Vectorial modal analysis of dielectric waveguides based on a coupled transverse-mode integral equation. II. Numerical analysis

摘要

We present numerical implementation and verification of a rigorous full-vector, integral-equation formulation suitable for analyzing modal characteristics of complex, two-dimensional (2D) rectangular-like dielectric waveguides. By dividing the waveguide into vertical slices, a system of integral equations we call vectorcoupled transverse-mode integral equations (VCTMIE) is derived. The entire electromagnetic mode fields are completely determined by one-dimensional unknown field functions on the slice interfaces. To further reduce numerical computation, we expand these functions in terms of the guiding modes of a slab waveguide with a large normalized frequency. Through orthogonal projection the resulting nonlinear eigenvalue and eigenvector matrix formulation enables us to obtain the effective mode index with 10~(-7) precision and to compute with high resolution the 2D vectorial mode field solutions of an open dielectric waveguide. We show stable and speedy convergence of our method as well as techniques to overcome the Gibbs phenomenon in the reconstruction of the transverse fields.