Numerical analysis of optical amplification in Er³⁺-Yb³⁺ codoped Ti: LiNbO₃ strip waveguides

Optical amplification at 1530 nm in 980-nm pumped Er³⁺-Yb ³⁺-diffused Ti:LiNbO₃ strip waveguides was numerically analyzed on the basis of rate equation model of Er³⁺-Yb³⁺ system and pump/signal power propagation equations. The model includes total eight energy levels of the Er³⁺-Yb³⁺ system and simultaneously takes into account the excited state absorption (ESA) and upconversion processes within the Er³⁺ ions as well as possible energy transfer processes between Yb³⁺ and Er³⁺ ions. A comparison of numerical results from the eight-level model and highly simplified five-level model has indicated that the ⁴S_3/2 manifold of Er ³⁺ ion must be included in the rate equation model. Dependences of threshold pump power and amplification gain on pump power (for gain only), Yb³⁺ surface concentration and waveguide length were calculated and discussed. The characteristics of pump power evolution along the waveguide axis and population density distribution, as well as the influences of energy transfer coefficient from Yb³⁺ to Er³⁺, 550-nm (Er³⁺), and 1060-nm (Yb³⁺) fluorescence lifetime and above-mentioned detrimental processes including ESA, upconversion, and cross-relaxation processes on numerical result were studied. The role of Yb³⁺ is demonstrated. A novel design idea that Yb³⁺ is only incorporated at the end of the waveguide is proposed.