Self-mode-locking of Ti:sapphire lasers: a matrix formalism

Abstract
An extension of the ray-pulse matrix formalism is presented that includes self-phase-modulation, self-focusing, bandwidth limitations, and Gaussian apertures. With this more complete set of matrices it is shown how self-mode-locked lasers can be modeled and how the different pulse-shaping mechanisms interact in order to provide a stable femtosecond output.