  Ultrashort pulses from Kerr-lens mode-locked oscillators have inspired a
variety of applications. The design and alignment of these laser resonators
have thus far been theoretically supported by the conventional analysis of beam
propagation. However, the well-established theoretical framework is sometimes
beyond the scope of high-peak-power oscillators. In this paper, we analyze the
geometry of ring resonators by extending the ABCD-matrix method to a
high-peak-power regime. The guidelines to achieving stable Kerr-lens
mode-locking is provided for high-peak-power pulses.
