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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 11 — May. 26, 2008
  • pp: 7818–7831

Spontaneous pattern formation upon incoherent waves: From modulation-instability to steady-state

Liad Levi, Tal Schwartz, Ofer Manela, Mordechai Segev, and Hrvoje Buljan  »View Author Affiliations


Optics Express, Vol. 16, Issue 11, pp. 7818-7831 (2008)
http://dx.doi.org/10.1364/OE.16.007818


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Abstract

We study the long-range propagation of incoherent light following the modulation instability (MI) process in non-instantaneous nonlinear Kerr-type media. We find that the system eventually reaches a steady-state characterized by a lower degree of coherence than in the initial state, with small fluctuations around a pronounced mean value. We find that the average values of the spatial correlation distance at steady-state and the fluctuations around it, which are obtained either through ensemble averaging, or by spatial averaging, or via temporal averaging, are all identical. This feature may be viewed as indication of ergodic behavior, which occurs in the long-time evolution following incoherent MI. Finally, we find that the steady-state properties of the system depend on the initial coherence but not on the nonlinearity strength, although the system evolves faster to steady-state as the strength of the nonlinearity is increased.

© 2008 Optical Society of America

OCIS Codes
(030.6600) Coherence and statistical optics : Statistical optics
(190.3100) Nonlinear optics : Instabilities and chaos
(190.3270) Nonlinear optics : Kerr effect

ToC Category:
Nonlinear Optics

History
Original Manuscript: March 10, 2008
Revised Manuscript: May 3, 2008
Manuscript Accepted: May 5, 2008
Published: May 15, 2008

Citation
Liad Levi, Tal Schwartz, Ofer Manela, Mordechai Segev, and Hrvoje Buljan, "Spontaneous pattern formation upon incoherent waves: From modulation-instability to steady-state," Opt. Express 16, 7818-7831 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-11-7818


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References

  1. M. C. Cross and P. C. Hohenberg, "Pattern formation outside of equilibrium," Rev. Mod. Phys. 65, 851-1112 (1993). [CrossRef]
  2. V. I. Bespalov and V. I. Talanov, "Filamentary structure of light beams in nonlinear liquids," Zh. Eksperim. i Teor. Fiz.-Pis'ma Redakt. 3, 471 (1966); [translation: JETP Letters 3, 307-312 (1966)].
  3. M. D. Iturbe-Castillo, M. Torres-Cisneros, J. J. Sanchez-Mondragon, S. Chavez-Cerda, S. I. Stepanov, V. A. Vysloukh, and G. E. Torres-Cisneros, "Experimental evidence of modulation instability in a photorefractive Bi12TiO20 crystal," Opt. Lett. 20, 1853 (1995). [CrossRef] [PubMed]
  4. R. Malendevich, L. Jankovic, G. Stegeman, and J. Stewart Aitchison, "Spatial modulation instability in a Kerr slab waveguide," Opt. Lett. 26, 1879-1881 (2001). [CrossRef]
  5. K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135-138 (1986). [CrossRef] [PubMed]
  6. L. A. Lugiato, Chaos Solitons Fractals 4, 1245-1251 (1994).
  7. F. T. Arecchi, S. Boccaletti, and P. Ramazza, "Pattern formation and competition in nonlinear optics," Phys. Rep. 318, 1-83 (1999). [CrossRef]
  8. R. W. Boyd, Nonlinear Optics (Academic Press, New York, 1994).
  9. M. Mitchell, Z. Chen, M. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996). [CrossRef] [PubMed]
  10. M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature (London) 387, 880-883 (1997). [CrossRef]
  11. M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Theory of self-trapped spatially incoherent light beams," Phys. Rev. Lett. 79, 4990-4993 (1997). [CrossRef]
  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, 467-470 �??2000). [CrossRef] [PubMed]
  13. S. M. Sears, M. Solja�?i�?, D. N. Christodoulides, and M. Segev, "Pattern formation via symmetry breaking in nonlinear weakly correlated systems," Phys. Rev. E 65, 036620-9 (2002). [CrossRef]
  14. H. Buljan, A. Šiber, M. Solja�?i�?, and M. Segev, "Propagation of incoherent "white" light and modulation instability in noninstantaneous nonlinear media," Phys. Rev. E 66, 035601-4 (2002). [CrossRef]
  15. D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000). [CrossRef] [PubMed]
  16. 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, 502-512 (2002). [CrossRef]
  17. J. Klinger, H. Martin, and Z. Chen, "Experiments on induced modulational instability of an incoherent optical beam," Opt. Lett. 26, 271-273 (2001). [CrossRef]
  18. T. Schwartz, T. Carmon, H. Buljan, and M. Segev, "Spontaneous pattern formation with incoherent white light," Phys. Rev. Lett. 93, 223901-5 (2004). [CrossRef] [PubMed]
  19. Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, "Clustering of solitons in weakly correlated wavefronts," PNAS 99, 5223-5227 (2002). [CrossRef]
  20. D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov,"Features of modulational instability of partially coherent light: Importance of the incoherence spectrum," Phys. Rev. E 69, 025601-025604 (2004). [CrossRef]
  21. D. Anderson, B. Hall, M. Lisak, and M. Marklund, "Statistical effects in the multistream model for quantum plasmas," Phys. Rev. E 65, 046417-5 (2002). [CrossRef]
  22. E. Fermi, J. Pasta, and S. Ulam, "Studies of non linear problems," Los Alamos Rpt. LA-1940 (1955).
  23. A. Picozzi, "Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics," Opt. Express 15, 9063-9083 (2007). [CrossRef] [PubMed]
  24. S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, "Velocity locking of incoherent nonlinear wave packets," Phys. Rev. Lett. 97, 033902-5 (2006). [CrossRef] [PubMed]
  25. S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharo., "Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear," Physica D (Amsterdam) 57, 96-160 (1992). [CrossRef]
  26. E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, "Nonlinear interaction of solitons and radiation," Physica D 87, 201-215 (1995) [CrossRef]
  27. The only exception we know of is M. Rigol, et al., Phys. Rev. Lett. 98, 050405-5 (2007) where a quantum integrable system relaxes to a steady state, carrying memory of initial conditions. [CrossRef] [PubMed]
  28. D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, and M. Segev, "Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media," Phys. Rev. E 63, 035601-035603 (R) (2001). [CrossRef]
  29. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995).
  30. E. T. Jaynes, "Information Theory and Statistical Mechanics," Phys. Rev. 106, 620-630 (1957). [CrossRef]
  31. E. T. Jaynes, "Information Theory and Statistical Mechanics. II," Phys. Rev. 108, 171-190 (1957). [CrossRef]
  32. V. G. Makhan�??kov and O. K. Pashaev, "Nonlinear Schrödinger equation with noncompact isogroup," Teor. Mat. Fiz. 53, 55 (1982) [Theor. Math. Phys. 53, 979-987 (1982)].
  33. M. Soljacic, K. Steiglitz, S. M. Sears, M. Segev, M. H. Jakubowski, and R. Squie, "Collisions of Two Solitons in an Arbitrary Number of Coupled Nonlinear Schrödinger Equations," Phys. Rev. Lett. 90, 254102-254105 (2003). [CrossRef] [PubMed]
  34. H. Buljan, M. Segev, and A. Vardi, "Incoherent Matter-Wave Solitons and pairing instability in an attractively interacting Bose-Einstein Condensate," Phys. Rev. Lett. 95, 180401-4 (2005). [CrossRef] [PubMed]

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