Pulse train dynamics in actively mode-locked lasers

Abstract

We consider a new model for the active modulation component of a modelocked laser cavity which allows for the construction of exact pulse train solutions. The model begins with the nonlinear Schrodinger equation for propagation in the laser cavity which is influenced by chromatic dispersion and Kerr induced self-phase modulation. Additionally, a bandwidth limited gain term is included to capture the amplification process in the cavity. The active modelocking element allows for periodically spaced regions of preferential gain. Thus a modelocked pulse train will align itself under the peaks of the gain region while radiation energy outside this region is attenuated. We consider a novel form of the periodic, active modelocking element by making use of the Jacobi elliptic functions. Two families of pulse train solutions are generated: one in which neighboring pulses are in-phase, and a second in which neighboring pulses are out-of-phase. The model predicts that only out-of-phase pulse train solutions can be stabilized. Under large perturbation, the pulse train is often stabilized to a two-pulse per round trip configuration. All in-phase solutions are unstable and are destroyed. Further, for the out-of-phase solutions, if the pulse spacing is not sufficiently far, then the nearest neighbor interactions can dominate and lead to Q-switching behavior. For short cavities, this Q-switching can result in quasi-periodic behavior of the pulse train. For long cavities, the resulting Q-switching is chaotic in nature.