Time-varying materials in the presence of dispersion: plane-wave propagation in a Lorentzian medium with temporal discontinuity

We study the problem of a temporal discontinuity in permittivity an unbounded medium with Lorentzian dispersion. More specifically, we tackle situation which monochromatic plane wave forward-traveling (generally lossy) Lorentzian-like scatters from interface that results instantaneous and homogeneous abrupt change its plasma frequency (while keeping resonance constant). In order to achieve momentum preservation across discontinuity, show how, unlike well-known nondispersive second-order nature dielectric function now gives rise two shifted frequencies. As consequence, whereas scenario continuity electric displacement D magnetic induction id="m2"> mathvariant="bold">B suffices find amplitude new forward backward wave, need extra boundary conditions. That is, waves are instantaneously generated response forward-only wave. also include transmission-line equivalent lumped circuit elements describes dispersive time-discontinuous under consideration.