Spatial chirp and angular dispersion of a laser crystal for a four-mirror cavity Kerr-lens mode-locked laser

We describe oscillating loops in a laser cavity and optical paths in a laser crystal of different wavelength rays for a four-mirror cavity Kerr-lens mode-locked laser. The relation between different wavelength ray paths and laser resonator parameters is deduced. The analytical expressions of second- and third-order dispersion including angular dispersion of the crystal are presented. The variations of group-delay dispersion (GDD) and third-order dispersion (TOD) with cavity parameters are calculated exactly. The calculation shows that GDD and TOD increase rapidly when the spacing between two folding mirrors approaches the boundary of a cavity stability zone. The rapid dispersion increase influences the mode-locked pulse width and the mode-locked stability.