Continuation of periodic solutions in the waveguide array mode-locked laser

PHYSICA D-NONLINEAR PHENOMENA

卷:240

Article

Williams, Matthew O.¹  Wilkening, Jon²  Shlizerman, Eli¹  Kutz, J. Nathan¹ 

[1] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

关键词: Periodic solutions;    Mode-locked lasers;    Waveguide arrays;   

DOI  :  10.1016/j.physd.2011.06.018

来源: Elsevier

【 摘 要 】

We apply the adjoint continuation method to construct highly accurate, periodic solutions that are observed to play a critical role in the multi-pulsing transition of mode-locked laser cavities. The method allows for the construction of solution branches and the identification of their bifurcation structure. Supplementing the adjoint continuation method with a computation of the Floquet multipliers allows for explicit determination of the stability of each branch. This 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 mode-locking model, the multi-pulsing transition is conjectured to be ubiquitous and these results agree with experimental and computational results from other models. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free