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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)

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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

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

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)

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