Complex finite-element method applied to the analysis of optical waveguide amplifiers

A complex finite-element method and a three-level model for erbium ions are applied to obtain gain and propagation constants for erbium-doped waveguide amplifiers (EDWA's). The complex refractive index profile includes the effect of the dopant polarization induced by the pump field. The method allows to consider arbitrary dopant density profile as well as the modal structure of the pump field. For different waveguide geometries we obtain gain curves as function of pump intensity as well as slight variations in the modal propagation constants. The threshold pump power is shown to be a function of the waveguide geometry, which agrees qualitatively with experimental results,.