporal modulation of the potential,” Sci. Rep. 5(1), 13268 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (1)

J. Jing and L. A. Wu, “Control of decoherence with no control,” Sci. Rep. 3, 2746 (2013).
[Crossref] [PubMed]

2012 (1)

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
[Crossref]

2010 (2)

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

2007 (2)

2005 (1)

R. L. Badzey and P. Mohanty, “Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance,” Nature 437(7061), 995–998 (2005).
[Crossref] [PubMed]

2004 (1)

R. Benzi and A. Sutera, “Stochastic resonance in two dimensional Landau Ginzburg equation,” J. Phys. Math. Gen. 37(32), 391–398 (2004).
[Crossref]

2002 (3)

L. Helczynski, D. Anderson, R. Fedele, B. Hall, and M. Lisak, “Propagation of partially incoherent light in nonlinear media via the Wigner transform method,” IEEE J. Quantum Electron. 8(3), 408–412 (2002).
[Crossref]

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(13), 133902 (2002).
[Crossref] [PubMed]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2A), 035602 (2002).
[Crossref] [PubMed]

2000 (3)

R. Fedele, D. Anderson, and M. Lisak, “Landau-type damping in non-linear wave packet propagation,” Phys. Scr. 2000(1T84), 27 (2000).
[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]

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]

1999 (1)

A. A. Sukhorukov and N. N. Akhmediev, “Coherent and incoherent contributions to multisoliton complexes,” Phys. Rev. Lett. 83(23), 4736–4739 (1999).
[Crossref]

1998 (1)

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[Crossref]

1997 (3)

R. Montagne and P. Colet, “Nonlinear diffusion control of spatiotemporal chaos in the complex Ginzburg-Landau equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(4), 4017–4024 (1997).
[Crossref]

H. Okamura, K. Takeuchi, T. Tanaka, and K. Kuroda, “Grating formation with very short pulses in photorefractive materials: weak excitation limit,” J. Opt. Soc. Am. B 14(10), 2650–2656 (1997).
[Crossref]

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]

1996 (2)

M. E. Bleich and J. E. S. Socolar, “Controlling spatiotemporal dynamics with time-delay feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(1), R17–R20 (1996).
[Crossref] [PubMed]

M. Franaszek and E. Simiu, “Stochastic resonance: A chaotic dynamics approach,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(2), 1298–1304 (1996).
[Crossref] [PubMed]

Akhmediev, N. N.

A. A. Sukhorukov and N. N. Akhmediev, “Coherent and incoherent contributions to multisoliton complexes,” Phys. Rev. Lett. 83(23), 4736–4739 (1999).
[Crossref]

Anderson, D.

L. Helczynski, D. Anderson, R. Fedele, B. Hall, and M. Lisak, “Propagation of partially incoherent light in nonlinear media via the Wigner transform method,” IEEE J. Quantum Electron. 8(3), 408–412 (2002).
[Crossref]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2A), 035602 (2002).
[Crossref] [PubMed]

R. Fedele, D. Anderson, and M. Lisak, “Landau-type damping in non-linear wave packet propagation,” Phys. Scr. 2000(1T84), 27 (2000).
[Crossref]

Badzey, R. L.

R. L. Badzey and P. Mohanty, “Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance,” Nature 437(7061), 995–998 (2005).
[Crossref] [PubMed]

Bartal, G.

Benzi, R.

R. Benzi and A. Sutera, “Stochastic resonance in two dimensional Landau Ginzburg equation,” J. Phys. Math. Gen. 37(32), 391–398 (2004).
[Crossref]

Bishop, C. A.

J. Jing, C. A. Bishop, and L. A. Wu, “Nonperturbative dynamical decoupling with random control,” Sci. Rep. 4, 6229 (2014).
[Crossref] [PubMed]

Blais, J. A. R.

M. Mansourpour, M. A. Rajabi, and J. A. R. Blais, “Effects and performance of speckle noise reduction filters on active radar and SAR images,” Proc. ISPRS, 14–16 (2006).

Bleich, M. E.

M. E. Bleich and J. E. S. Socolar, “Controlling spatiotemporal dynamics with time-delay feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(1), R17–R20 (1996).
[Crossref] [PubMed]

Botey, M.

