Near and Far Fields of a Dipole Antenna: A Unified Model

The dipole antenna is one of the oldest and most widely used devices in electromagnetic engineering, yet the behavior of its near-field during emission remains only partially captured by classical models. In the source-free region surrounding the arms, the vacuum Maxwell–Heaviside equations provide an insufficient number of configurations to describe the transient through which a bound signal becomes a freely propagating wave. We revisit the model equations, introducing an extended formulation in which an auxiliary velocity field complements the electromagnetic fields. Similarly to plasma physics, the outgoing signal is treated as an electromagnetic fluid carrying a charge density. As the far field is concerned, the resulting system admits an exact family of spherical free-wave solutions that follow the rules of geometrical optics. The near-to-far field transition also acquires a concrete dynamical description, thanks to the introduction of the pseudocharge, which is a charge-like density identified with the divergence of the electric field. In addition, a pressure-like potential, vanishing in the far field, tracks the conversion between bound and radiating energy. The approach is illustrated on a standard dipole antenna through direct numerical simulation of the full coupled system. The results suggest a unified analytical and computational pathway for antenna modeling, with natural extensions to more complex geometries and other radiating devices.