Spectral Methods for Determining the Stability and Noise Performance of Passively Modelocked Lasers

We describe spectral or dynamical methods that can be used to determine the stability and noise performance of modelocked lasers.We first review methods that have been used to date to theoretically and computationally study passively modelocked lasers, contrasting evolutionary and dynamical approaches and their application to full, averaged, and reduced models. We then develop the spectral methods and show how they can be used to determine the stability and to calculate the timing jitter and power spectral density for any averaged model with any equilibrium pulse shape. We review work that has been done on soliton lasers using soliton perturbation theory from this dynamical perspective, and we contrast the simplicity and generality of our methods to prior work. We close with a discussion of how to extend our approach from averaged models to full models.