An efficient modal FDTD for absorbing boundary conditions and incident wave generator in waveguide structures

When the finite-difference time-domain method is used to compute waveguide structures, incident waves are needed for calculating electrical parameters (e.g., the scattering parameters), and effective absorbing boundary conditions are required for terminating open waveguide structures. The incident waves are conventionally obtained with inefficient three-dimensional (3D) simulations of long uniform structures, while the absorbing boundary conditions reported so far do not perform well at or below cut-off frequencies. To address the problems, we propose a novel one-dimensional (1D) finite-difference time-domain method in this paper. Unlike the other methods developed so far, the proposed method is derived from the finite-difference time-domain formulation, and therefore has the same numerical characteristics as that of the finite-difference time-domain method. As a result, when used to obtain an incident wave, it produces results almost identical to those produced by the conventional finite-difference time-domain method except computer rounding-off errors. When used as the absorbing boundary condition, it produces reflections of less than -200 dB in entire frequency spectrum including the cut-off frequencies.