Rate-equation approach for frequency-modulation mode locking using the moment method

A semianalytic approach based on the moment method is used for investigating pulse evolution in mode-locked lasers in which intracavity dispersive and nonlinear effects play a significant role. Its application to an FM mode-locked laser allows us to perform fast parametric studies while predicting the important pulse parameters. When third-order dispersive effects are negligible, a fully analytic treatment is developed that predicts how cavity parameters affect the final steady state. Our analytic approach also allows us to predict relaxation-oscillation behavior as the pulse approaches its steady state. We use this technique to investigate novel aspects specific to FM mode-locked lasers such as stability of and switching between the multiple steady-state solutions. All results obtained are in excellent agreement with numerical simulations. (c) 2005 Optical Society of America