Different routes to chaos in the Ti:Sapphire laser

MARCELO KOVALSKY; ALEJANDRO HNILO

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

Año: 2004 vol. 70 p. 1 - 10

1050-2947

Kerr-lens mode-locked, femtosecond Ti:sapphire lasers can operate in two coexistent pulsed modes of operation, named P1 (transform limited output pulses) and P2 (chirped output pulses). We study, both theoretically and experimentally, the transition to chaotic behavior for each of these two modes of operation as the net intracavity group velocity dispersion parameter approaches to zero. We find that P1 reaches chaos through a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors and experimentally, the transition to chaotic behavior for each of these two modes of operation as the net intracavity group velocity dispersion parameter approaches to zero. We find that P1 reaches chaos through a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors and experimentally, the transition to chaotic behavior for each of these two modes of operation as the net intracavity group velocity dispersion parameter approaches to zero. We find that P1 reaches chaos through a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors P1 (transform limited output pulses) and P2 (chirped output pulses). We study, both theoretically and experimentally, the transition to chaotic behavior for each of these two modes of operation as the net intracavity group velocity dispersion parameter approaches to zero. We find that P1 reaches chaos through a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors P1 reaches chaos through a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors (and also the kurtosis for the intermittent regime) are theoretically predicted and also measured, showing a satisfactory agreement. We consider that this finding of a low-dimensional system of widespread practical use with (at least) two coexistent chaotic scenarios will have a broad impact on the studies on nonlinear dynamics. satisfactory agreement. We consider that this finding of a low-dimensional system of widespread practical use with (at least) two coexistent chaotic scenarios will have a broad impact on the studies on nonlinear dynamics. satisfactory agreement. We consider that this finding of a low-dimensional system of widespread practical use with (at least) two coexistent chaotic scenarios will have a broad impact on the studies on nonlinear dynamics. and also the kurtosis for the intermittent regime) are theoretically predicted and also measured, showing a satisfactory agreement. We consider that this finding of a low-dimensional system of widespread practical use with (at least) two coexistent chaotic scenarios will have a broad impact on the studies on nonlinear dynamics.(at least) two coexistent chaotic scenarios will have a broad impact on the studies on nonlinear dynamics.