Modeling and parameter recovering of rare-earth-doped/co-doped glass and glass ceramics optical devices

The theoretical model of rare earth doped optical devices based on the rate equations and the power propagation equations can be employed for recovering, via an indirect approach, the rare earth spectroscopic parameters. As an example, the model for an erbium doped silica-tin dioxide, SiO₂ - SnO₂ : Er³⁺, glass ceramic waveguide is considered. Two different pumping schemes are employed to excite the erbium ions, the direct pumping at 378 nm and the indirect pumping at 307 nm via the tin dioxide. The achievable optical gain per unit length at 1533 nm is then evaluated for both pumping cases. The ratio between the two simulated optical gains is compared with the emission intensity measurements to estimate the value of the SnO₂-Er³⁺ energy transfer coefficient. The particle swarm optimization algorithm is applied in order to find the SiO₂ - SnO₂ : Er³⁺ glass ceramic spectroscopic parameters which properly match the simulated optical gains ratio with the experimentally measured emission ratios. In the same way, the pump power coupled in the glass ceramic waveguide is also recovered. The SnO₂-Er³⁺ energy transfer coefficient is estimated to be about 6.1 × 10^-22 m³/s.