Low-dispersive super high-order FDTD schemes

Recently, many efforts have been placed in developing FDTD schemes with extremely low numerical dispersion for electromagnetic modelling. Among the schemes developed so far are the pseudo-spectral time-domain (PSTD) and multi-resolution time-domain (MRTD) methods. In these, transforms are required and field quantities are computed indirectly. In this paper, we show that a systematic way of developing arbitrary high-order FDTD schemes can also achieve numerical dispersion as low as that of PSTD and MRTD. The advantages of the present method are: (1) it is simple and straightforward, as the field quantities are calculated directly; and (2) it can also achieve low spatial sampling rates down to two grid points per wavelength and yet the memory requirements are similar to those for MRTD and PSTD. Numerical examples are given to validate the method.