S. Kumar, R. Herrero, M. Botey, and K. Staliunas, “Taming of modulation instability by spatio-temporal modulation of the potential,” Sci. Rep. 5(1), 13268 (2015).
[Crossref] [PubMed]

Buljan, H.

Cai, Y.

Cao, G.

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(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]

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]

Clerc, M. G.

Colet, P.

R. Montagne and P. Colet, “Nonlinear diffusion control of spatiotemporal chaos in the complex Ginzburg-Landau equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(4), 4017–4024 (1997).
[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.

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]

Dylov, D. V.

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]

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

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]

Fedele, R.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2A), 035602 (2002).
[Crossref] [PubMed]

L. Helczynski, D. Anderson, R. Fedele, B. Hall, and M. Lisak, “Propagation of partially incoherent light in nonlinear media via the Wigner transform method,” IEEE J. Quantum Electron. 8(3), 408–412 (2002).
[Crossref]

R. Fedele, D. Anderson, and M. Lisak, “Landau-type damping in non-linear wave packet propagation,” Phys. Scr. 2000(1T84), 27 (2000).
[Crossref]

Fleischer, J. W.

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

Franaszek, M.

M. Franaszek and E. Simiu, “Stochastic resonance: A chaotic dynamics approach,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(2), 1298–1304 (1996).
[Crossref] [PubMed]

Gammaitoni, L.

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[Crossref]

González-Cortés, G.

Goodman, A. J.

A. J. Goodman and W. A. Tisdale, “Enhancement of second-order nonlinear-optical signals by optical stimulation,” Phys. Rev. Lett. 114(18), 183902 (2015).
[Crossref] [PubMed]

Hall, B.

L. Helczynski, D. Anderson, R. Fedele, B. Hall, and M. Lisak, “Propagation of partially incoherent light in nonlinear media via the Wigner transform method,” IEEE J. Quantum Electron. 8(3), 408–412 (2002).
[Crossref]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2A), 035602 (2002).
[Crossref] [PubMed]

Hanggi, P.

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[Crossref]

Helczynski, L.

L. Helczynski, D. Anderson, R. Fedele, B. Hall, and M. Lisak, “Propagation of partially incoherent light in nonlinear media via the Wigner transform method,” IEEE J. Quantum Electron. 8(3), 408–412 (2002).
[Crossref]

Herink, G.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
[Crossref]

Herrero, R.

S. Kumar, R. Herrero, M. Botey, and K. Staliunas, “Taming of modulation instability by spatio-temporal modulation of the potential,” Sci. Rep. 5(1), 13268 (2015).
[Crossref] [PubMed]

Huang, N.

Jablan, M.

Jalali, B.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
[Crossref]

Jeng, C. C.

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(13), 133902 (2002).
[Crossref] [PubMed]

Jing, J.

J. Jing, C. A. Bishop, and L. A. Wu, “Nonperturbative dynamical decoupling with random control,” Sci. Rep. 4, 6229 (2014).
[Crossref] [PubMed]

J. Jing and L. A. Wu, “Control of decoherence with no control,” Sci. Rep. 3, 2746 (2013).
[Crossref] [PubMed]

Jung, P.

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[Crossref]

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(5491), 495–498 (2000).
[Crossref] [PubMed]

Kumar, S.

S. Kumar, R. Herrero, M. Botey, and K. Staliunas, “Taming of modulation instability by spatio-temporal modulation of the potential,” Sci. Rep. 5(1), 13268 (2015).
[Crossref] [PubMed]

Kuroda, K.

Li, X.

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(13), 133902 (2002).
[Crossref] [PubMed]

Lisak, M.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2A), 035602 (2002).
[Crossref] [PubMed]

L. Helczynski, D. Anderson, R. Fedele, B. Hall, and M. Lisak, “Propagation of partially incoherent light in nonlinear media via the Wigner transform method,” IEEE J. Quantum Electron. 8(3), 408–412 (2002).
[Crossref]

R. Fedele, D. Anderson, and M. Lisak, “Landau-type damping in non-linear wave packet propagation,” Phys. Scr. 2000(1T84), 27 (2000).
[Crossref]

Liu, H.

Manela, O.

Mansourpour, M.

M. Mansourpour, M. A. Rajabi, and J. A. R. Blais, “Effects and performance of speckle noise reduction filters on active radar and SAR images,” Proc. ISPRS, 14–16 (2006).

