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 ti me-domain (FDTD) method. Small errors will appear due to numerical dispersi on when a plane wave is generated by Huygens' sources using an analytical e xpression fur the incident field. These errors can be derived from the nume rical dispersion relation in the frequency domain. By using a second-order approximation of the numerical wavenumber it is shown that a simple approxi mative time-domain compensation procedure for the dispersion can be derived . This has been implemented in a Huygens' source routine and in a time-doma in near- to far-zone transformation routine. It is shown that this compensa tion significantly reduces the errors produced when calculating far-zone sc attered 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 prop agation through empty space and scattering of a dipole have been studied.