Dispersion compensation for Huygens´ sources and far-zone transformation in FDTD

The equivalence principle is utilized for generation of both incident plane waves and for near- to far-zone transformation in the finite-difference time-domain (FDTD) method. Small errors will appear due to numerical dispersion when a plane wave is generated by Huygens´ sources using an analytical expression for the incident field. These errors can be derived from the numerical dispersion relation in the frequency domain. By using a second-order approximation of the numerical wavenumber it is shown that a simple approximative time-domain compensation procedure for the dispersion can be derived. This has been implemented in a Huygens´ source routine and in a time-domain near- to far-zone transformation routine. It is shown that this compensation significantly reduces the errors produced when calculating far-zone scattered fields of low amplitude. It is also shown that it is sufficient to compensate either the Huygens´ sources or the time-domain near- to far-zone transformation with respect to dispersion. For validation, plane wave propagation through empty space and scattering of a dipole have been studied