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

Liad Levi*, Tal Schwartz, Ofer Manela, Mordechai Segev, Hrvoje Buljan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)7818-7831
Number of pages14
JournalOptics Express
Issue number11
StatePublished - 26 May 2008
Externally publishedYes


Dive into the research topics of 'Spontaneous pattern formation upon incoherent waves: From modulation-instability to steady-state'. Together they form a unique fingerprint.

Cite this