Marchesoni, F.

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[Crossref]

Mitchell, M.

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]

Mohanty, P.

R. L. Badzey and P. Mohanty, “Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance,” Nature 437(7061), 995–998 (2005).
[Crossref] [PubMed]

Montagne, R.

R. Montagne and P. Colet, “Nonlinear diffusion control of spatiotemporal chaos in the complex Ginzburg-Landau equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(4), 4017–4024 (1997).
[Crossref]

Odent, V.

Okamura, H.

Rajabi, M. A.

M. Mansourpour, M. A. Rajabi, and J. A. R. Blais, “Effects and performance of speckle noise reduction filters on active radar and SAR images,” Proc. ISPRS, 14–16 (2006).

Ropers, C.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
[Crossref]

Segev, M.

M. Jablan, H. Buljan, O. Manela, G. Bartal, and M. Segev, “Incoherent modulation instability in a nonlinear photonic lattice,” Opt. Express 15(8), 4623–4633 (2007).
[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]

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]

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]

Semenov, V. E.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2A), 035602 (2002).
[Crossref] [PubMed]

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(13), 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(13), 133902 (2002).
[Crossref] [PubMed]

Simiu, E.

M. Franaszek and E. Simiu, “Stochastic resonance: A chaotic dynamics approach,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(2), 1298–1304 (1996).
[Crossref] [PubMed]

Socolar, J. E. S.

M. E. Bleich and J. E. S. Socolar, “Controlling spatiotemporal dynamics with time-delay feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(1), R17–R20 (1996).
[Crossref] [PubMed]

Soljacic, 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(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]

Solli, D. R.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
[Crossref]

Staliunas, K.

S. Kumar, R. Herrero, M. Botey, and K. Staliunas, “Taming of modulation instability by spatio-temporal modulation of the potential,” Sci. Rep. 5(1), 13268 (2015).
[Crossref] [PubMed]

Sukhorukov, A. A.

A. A. Sukhorukov and N. N. Akhmediev, “Coherent and incoherent contributions to multisoliton complexes,” Phys. Rev. Lett. 83(23), 4736–4739 (1999).
[Crossref]

Sun, Q.

Sutera, A.

R. Benzi and A. Sutera, “Stochastic resonance in two dimensional Landau Ginzburg equation,” J. Phys. Math. Gen. 37(32), 391–398 (2004).
[Crossref]

Takeuchi, K.

Tanaka, T.

Tisdale, W. A.

A. J. Goodman and W. A. Tisdale, “Enhancement of second-order nonlinear-optical signals by optical stimulation,” Phys. Rev. Lett. 114(18), 183902 (2015).
[Crossref] [PubMed]

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]

Wang, F.

Wilson, M.

Wu, L. A.

J. Jing, C. A. Bishop, and L. A. Wu, “Nonperturbative dynamical decoupling with random control,” Sci. Rep. 4, 6229 (2014).
[Crossref] [PubMed]

J. Jing and L. A. Wu, “Control of decoherence with no control,” Sci. Rep. 3, 2746 (2013).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

L. Helczynski, D. Anderson, R. Fedele, B. Hall, and M. Lisak, “Propagation of partially incoherent light in nonlinear media via the Wigner transform method,” IEEE J. Quantum Electron. 8(3), 408–412 (2002).
[Crossref]

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

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

J. Phys. Math. Gen. (1)

R. Benzi and A. Sutera, “Stochastic resonance in two dimensional Landau Ginzburg equation,” J. Phys. Math. Gen. 37(32), 391–398 (2004).
[Crossref]

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]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6(7), 463–468 (2012).
[Crossref]

Nature (1)

R. L. Badzey and P. Mohanty, “Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance,” Nature 437(7061), 995–998 (2005).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2A), 035602 (2002).
[Crossref] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (3)

R. Montagne and P. Colet, “Nonlinear diffusion control of spatiotemporal chaos in the complex Ginzburg-Landau equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(4), 4017–4024 (1997).
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M. Franaszek and E. Simiu, “Stochastic resonance: A chaotic dynamics approach,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(2), 1298–1304 (1996).
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M. E. Bleich and J. E. S. Socolar, “Controlling spatiotemporal dynamics with time-delay feedback,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(1), R17–R20 (1996).
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Phys. Rev. Lett. (5)

