Method for Accurate Gain Calculation of a Highly ${\rm Yb}^{3+}/{\rm Er}^{3+}$ -Codoped Waveguide Amplifier in Migration-Assisted Upconversion Regime

The performance of a highly Yb³⁺/Er³⁺-codoped phosphate glass femtosecond-laser written waveguide amplifier is numerically analyzed using a macroscopic rate-equation propagation model where concentration-dependent rates for the interatomic migration-assisted energy-transfer mechanisms are considered. The Er³⁺-upconversion rate is obtained by a rigorous microscopic statistical modeling of the migration-assisted homogeneous upconversion, and the concentration dependence of the experimental Yb³⁺-sensitization rate utilized reflects the presence of migration among the Yb³⁺ ions. The results of the amplifier gain dependence on the dopant concentrations illustrate the influence of migration and the need of a careful modeling of interatomic energy-transfer mechanisms for high-concentration rare-earth-doped fiber or waveguide active devices.