Time-dependent modeling of erbium-doped waveguide lasers in lithium niobate pumped at 980 and 1480 nm

We have developed a rigorous phenomenological model for analyzing rare-earth doped waveguide lasers. The model is based on time-dependent laser rate equations for an arbitrary rare-earth-doped laser host with multiple energy levels. The rate equations are coupled with the laser signal and pump photon flux equations that have time-dependent boundary conditions. The formulation results in a large and stiff set of transcendental and coupled differential equations that are solved using finite difference discretization and the method of lines. Solutions for the laser signal power, pump power, and populations of ion energy levels as functions of space and time are obtained for waveguide lasers. We have used the model to predict the CW characteristics and Q-switched performance of waveguide lasers in lithium niobate pumped by a 980-nm source. Our analysis shows that hole burning can occur in erbium-doped lithium niobate lasers because of the intensity variation across guided transverse modes. We have predicted that Q-switch pulse peak powers can exceed 1 kW with pulsewidths less than 1 ns. Moreover, we have compared the CW and Q-switched performance of 980-nm pumped waveguide lasers and 1480 nm pumped waveguide lasers. An analysis of the effects of host- and fabrication-dependent parameters on CW 980-nm pumped lasers is included. These parameters include cooperative upconversion, excited state absorption, doping concentration, excess waveguide loss, cavity length, and mirror reflectance values. We demonstrate good quantitative agreement with waveguide laser experimental data obtained in our laboratory and with results from the literature.