Stability and noise in frequency combs: efficient and accurate computation using dynamical methods

Key issues in the design of any passively modelocked laser system are determining the parameter ranges within which it can operate stably, determining its noise performance, and then optimizing the design to achieve the best possible output pulse parameters. Here, we review work within our research group to use computational methods based on dynamical systems theory to accurately and efficiently address these issues. These methods are typically many orders of magnitude faster than widely used evolutionary methods. We then review our application of these methods to the analysis and design of passively modelocked fiber lasers that use a semiconductor saturable absorbing mirror (SESAM). These lasers are subject to a wake instability in which modes can grow in the wake of the modelocked pulse and destroy it. Even when stable, the wake modes can lead to undesirable radio-frequency sidebands. We demonstrate that the dynamical methods have an advantage of more than three orders of magnitude over standard evolutionary methods for this laser system. After identifying the stable operating range, we take advantage of the computational speed of these methods to optimize the laser performance over a three-dimensional parameter space.