A scalar variational conformal mapping technique for weakly guiding dielectric waveguides

A novel approach of combining the finite-element method with the conformal mapping technique is proposed for solving the scalar variational formulas for weakly guiding dielectric waveguides. This approach avoids spurious modes and gives satisfactory results even for modes near cutoff, requiring less computer memory and time. Various specific dielectric structures, such as the rectangular guide, channel guide, and rib guide, are considered to estimate the error associated with the scalar formulation relative to the vectorial formulation. The efficiency of this approach is demonstrated with an analysis of a directional coupler whose coupling properties are described by means of numerical results such as propagation constants, field distributions, etc.