Modeling of electromagnetic radiation using a dual four-potential representation: from dipole blade radiators to ribbon loop-like antennas

In this paper, we explore classical electromagnetic radiation using a dual four-dimensional potential Θ^μ approach. Our focus is on the Planar Dipole Blade Antenna (PDBA), a system consisting of two flat perfect conductive regions on the xy-plane, separated by a gap G , with alternating potentials applied to the conductors. This method emphasizes the use of the scalar magnetic potential Ψ(r, t) and the electric vector potential Θ, which generates the electric field E(r, t) = ∇ × Θ(r, t) in free space. These potentials replace the standard magnetic vector potential A and the scalar electric potential Φ in our analysis. For harmonic radiation, the electromagnetic field can be expressed in terms of the electric vector potential Θ(r, t). We derive a corresponding retarded vector potential for Θ in terms of a two-dimensional vector field W(r, t), which flows through the gap region G . This dual analytical approach yields mathematically equivalent expressions for modeling Planar Blade Antennas, analogous to those used for ribbons in the region G , simplifying the mathematical problem. In the gapless limit, this approach reduces the two-dimensional radiator (PDBA) to a one-dimensional wire-loop-like antenna, significantly simplifying the problem's dimensionality. This leads to a dual version of Jefimenko's equations for the electric field, where W behaves like a surface current in the gap region and satisfies a continuity condition. To demonstrate the utility of this approach, we provide an analytical solution for a PDBA with a thin annular gap at low frequency.