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Multidimensional quasiperiodic antiphase dynamics.

A G Vladimirov1, E A Viktorov, P Mandel

  • 1Physics Faculty, St. Petersburg State University, 198904 St. Petersburg, Russia.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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We analyzed degenerate Hopf bifurcations in solid-state lasers. Stable periodic solutions appear for N=3, quasiperiodic for N=4, and chaotic behavior for N>4.

Area of Science:

  • Nonlinear dynamics
  • Laser physics
  • Quantum optics

Background:

  • Solid-state lasers with intracavity second harmonic generation exhibit complex dynamics.
  • Degenerate Hopf bifurcations occur when multiple stationary modes become unstable simultaneously.

Purpose of the Study:

  • To analytically investigate the (N-1)-fold degenerate Hopf bifurcation in a specific laser model.
  • To characterize the stability and types of solutions emerging from this bifurcation.

Main Methods:

  • Analytical study using the normal form method.
  • Exploitation of problem symmetries.
  • Numerical simulations for N>4.

Main Results:

  • For N=3, stable periodic antiphased solutions emerge.

Related Experiment Videos

  • For N=4, stable quasiperiodic solutions arise.
  • For N>4, unstable quasiperiodic solutions can lead to chaotic itineracy.

    • Conclusions:

    • The behavior of the laser system transitions from periodic to quasiperiodic and then to chaotic dynamics as the number of unstable modes increases.
    • The study provides insights into the complex dynamics of degenerate Hopf bifurcations in optical systems.