Long-Range Longitudinal Electric Wave in Vacuum Radiated by Electric Dipole: Part I

TL;DR

This paper extends classical electric dipole radiation theory by considering cases where wavelength is much smaller than charge separation, revealing the dominance of longitudinal electric waves and focused emission.

Contribution

It introduces a generalized solution for electric dipole radiation that accounts for long-range longitudinal electric waves, surpassing classical assumptions.

Findings

Longitudinal electric waves are significant when wavelength is much smaller than charge separation.

Total radiated power depends on frequency and charge separation distance, with different regimes.

Most power is emitted in a narrow beam along the dipole axis, similar to laser emission.

Abstract

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 non-negligible; c) total radiated power is proportional to the fourth degree of frequency and to the second degree of the charge separation distance; 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; d) most of the power is emitted in a narrow beam along the dipole axis, thus emission of waves is focused as with lasers.