Long-range longitudinal electric wave in vacuum radiated by electric dipole: Part I

In this work, by using the assumptions that wavelength is much smaller than charge separation distance of an electric dipole, which in turn is much smaller than a distance up to the point of observation, the new results for radiation of an electric dipole were obtained. These results generalize and extend the standard classical solution, and they indicate that under the above assumptions, the electric dipole emits both long-range longitudinal electric and transverse electromagnetic waves. For a specific values of the dipole system parameters, the longitudinal and transverse electric fields are displayed. Total power emitted by electric and electromagnetic waves are calculated and compared. It was shown that under the standard assumption of charge separation distance being much smaller than wavelength, (a) classical solution correctly describes the transverse electromagnetic waves only; (b) longitudinal electric waves are nonnegligible; (c) total radiated power is proportional to the fourth degree of frequency and to the second degree of the charge separation distance; and (d) transverse component of our solution reduces to classical solution. In case wavelength is much smaller than charge separation distance, (a) the classical solution is not valid, and it overestimates the total radiated power; (b) longitudinal electric waves are dominant and transverse electromagnetic waves are negligible; (c) total radiated power is proportional to the third degree of frequency and to the charge separation distance; and (d) most of the power is emitted in a narrow beam along the dipole axis; thus, emission of waves is focused as with lasers.