Q-switched rate equations for diode side-pumped slab and zigzag slab lasers including Gaussian beam shapes

A set of rate equations accounting for the transverse spatial distributions of both the laser mode and inversion density is developed for side-pumped Q-switched oscillators. The equations can be reduced to a simple form by assuming a Gaussian laser mode, a one-dimensional Gaussian pump beam and a few additional basic assumptions, allowing for rapid numerical solution. The derived spatial rate equations are then used to model an experimentally well-characterized Nd⁺³:YAG zigzag slab laser to demonstrate their simplicity and accuracy in predicting oscillator performance.