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I analyse and numerically evaluate the radiation field generated by anexperimentally realized embodiment of an electric polarization current whoserotating distribution pattern moves with linear speeds exceeding the speed oflight in vacuum. I find that the flux density of the resulting emission (i) hasa dominant value and is linearly polarized within a sharply delineatedradiation beam whose orientation and polar width are determined by the range ofvalues of the linear speeds of the rotating source distribution, and (ii)decays with the distance $d$ from the source as $d^{-\alpha}$ in which thevalue of $\alpha$ lies between $1$ and $2$ (instead of being equal to $2$ as ina conventional radiation) across the beam. In that the rate at which boundariesof the retarded distribution of such a source change with time depends on itsduration monotonically, this is an intrinsically transient emission process:temporal rate of change of the energy density of the radiation generated by ithas a time-averaged value that is negative (instead of being zero as in aconventional radiation) at points where the envelopes of the wave frontsemanating from the constituent volume elements of the source distribution arecusped. The difference in the fluxes of power across any two spheres centred onthe source is in this case balanced by the change with time of the energycontained inside the shell bounded by those spheres. These results are relevantnot only to long-range transmitters in communications technology but also toastrophysical objects containing rapidly rotating neutron stars (such aspulsars) and to the interpretation of the energetics of the multi-wavelengthemissions from sources that lie at cosmological distances (such as radio andgamma-ray bursts). The analysis presented in this paper is self-contained andsupersedes my earlier works on this problem.

The electromagnetic radiation whose decay violates the inverse-square law: detailed mathematical treatment of an experimentally realized example