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.,
\epsilon(z,t) = \epsilon_{0}\epsilon_{r}[1 + \epsilon_{1} \cos (Kz - \Omega t)]
and
N(z,t) = N_{0}[1 + N_{1} \cos (Kz - \Omega t)])
. The solution also covers the limit case of a sinusoidally stratified medium (
\Omega = 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
\epsilon(z,t)
and
N(z,t)
behave as
\eta(z,t) = \eta_{0}[1 + \eta_{1}f(Kz - \Omega t)]
where
f(\xi)
is any periodic function.