Stability of mode-locked pulse solutions subject to saturable gain: computing linear stability with the Floquet-Fourier-Hill method

The stability of local structures in optical systems is of great importance. We demonstrate that using the Floquet-Fourier-Hill (FFH) method provides a substantial improvement in both speed and accuracy over finite-difference methods that are commonly used. Furthermore, we show how to incorporate the effect of non-local saturable gain in the linearization and stability predictions. Several examples of problems are worked with both the FFH and finite-difference methods and compared in the context of mode-locked laser models. (C) 2010 Optical Society of America