Analysis of dielectric waveguides by a modified Fourier decomposition method with adaptive mapping parameters

The adaptive modified Fourier decomposition method (A-MFDM), a recently proposed technique to perform the modal analysis of linear and nonlinear two-dimensional dielectric waveguides, is now extended to three-dimensional scalar structures for the first time. The method includes a strategy to automatically find quasioptimum numerical parameters of the technique, which, on the one hand, improves the accuracy in relation to the known Fourier decomposition method (FDM) and, on the other, makes the method self-adaptive. To validate the performance of the method, two linear dielectric waveguides with exact solutions have been defined and analyzed. Finally, the modal analysis of an asymmetrical rib waveguide directional coupler is carried out and the obtained results confirm the clear superiority of the A-MFDM in realistic situations.