Full-Vectorial Optical Waveguide Mode Solvers Using Multidomain Pseudospectral Frequency-Domain (PSFD) Formulations

Abstract

New full-vectorial optical waveguide eigenmode solvers using pseudospectral frequency-domain (PSFD) formulations for optical waveguides with arbitrary step-index profile are presented. Both Legendre and Chebyshev collocation methods are considered in the formulation. By applying Legendre-Lagrange or Chebyshev-Lagrange interpolating polynomials to the approximation of spatial derivatives at collocation points, the Helmholtz equations for the transverse-electric or transverse-magnetic components are converted into a matrix eigenvalue equation which is then solved for the eigenmodes by the shift inverse power method. Suitable multidomain division of the computational domain is arranged to deal with general curved interfaces of the refractive-index profile together with a curvilinear mapping technique for each subdomain so that field continuity conditions can be carefully imposed across the dielectric interfaces, which is essential in achieving high numerical accuracy. The solver is applied to the optical fiber for the assessment of its numerical performance, to the classical benchmark rib waveguide for comparing with existing high-accuracy results, and to the fused fiber structure for demonstrating its robustness in calculating the form birefingence.