Analytical model of passively Q-switched Nd:YAG/V:YAG microchip laser

An analytical model of a CW pumped passively Q-switched microchip laser in plane wave approximation is presented. The dynamics of such laser can be described by set of rate equation. Our model is based on possibility to express the analytical solution of simplified rate equations with the help of LambertW function. The LambertW function is now commonly available in most of mathematical software and became to be easy to use. Next, the significant simplification of saturable absorber dynamics is made and its presence is described only by its initial and saturated transmission. The analytical form of solution allows to study quickly and transparently the behavior of the laser with a sufficient accuracy. Using this model it is possible to estimate giant pulse parameters, like pulse length and energy density, the pulse repetition rate, and the laser input-output power characteristic. The validity limits of this model were verified using numerical solution of more complicated rate equations model which included nonlinear response of the modulator. The model was also compared with experimental results obtained for passively Q-switched diode pumped Nd:YAG/V:YAG microchip laser operating at 1338 nm and good agreement was obtained. Although the described model was designed primary for such kind of compact short cavity laser, the results are useful for any other passively or actively Q-switched laser with a fast-operating modulator.