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Modulational instability in periodic quadratic nonlinear materials.

J F Corney1, O Bang

  • 1Department of Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark.

Physical Review Letters
|October 3, 2001
PubMed
Summary

Modulational instability in nonlinear materials is investigated. Periodicity of gratings alters gain spectrum but never eliminates instability, with low-frequency gain disappearing for certain gratings.

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Area of Science:

  • Nonlinear optics
  • Wave propagation in periodic media

Background:

  • Quadratic nonlinear materials exhibit complex wave dynamics.
  • Quasi-phase-matching gratings are used to enhance nonlinear interactions.
  • Modulational instability can disrupt coherent wave propagation.

Purpose of the Study:

  • To investigate modulational instability in plane waves within quadratic nonlinear materials.
  • To analyze the effect of linear and nonlinear quasi-phase-matching gratings on this instability.
  • To understand the spectral features of the gain in such systems.

Main Methods:

  • Exact Floquet calculations were performed.
  • Numerical simulations were used for confirmation.
  • An averaged theory was employed to predict spectral features.

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Main Results:

  • Periodicity of gratings significantly alters the gain spectrum.
  • Instability is never completely removed by grating periodicity.
  • Low-frequency gain is accurately predicted by averaged theory and can disappear.
  • High-frequency gain is a consistent feature linked to non-phase-matched material.

Conclusions:

  • Grating periodicity offers control over modulational instability but not elimination.
  • Averaged theory effectively describes low-frequency spectral behavior.
  • High-frequency gain is an intrinsic property of the nonlinear material under non-phase-matched conditions.