Combining modal analysis and the finite-difference time-domain method in the study of dielectric waveguide problems

A numerical approach that combines the finite-difference time-domain (FDTD) method with a compatible method of extracting the modal information from the FDTD results in the analysis of dielectric waveguide problems is presented. The junction is analyzed by the FDTD method; the result obtained from the FDTD method is in the form of total field distributions at the discretized locations and time intervals. The modal amplitudes at the various waveguides are extracted from the total field distribution by a least-squares approach. While this approach exploits the flexibilities of FDTD method, which can analyze arbitrarily shaped geometries that may contain multiple inputs and outputs and/or anisotropies, the results can still be expressed in the simple form of the modal solution. The methodology for model extraction is presented.>