Modeling and optimization of cascaded erbium and holmium doped fluoride fiber lasers

Numerical modeling of cascade erbium-doped and holmium-doped fluoride fiber lasers is presented. Fiber lengths were optimized for cascade lasers that had fixed or free-running wavelengths using all known spectroscopic parameters. The performance of the cascade laser was tested against dopant concentration, energy transfer process, heat generation, output coupling, and pump schemes. The results suggest that the slope efficiencies and thresholds for both transitions increase with increasing Ho³⁺ or Er³⁺ concentration with the slope efficiency stabilizing after 1 mol% rare earth doping. The heat generation in the Ho³⁺-based system is lower compared to the Er ³⁺-based system at low dopant concentration as a result of the lower rates of multiphonon relaxation. Decreasing the output coupling for the upper (∼3 μm) transition decreases the threshold of the lower transition and the upper transition benefits from decreasing the output coupling for the lower transition for both cascade systems. The highest slope efficiency was achieved under counter-propagating pump conditions. Saturation of the output power occurs at comparatively higher pump power with dilute Er³⁺ doping compared with heavier doping. Overall, we show that the cascade Ho³⁺ -doped fluoride laser is the best candidate for high power output because of its higher slope efficiency and lower temperature excursion of the core and no saturation of the output.