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

Abstract

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.