Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser

A model for an end-pumped double-pass alkali vapour laser is set up which has considered all the main physical features, including the fine-structure mixing rate that represents the three-level nature of this kind of laser, the spectral dependence of pump light absorption for broadband pumping, the longitudinal population variation and the distributed intra-cavity losses. To solve this model, we have proposed a searching algorithm for a single-pass configuration and developed a novel iterative algorithm for a double-pass case which has taken the single-pass solution as an initial value. The calculation process demonstrates a fast rate of convergence and high degree of accuracy. By this algorithm, some special cases, for example, the non-uniform longitudinal distribution of alkali atom concentration, can also be solved well. The model and the numerical approach described in this paper demonstrate a new method to simulate the CW end-pumped quasi-three- or three-level lasers. In this way, no significant assumptions or simplifications are needed in the model, and both the detailed intra-cavity information and pump power distribution can be obtained. To ensure the correctness of our model, a comparison between our model and Beach et al's model is made. The result shows that when the non-uniformity of the longitudinal population distribution is less than 20% or the pump intensity is far beyond the threshold, the assumption of longitudinal population average is valid and the two models are equivalent. When the pump intensity is near the threshold, this assumption may be invalid due to the large longitudinal population variation. If this case happens or more detailed laser information is required, we could use this model to obtain a more accurate solution.