Sampling criteria for resonant antennas and scatterers

From a knowledge of the characteristic constant of an antenna or scatterer, simple expressions are found for the modal bandlimits and near-field sample spacing in planar, cylindrical and spherical coordinates required to reconstruct the fields everywhere outside the antenna or scatterer (except possibly within a small fraction of a wavelength from discontinuities in the surface of the antenna or scatterer). For resonant antennas and scatterers the modal bandwidths can be much larger and the required sample spacings much smaller than for nonresonant antennas and scatterers. The modal bandwidths also determine upper bounds on the gain and effective area of antennas, and on the total and bistatic scattering cross sections of scatterers. The maximum possible radius of the significant reactive fields of an antenna or scatterer is shown to equal the radius of the maximum possible effective area of an antenna, or the radius of the maximum possible total scattering cross section of a scatterer. For resonant antennas and scatterers, this radius can be much larger than the radius of the sphere circumscribing the physical antenna or scatterer.