Dynamics of the output of heavily Tm-doped double-clad silica fiber lasers

The relaxation oscillations that are present in the output of a high-power free-running diode-pumped Tm-doped silica fiber laser are characterized and modeled. The laser operates on the ³H₄ → ³H₆ quasi-three-level transition and operates efficiently from ∼1.9 to ∼2.0 μm. From the measurements of the ³F₄ → ³H₄ fluorescence after 1.98-μm pumping of a separate, heavily Tm-doped silica fiber, it is established that the ³H₄, ³H₄ → ³H₆, ³F₄ upconversion process is significant in heavily Tm-doped silica fibers. This process causes the saturable absorption that is indicated by the presence of the relaxation oscillations. A detailed theoretical model that describes the ion-pair dynamics relevant to the Tm-doped silica system is presented. Equations for the steady-state intracavity photon density and for the steady-state population densities of the isolated and paired ions are derived. A linear stability analysis and numerical analysis are also carried out. It is established that, for large emission-to-absorption cross-section ratios that are relevant to Tm-doped silica and for pump rates for which stable output is predicted, the oscillations are weakly damped before the steady state is reached. Best agreement between the experimental and model results is achieved when all the Tm³⁺ ions within the present fiber are considered paired.