Analysis of erbium-doped waveguide amplifiers by a full-vectorial finite-element method

Erbium-doped waveguide amplifiers are analyzed by solving numerically Maxwell equations and propagation-rate equations of a homogeneous three-level laser medium. In these new devices, the large refractive index changes and the complex geometries of the waveguides require an electromagnetic analysis which has to incorporate vectorial effects. A full-vectorial finite-element code is used to account for the effect of spatial mode distributions, and an iterative procedure, based on the Runge-Kutta algorithm, makes it possible to compute both gain and amplified spontaneous emission spectra with standard rate-equations and propagation equations. The method proposed allows one to model waveguide structures of practical interest and to identify an optimum configuration with regard to polarization effects on the signal gain, maximum gain, pumping efficiency and noise characteristics. Numerical results are reported regarding rib, channel, and thin-film erbium-doped silica waveguide amplifiers