Approximations in analytic models of laser oscillators

Rate equation analyses of laser oscillator dynamics generally include an integrodifferential equation that describes the time dependence of the intracavity photon number. 1,2 This rate equation usually gives reasonable predictions for continuous-wave characteristics of low gain lasers. However, these predictions are inconsistent with Poynting’s theorem and disagree significantly with plane-wave calculations for high-gain lasers. It is often assumed that only first-order saturation effects are important 2 and that the laser mode is well-collimated within the gain medium. 1 I present a model of multimode laser oscillator dynamics that is consistent with both continuous-wave high-gain plane-wave analyses and rate-equation descriptions of Q-switched lasers. As an example, I describe a detailed analytic model of a continuous- wave high-gain end-pumped four-level laser, including thermal loading effects. I compute the maximum errors incurred by neglecting higher-order saturation terms and Gaussian beam expansion, and I simultaneously optimize both the output coupling and the laser mode waist.