An analytical model for longitudinally pumped continuous-wave laser

An analytical model for a longitudinally end-pumped laser is developed using the circulating photon flux approach, and the threshold pump intensity and slope efficiency are expressed with the laser parameters. The thermal population in the lower laser level is included in the model. The threshold pump intensity decreases as the absorption cross section increases. The model shows that the threshold pump intensity increases as the length of the laser rod increases over the optimum value. The slope efficiency of the system depends on the laser rod length, the absorption cross section, and the reflectance of the output mirror. When the model is applied to a GaAlAs diode laser pumped Nd:YAG laser, the achievable slope efficiency reaches up to 76%, which is the ultimate quantum efficiency, at the output mirror reflectance lower than 50% with a laser crystal of loss coefficient 0.1%/cm. The experimental results of 946 nm Nd:YAG laser by Fan and Byer, Opt. Lett. 12, 809 (1987) are compared with the present model, and shows a good agreement with calculations.