Modeling of an Er³⁺-Doped ZBLAN Fiber Laser with Ion Clustering Effect

In this study, we proposed a numerical model incorporating ion clustering effect for an Er3+-doped ZBLAN fiber laser. Our proposed model does not use weak-interaction (WI) energy transfer parameters, instead, it is based on two separate rate equations for isolated and clustered ions, respectively, using conventional ionic interaction parameters, unlike the previously proposed WI model. We verified the efficacy of our proposed model by comparing the numerically calculated output curves with the experimentally measured ones in a Fabry-Pérot laser setup based on two different lengths of commercially available Er3+-doped ZBLAN fiber. The proposed model can readily provide an accurate prediction of the laser output performance without using WI energy transfer parameters. In addition, with the numerical calculation of the model, the relative number of clustered ions in a commercial ZBLAN fiber was indirectly found to be ~18.1%. Lastly, we compared the calculation results of our model with those with strong-interaction (SI) and WI model, which are commonly used for Er3+-doped ZBLAN fiber lasers.