Dynamic modal analysis of monolithic and multi-GHz mode-locked semiconductor lasers

The authors' approach makes use of the fact that in many practical devices, the lasing spectrum is restricted to only a few longitudinal modes, either by virtue of high repetition rate or by an artificial spectrally selective element such as a distributed Bragg reflector. These lasers therefore render themselves more naturally, not to the fully-time-domain analysis, but to a time-frequency-domain approach. The model is applicable to a wide variety of realistic actively, passively and hybridly mode-locked structures, and takes into account both slow and fast nonlinearities in the active medium. With this model, we can describe, on the same footing, a wide variety of transient as well as steady-state regimes including CW lasing, fully or partially rendered mode-locking (ML), and more complex dynamics including self-pulsing and chaotic instabilities. In our approach, the lasing light is decomposed into a set of longitudinal modes of the realistic (open and inhomogeneous) cavity. We first apply the model to a Fabry-Perot passively mode-locked (F=100 GHz) laser; the resulting steady-state spectra agree well with distributed time-domain model (DTDM) simulations, whilst providing an increase of about an order of magnitude in computation speed. Next, the model is applied to colliding-pulse ML (CPM) lasers (F-200 GHz); as expected, all the "odd" modes die out during the first 1-2 ns of the transient regime and are suppressed by at least 20 dB in the resulting spectrum, which corresponds to a full repetition frequency doubling of the ML pulse train. We also apply the model to harmonic sub-terahertz mode-locking.