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Resonances between fundamental frequencies for lasers with large delayed feedbacks.

Anton V Kovalev1, Md Shariful Islam2,3, A Locquet2,3

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Semiconductor lasers with delayed feedback exhibit high-order frequency locking. This study explains the two-bifurcation process leading to two-frequency pulse generation and confirms experimental observations.

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Area of Science:

  • Nonlinear dynamics
  • Laser physics
  • Optoelectronics

Background:

  • Semiconductor lasers with delayed optical feedback can exhibit complex dynamics.
  • High-order frequency locking, where the relaxation oscillation frequency locks to harmonics of the feedback frequency, has been experimentally observed.

Purpose of the Study:

  • To analyze the dynamical behavior of semiconductor lasers subject to large delayed optical feedback.
  • To explain the underlying mechanisms of high-order frequency locking phenomena.
  • To provide a theoretical framework for experimental investigations.

Main Methods:

  • Analysis of rate equations for laser dynamics.
  • Derivation of an amplitude equation near the first Hopf bifurcation.
  • Numerical simulations to observe frequency locking.
  • Formulation of a closed system of ordinary differential equations.

Main Results:

  • The onset of two-frequency pulse generation occurs via two successive Hopf bifurcations.
  • A secondary Hopf bifurcation leads to a two-frequency regime with resonant frequencies.
  • Frequency locking phenomena were numerically observed and analytically explained.
  • Experimental observations confirmed the frequency locking and the nearly constant slow period.

Conclusions:

  • The study provides a mathematical explanation for high-order frequency locking in semiconductor lasers with delayed feedback.
  • The findings confirm previous experimental observations and highlight the importance of the first two bifurcations.
  • The derived theoretical framework can guide future experimental research in this area.