Poynting´s theorem and time-harmonic radiators

An important parameter of any antenna is the ratio of standing reactive energy stored about the antenna to the radiated power; by definition, quality factor Q is ω times that ratio. Q is often inversely proportional to the operational bandwidth of the antenna. Extensive experience and electromagnetic theory arguments based upon Q seem to agree that an efficient antenna must be about a half wavelength long in at least one dimension. But is this a general property of radiation fields, or is it due to an inadequate understanding on our part? Can the size limitations be mitigated or even bypassed? In this paper we re-examine the fundamentals of radiating fields and conclude that there is a significant special case that has not been adequately examined previously. We examine it and conclude that errors of omission are made in previous analyses, and significant improvements in the operation of small antennas may be possible. The complex Poynting vector is derived from the time-domain equations. Using it there are two types of radiation fields that have convenient solutions, and these are presented