Abstract

The matrix formalism presented by Kostenbauder¹ is extended to account for self-phase modulation and self-focusing. Complex coefficients are included to account for the gain guiding, limiting apertures, and bandwidth limitations. The self-actions are taken into account by redefining the matrix elements in each transit as a function of the input pulse. In this manner a standard self-mode-locked Ti:sapphire laser² was analyzed. The matrices include the group delay dispersion from the prism pair, Gaussian transmission is used to describe the limiting apertures. For the gain medium the gain profile, dispersion, gain bandwidth and self-focusing are considered.

© 1992 Optical Society of America