FD-TD METHOD WITH PMLS ABC BASED ON THE PRINCIPLES OF MULTIDIMENSIONAL WAVE DIGITAL-FILTERS FOR DISCRETE-TIME MODELING OF MAXWELL EQUATIONS

We present a finite-difference time-domain (FD-TD) method with the per fectly matched layers (PMLs) absorbing boundary condition (ABC) based on the multidimensional wave digital filters (MD-WDFs) for discrete-ti me modelling of Maxwell's equations and show its effectiveness. First we propose modified forms of the Maxwell's equations in the PMLs and i ts MD-WDFs' representation by using the current-controlled voltage sou rces. In order to estimate the lower bound of numerical errors which c ome from the discretization of the Maxwell's equations, we examine the numerical dispersion relation and show the advantage of the FD-TD met hod based on the MD-WDFs over the Yee algorithm. Simultaneously, we es timate numerical errors in practical problems as a function of grid ce ll size and show that the MD-WDFs can obtain highly accurate numerical solutions in comparison with the Yee algorithm. Then we ana lyze seve ral typical dielectric optical waveguide problems such as the tapered waveguide and the grating filter, and confirm that the FD-TD method ba sed on the MD-WDFs can also treat radiation and reflection phenomena, which commonly done using the Yee algorithm.