Time domain near-field to near-field transformation using a spherical-multipole approach

The time domain electromagnetic field of an arbitrary localized radiating structure can be efficiently obtained by means of a time domain spherical-multipole expansion valid outside a minimum sphere enclosing all radiating elements. The method is based on the Fourier transform of the frequency-domain spherical-multipole expansion and on a finite expansion of the spherical Hankel function of the 2nd kind leading to a triple sum of multipoles instead of the well-known double sum in case of the frequency-domain multipole expansion. It is shown that those time domain multipole amplitudes which are relevant only in the near-field can be recursively deduced from the time domain amplitudes dominant in the far field. The latter can be obtained by a recently proposed spherical-multipole based time domain near-field to far-field algorithm which has been shown to be particularly suited for the Finite-Difference Time Domain (FDTD) method.