A. J. Goodman and W. A. Tisdale, “Enhancement of second-order nonlinear-optical signals by optical stimulation,” Phys. Rev. Lett. 114(18), 183902 (2015).
[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(13), 133902 (2002).
[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]

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]

A. A. Sukhorukov and N. N. Akhmediev, “Coherent and incoherent contributions to multisoliton complexes,” Phys. Rev. Lett. 83(23), 4736–4739 (1999).
[Crossref]

Phys. Scr. (1)

R. Fedele, D. Anderson, and M. Lisak, “Landau-type damping in non-linear wave packet propagation,” Phys. Scr. 2000(1T84), 27 (2000).
[Crossref]

Rev. Mod. Phys. (1)

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[Crossref]

Sci. Rep. (3)

S. Kumar, R. Herrero, M. Botey, and K. Staliunas, “Taming of modulation instability by spatio-temporal modulation of the potential,” Sci. Rep. 5(1), 13268 (2015).
[Crossref] [PubMed]

J. Jing, C. A. Bishop, and L. A. Wu, “Nonperturbative dynamical decoupling with random control,” Sci. Rep. 4, 6229 (2014).
[Crossref] [PubMed]

J. Jing and L. A. Wu, “Control of decoherence with no control,” Sci. Rep. 3, 2746 (2013).
[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(5491), 495–498 (2000).
[Crossref] [PubMed]

Other (2)

R. W. Boyd, Nonlinear Optics (Academic, 2003).

M. Mansourpour, M. A. Rajabi, and J. A. R. Blais, “Effects and performance of speckle noise reduction filters on active radar and SAR images,” Proc. ISPRS, 14–16 (2006).

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Figures (4)

Fig. 1
Fig. 1 The instability growth rate with various perturbation of wavenumber. (a) s = 3; (b) c = 0.55, d = 0.25.
Fig. 2
Fig. 2 The cross-correlation between output and initial input versus (a) propagation time and (b) normalized noise intensity D. Here, c = 0.55, d = 0.25.
Fig. 3
Fig. 3 (a) The cross-correlation versus time under different parameters. (b)-(d) three groups of time-varying output.
Fig. 4
Fig. 4 Input noise-hidden images (a)-(c) with corresponding output (d)-(f). (g) SNR enhancement as a function of D.

Equations (16)

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t A = ( 1 i c ) ( 1 | A | 2 ) A + ( i + d ) x 2 A ,
f ( r , k , t ) = 1 ( 2 π ) 3 + φ * ( r + ξ 2 , t ) φ ( r ξ 2 , t ) exp ( i k ξ ) d 3 ξ .
f t + 2 ( 1 i d ) k r f 2 ( i + c ) ( 1 | φ | 2 ) sin ( 1 2 r k ) f = 0.
f ( r , k , t ) = f 0 ( k , t ) + a ρ a ( k , t ) e i a r ,
r ε ( r , t ) = κ a [ e i a r + ρ a ( k , t ) d 3 k ] ,
ρ a t + i β k a ρ a κ 2 i a α 2 + ρ a ( k , t ) d 3 k k f 0 = 0 ,
α κ 2 = + k f 0 i g β k a d 3 k .
g i n c o h = α β Δ k + κ 2 β I 0 .
I 0 > α 2 β Δ k 2 κ 2 .
I 0 t h l c 2 = 2 α 2 1 + 2 c d c 2 ( c 2 + 1 ) 2 .
f m i x = I 0 Δ k π ( Δ k 2 + k 2 ) + s I 0 m 0 [ J m δ ( k + k m ) J m δ ( k k m ) ] .
α β I 0 ( α β Δ k + g m i x ) 2 i π s I 0 α β = α κ 2 .
g m i x = α β Δ k + α β 2 I 0 i π s I 0 2 α 2 β / κ 2 .
g R = 2 α Δ k + 2 α I 0 v 2 + u 2 [ ( c d 1 ) u 2 + v 2 + u + ( c + d ) u 2 + v 2 u ] .
I t h ' = 2 α 2 [ 2 c d l c 2 2 π s c ( l c 2 + π s d ) ( c 2 1 ) ] [ 2 π s c + l c 2 ( c 2 1 ) ] 2 + [ 2 c l c 2 + π s ( c 2 1 ) ] 2 .
l c 2 X < π s Y .

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