Dipole antenna in space-time periodic media

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) = ε₀εᵣ[1 + ε₁ cos (Kz - Ω t)]andN(z,t) = N₀[1 + N₁ cos (Kz - Ω t)]). 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 whereε(z,t)andN(z,t)behave asη(z,t) = η₀[1 + η₁f(Kz - Ω t)]wheref(ξ)is any periodic function.