A numerical model for spiral and folded erbium-doped planar waveguide amplifiers has been developed, based on a rate equation model of the local complex dielectric constant and beam propagation by the method of lines. A five-level system is used to describe the ion-ion interactions that occur at high erbium concentrations. A suitable form of the method of lines is presented in polar coordinates, and absorbing boundary conditions based on the third-order rational series approximation are derived. Using this model, amplification in both straight and curved slab guides can be simulated, and examples of propagation in typical folded amplifier structures are presented.
Weibin Huang and Richard R. A. Syms, "Analysis of Folded Erbium-Doped Planar Waveguide Amplifiers by the Method of Lines," J. Lightwave Technol. 17, 2658- (1999)