Dipole antenna in space-time periodic media

Abstract

The problem of dipole radiation in sinusoidally spacetime periodic media is studied and solved. The space-time periodicity can be considered as due to a strong pump wave and is expressed as a traveling-wave type change in the dielectric constant or the plasma density (i.e., ϵ(z,t) = ϵ_0 ϵ_r[1 + ϵ_1 cos (Kz - Ωt)] and N(z,t) = N_0[1 + N_1 cos (Kz - Ωt)]). The solution also covers the limit case of a sinusoidally stratified medium (Ω = 0). The solution is formulated in a matrix form, such that the basic results and diagrams apply, with minor changes, to the different cases studied: electric and magnetic dipole in a dielectric, plasma, and uniaxial plasma. The wave-vector diagram is used extensively in studying and presenting the different properties of the solution: caustics, effect of the disturbance (pump wave) motion, harmonics, radiation outside the allowed cone in a uniaxial plasma. Many dipole radiation patterns are given and their features explained physically. Finally, our solution and results are extended to the generally space-time periodic media where ϵ(z,t) and N(z,t) behave as η(z,t) = η_0[1 + η_f(Kz - Ωt)]where f(ζ)is any periodic function.