| Summary: | 博士 === 國立交通大學 === 光電工程系所 === 97 === We experimentally observed the transient state from the laser starting to reaching a stable mode-locking (ML) state in a self-starting Kerr-lens mode-locked Ti:sapphire laser without external modulation and feedback control. By Grassberger-Procaccia analysis for the transient state, the correlation dimension of the transient state is a non-integer which implies it is a chaotic state. The chaotic characteristic can be further confirmed by observing the revivals of the autocorrelation function for long delay time.
Pulse-train modulation was observed in this laser with pump-power dependence when it was operated around the degenerate cavity configuration. By increasing the optical pumping power, the envelope of periodic amplitude modulation splits into two or three clusters with enhanced modulation depth, and the amplitude modulation eventually becomes disordered at higher pump power. The amplitude modulation may be supported by exciting two sets of non-degenerate longitudinally mode-locked supermodes due to spatially inhomogeneous gain modulation in the Ti:sapphire crystal.
We also numerically studied suppressing chaos to reaching completely mode-locking in this self-starting Kerr-lens mode-locked (KLM) laser. By thin slab approximation, we can describe transverse effect of a pulse propagates in a resonator. Based on Fox-Li’s approach, we used the Collins integral and rate equations with and without the self-focusing effect, we found without the self-focusing effect typical laser output and the feature of a power dip agrees with the observation of experiment for all calculated cavity configurations around the degeneracy at various pump powers. However, by adding the self-focusing effect, the time evolution of the pulse-train envelope presents various states including continuous wave or periodic state and
instability such as period, period-2, and irregular states. The simulated self-starting KLM output, which possesses transient irregularity before reaching a constant amplitude output, occurs between the instability and continuous wave regions. The different runs of the simulated self-starting from the spontaneous emission reveal the buildup time of mode-locking not only is sensitive to the initial condition but also presents the distribution with exponential decay. Its return map presents chaotic state with a strange attractor in the initial stage. It transits to the quasi-periodic state and finally converges to a fixed point with time evolution. The theoretical simulation reveals that the self-focusing effect is responsible for the self-adaptation.
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