Waves in Linear Time-Varying Dielectric Media

In this paper, focusing on the frequency domain, we write the constitutive relation and the Helmholtz equation for linear, dispersive, and inhomogeneous time-varying media. Next, by assuming spatial homogeneity, we simplify the equations and explain how to calculate dispersion curves (the angular frequency with respect to the wave vector) for propagating waves. Furthermore, we show that under the simplifying assumption of instantaneous response, the developed general approach provides the same dispersion curves as reported earlier for the dispersion-less model of time-varying dielectric media. We believe that this study is important for investigations of wave phenomena in time-varying media, properly taking into account inevitable frequency dispersion of materials.