期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 240, 期 22, 页码 1791-1804出版社
ELSEVIER
DOI: 10.1016/j.physd.2011.06.018
关键词
Periodic solutions; Mode-locked lasers; Waveguide arrays
资金
- National Science Foundation (NSF) [DMS-1007621, DMS-0955078]
- US Air Force Office of Scientific Research (AFOSR) [FA9550-09-0174]
- Office of Science, Computational and Technology Research, US Department of Energy [DE-AC02-05CH11231]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1007621, 0955078] Funding Source: National Science Foundation
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.
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