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Nonlinearity and Localization in One-Dimensional Random Media

  • R. Knapp
  • G. Papanicolaou
  • B. White
Part of the Springer Proceedings in Physics book series (SPPHY, volume 39)

Abstract

A nonlinear Fabry-Perot etalon with random inhomogeneities is modeled by a one-dimensional stochastic Helmholtz equation. An asymptotic estimate of the threshold intensity needed for optical bistability is found for homogeneous media as a function of length. In the random case localization is affected and estimates of the energy growth are derived for large lengths with fixed output. Comparisons of the theory and numerical simulations are presented.

Keywords

Correlation Length Transmission Coefficient Elliptic Function Nonlinear Medium Random Medium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • R. Knapp
    • 1
  • G. Papanicolaou
    • 2
  • B. White
    • 3
  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisUSA
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  3. 3.Exxon Research and Engineering CompanyAnnandaleUSA

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