Finite—element formulation for nonlinear dielectric slab waveguides

Abstract

AbstractThis paper proposes a new general‐purpose numerical method based on the finite‐element method for both TE and TM polarizations, by which the guided mode behaviors in a dielectric slab waveguide with an arbitrary nonlinear material and an arbitrary refractive index profile can be analyzed systematically. The matrix equation derived in this paper is a nonlinear matrix eigenvalue problem with the effective relative permittivity as an eigenvalue and the principal electromagnetic field as an eigenvector. The equation can be solved in a self‐consistent way by an iterative calculation with the linear solution as an initial value. In the present formulation, the biaxial anisotropy of the nonlinear permittivity tensor for the TM wave is taken into account rigorously. A uniaxial approximation which has often been used is not employed at all. From these features, the present method is considered to be a powerful analysis method for a practical nonlinear dielectric slab waveguide. Further, it can be used for investigation of the validity of various approximate methods. The present method is applied to the nonlinear TE and TM wave propagation in a symmetric three‐layered slab waveguide with a nonlinear core layer and the effectiveness of the method is confirmed.