With the help of the self-consistent ABCD matrix method, the fundamental TEM00 mode of a four-mirror cavity with an active rod and a hard aperture is analyzed. Cavity parameter ranges with small diffraction losses at the hard aperture and decreased diffraction losses for mode intensities increased by self-focusing in the active medium (that is, ranges of fluctuation discrimination) are determined for practical Kerr-lens mode-locked Ti:sapphire lasers. To do this we have obtained the generalized solution of the wave propagation equation in a self-focusing medium for an arbitrary-radius-of-curvature phase front of an incident Gaussian beam, and we have analyzed the transformation of the fundamental mode by diffraction and intracavity elements for one complete round trip through the cavity. The fluctuation model of self-mode-locked lasers is used to demonstrate the generation of a stable ultrashort pulse train by the system under constant pumping for the obtained cavity parameters. The correlation among the cavity parameters for effective mode locking and fluctuation discrimination for cw and impulse flash-lamp pumping is shown.
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