A compact one-dimensional modal FDTD method

The finite-difference time-domain (FDTD) method is an effective technique for computing wideband electrical parameters such as scattering parameters of waveguide structures. in the computations, a known incident is normally required and is usually obtained with a simulation of a long uniform structure. For a three-dimensional problem, simulation of a long structure can be very memory- and CPU time-intensive. In addition, effective absorbing boundary conditions are needed to effectively terminate the structure even at and below the cutoff frequencies. To address these issues, many one-dimensional FDTD methods and absorbing schemes were proposed. However, they all have dispersion characteristics different from those of the conventional FDTD method, leading to undesired errors or reflections. In this paper, a new one-dimensional scheme is developed that has numerical dispersion characteristics very similar to that of the conventional FDTD method. When used as the absorbing boundary condition, it generates reflections of less than -200 dB even at and below the cutoff frequencies for the considered modes. When used to obtain the incident wave, its results have difference of less than -200 dB from that produced by the conventional FDTD method. Copyright (c) 2007 John Wiley & Sons, Ltd.