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Low-frequency fluctuations in the Lang-Kobayashi equations.

D Pieroux1, Paul Mandel

  • 1Optique Nonlinaire Theorique, Universit Libre de Bruxelles, Campus Plaine Code Postal 231, B-1050 Bruxelles, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
Summary

This study simplifies the Lang-Kobayashi equations to analyze laser dynamics. It reveals that low-frequency fluctuations arise from unstable steady states in bistable laser systems.

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Area of Science:

  • Nonlinear dynamics
  • Laser physics
  • Optical engineering

Background:

  • The Lang-Kobayashi equations model the dynamics of semiconductor lasers with external optical feedback.
  • Understanding complex dynamics like low-frequency fluctuations (LFF) is crucial for laser stability and applications.

Purpose of the Study:

  • To simplify the Lang-Kobayashi equations for analyzing long-delay-time dynamics.
  • To investigate the origins of low-frequency fluctuations (LFF) in bistable laser systems.

Main Methods:

  • Local analysis of the Lang-Kobayashi equations in the long-delay-time limit.
  • Focus on a single mode-antimode pair.
  • Analysis of dynamics within the hysteresis domain between steady states.

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Main Results:

  • Simplification reveals LFF in regions of bistability with unstable steady states.
  • High-frequency oscillations correlate with dynamics near unstable upper steady states.
  • Drop-offs in LFF correspond to dynamics near unstable lower steady states.

Conclusions:

  • The study provides a simplified framework for understanding complex laser dynamics.
  • Unstable steady states play a critical role in generating LFF in bistable lasers.
  • The findings offer insights into controlling and predicting laser behavior under optical feedback.