准二能级阈值泵浦光纤激光器的理论分析

Theoretical analysis on threshold pumped fiber lasers doped with quasi two-energy-level ions

根据含损耗系数的稳态速率方程组,对掺准二能级稀土粒子光纤激光器的泵浦阈值进行了分析和完全解析求解。求得了泵浦阈值功率的显函数解析式,得到了泵浦光阈值功率随光纤位置变化的隐函数表达式,以及信号光功率和上能级粒子数随光纤位置变化的解析表达式。对所得的解进行了数值分析,并与已有的理论和实验结果进行了比较分析。结果表明:由于忽略了信号光和泵浦光损耗系数,不同近似条件下给出的泵浦阈值功率均比实验值低,但所导出的理论研究结果与已有实验结果的差异最小。

The rate equations including loss coefficients describing threshold pumped fiber lasers doped with quasi two-energy-level rare-earth ions have been analytically and fully solved. An analytical expression of the threshold pump power has been deduced, a closed-form expression for the variation of the pump power along the fiber has also been obtained, together with analytical solutions to the laser power in terms of the pump power and the position dependent atom population density. A comparison has been made between the analytical result and the previously reported ones. It indicates that various approximations have underestimated the threshold pump powers after neglecting the loss coefficients of both the laser and pump waves, while our theoretical predication is the closest to the experimental result.