Spherical-multipole based time-domain near-field to near-field transformation

A spherical-multipole based approach is introduced to efficiently obtain the time-domain near- and far-field of any arbitrary localized current or equivalent-current source distribution. 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. It leads to a time-domain spherical-multipole expansion valid in the free space outside a minimum sphere containing all electromagnetic sources. By means of new recurrence relations the additional time-domain multipole amplitudes needed for the complete representation of the near field can be very efficiently calculated 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 is particularly suited for FDTD.