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

Optical amplification at 1530 nm in 980-nm pumped Er3+-Yb3+-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 S-4(3/2) manifold of Er3+ 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.