Algebraic solutions for Z-fold resonators of arbitrary proportions suitable for pulsed lasers

The stability criteria for Z-fold cavities with astigmatic compensation are calculated here algebraically for cavities of arbitrary proportions. Calculations previously performed to achieve astigmatic compensation are valid only for cavities with long arms. Stable cavities with a short round-trip distance are important for pulsed laser pumping of tunable laser crystals such as titanium sapphire so as to reduce the cavity build-up time as well as increase the beam waist size within the crystal.