Analysis of cavities for self-starting Kerr-lens mode-locked lasers

We used the ABCD law to derive the transfer matrix of beam propagation in a Kerr-lens mode-locked laser. On the basis of the transfer matrix and the formulas of the cavity stability G parameters that differ from the simple cavity g parameters, we give the expressions for Kerr-lens mode-locking (KLM) strength and some equations for cavity geometric parameters. The expressions and the equations can be used to construct a laser resonator to achieve self-starting oscillation of KLM. In addition we made a numerical simulation of the KLM strength at different positions in a mode-locked Ti:sapphire laser. The numerical results provide a good explanation of some of the physical phenomena observed in our experiments.