Shear of the vector potential in electric-dipole radiation

Electric-dipole radiation has the well-known far-field solutions of transverse electric and magnetic (TEM) fields with peak values propagating normal to (and going to zero along) the dipole axis. The calculation of these electromagnetic fields is based on the use of the magnetic vector potential: Its time derivative and divergence for the electric field E, and its curl for the magnetic field B. In this paper, we suggest the possibility of additional radiation fields, namely, those based on the shear of the vector potential. Our results show that these shear waves have a 1/r dependence on far-field distance, with four radiative components: (1)-(3) an orthogonal triad consisting of two transverse waves and a longitudinal wave propagating along the dipole axis (analogous to an acoustic dipole); and (4) a transverse wave propagating into the same solid angle as E and B, parallel to the E-field but with one-half the magnitude of the B-field. If confirmed by experiment, possible applications include RF communications, novel biomedical sensors, and a new tool in the search for extra-terrestrial intelligence (SETI).