Radiation By a Moving Wire-Antenna in the Presence of a Plane Interface

Abstract

This paper studies the electromagnetic field radiated by an infinitely long thin wire-antenna which uniformly translates in a direction parallel to a plane interface. An exact relativistic solution is performed through the application of Lorentz field transformation formulae to the plane wave spectrum representing the radiated field in the rest frame of the antenna. The occurrence of peculiar relativistic phenomena is highlighted by means of numerical examples.

The Method of Images in Velocity-Dependent Systems

“…It follows that similarly to (18) we now have in Γ on both sides of the perfectly-conducting plane-interface, in the corresponding regions {1 }, {2 },…”

“…The symmetry conditionÑ · (k − k) = 0 is usually referred to as Snell's law, obviously it is not a law, but a result of applying boundary conditions. Inasmuch as the pair of plane waves (15), (17), subject to (18), satisfies the boundary conditions, it is feasible to extend the waves into region {2 }, the half-space initially shielded by the perfectly-conducting plane-interface, and remove the perfectly-conducting plane-interface, without altering the original waves (15), (17), in region {1 }. The tangential components of both the electric and magnetic fields are continuous across the interface, therefore no equivalent surface charge and current density sources are required.…”

“…In Γ we have the conditions (18). By transformation into Γ , the formulas for reflection of a plane wave from a moving mirror [5] are obtained, often dubbed as the relativistic aberration effect.…”

“…The same waves (15), (17), exist here. The boundary conditions at the perfectly-conducting plane are once again satisfied by (18). Also, by extending the waves and the medium from the initial half-space {1 } to the half-space {2 }, the fields in {1 } remain unaltered.…”

“…In the present case the boundary conditions are evaluated in Γ, at the plane-interface at-rest, hence the same boundary condition (18) are prescribed here too. However, because of the medium motion, an equivalent anisotropic medium is encountered here, depending on the velocity-field v .…”