Optimum sampling of the near field for the prediction of antenna patterns

A method is presented for the determination of the maximum modal spectral band-limits for cylindrical and spherical wave functions in the radiated field. This development is based on the Dyadic Green's function of free space expressed in the corresponding vector wave functions. An expression is obtained for the wave expansion coefficients for an arbitrary source. An upper limit depending on the maximum radial extent of the source is derived for these coefficients for sources which are square integrable with respect to spacial distributions. The resulting expression for the contribution of each field harmonic to the radiated field is found to be broad banded very close to the source surface. With radial distance from the source, free space attenuates the higher modes so the maximum spectrum becomes bandlimited. The band-limits are found to approach ka in the radiative fields, particularly for very large antennas.