Generalized Far-Field Distance of Antennas and the Concept of Classical Photons

A generalized far-field (Rayleigh) distance is derived for a frequency-domain or time-domain antenna in terms of the radius of the significant reactive power of the antenna, where this radius is given in terms of the maximum value N of the degree number n of the spherical waves needed to accurately represent the far-field of the antenna. The maximum possible gain of the antenna is given in terms of the radius of the significant reactive power, which enables supergain to be defined in terms of the physical radius of the antenna. Although the energy in pulses from finite-energy, finite-extent sources, including the energy in “electromagnetic missiles,” must eventually decay, it is shown that wavelength-size wavepackets with a well-defined center frequency can remain localized in free space for a limited amount of travel time and distance. These quasi-monochromatic “classical photons” are used, along with Planck’s constant, to determine the electromagnetic energy density below which quantum scattering theory, rather than the classical Maxwell equations, may be required to determine electromagnetic scattering.