The Kerr-lens mode locking of a folded-cavity four-mirror linear Ti:sa
pphire laser is simulated by applying the ABCD ray-tracing technique f
or a Gaussian beam. The intensity dependent Kerr-lens ABCD matrix of t
he Brewster-plate shaped active medium is derived. A split-step parabo
lic refractive index model is used. The astigmatism compensation condi
tion is derived from the ABCD ray-tracing. Simulations are carried out
for a symmetric resonator and an asymmetric resonator design. Hard-ap
erture loss mode locking and soft-aperture gain mode locking are discu
ssed. The optimum design parameters (slit position for hard-aperture l
oss mode locking, pump beam focusing for soft-aperture gain mode locki
ng, gain cavity spacing, gain medium position) for Kerr-lens mode lock
ing are determined.