Self-focusing by a Kerr nonlinearity in combination with an intracavit
y aperture creates a power-dependent loss in lasers, which has been us
ed as a method for passive mode locking of lasers. An analytical treat
ment is presented that yields closed-form expressions for the modulati
on efficiency. Comparisons between analytical results and numerical ca
lculations are performed. General features of this mode-locking techni
que are discussed, and a procedure for the optimization of hard-apertu
re Kerr-lens mode-locking performance is given.