Continuation of periodic solutions in the waveguide array mode-locked laser. (English) Zbl 1235.78034
Authors’ abstract: We apply the adjoint continuation method to characterize the bifurcation structure of the multi-pulsing instability associated with the periodic solution branches in mode-locked laser cavities. Supplementing the method with a computation of the Floquet multiplies allows for explicit determination of the stability of each branch. The method reveals that, when gain is increased, the multi-pulsing transition starts with a Hopf bifurcation, followed by a period-doubling bifurcation, and a saddle - node bifurcation for limit cycles. Finally, the system exhibits chaotic dynamics and transitions to the double-pulse solutions. Although this method is applied specifically to the waveguide array made-locking model, the multi-pulsing transition is conjectured to be ubiquitous and these results agree with experimental and computational results from models.
Reviewer: Shoukry S. Hassan (Bahrain)
MSC:
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
| 78A50 | Antennas, waveguides in optics and electromagnetic theory |
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