Modifying the Drexhage effect with a time-varying dielectric

The decay of an electric dipole oscillator can be modified by the environment in which it is situated, a phenomenon known as the Purcell effect. This effect has enabled the design of light-emitting devices and the development of microscopy techniques. A well-known configuration is a dipole in front of an infinite mirror, where the emitted field is reflected by the mirror, modifying the decay as a function of the distance to the mirror, known as the Drexhage effect. In this study, we extend this concept by exploring the effects induced by time-modulation of the permittivity surrounding the dipole, while keeping the properties of the mirror constant. We find conditions that enable parametric amplification of the dipole amplitude and highlight similarities with the effects obtained by mechanically modulating the position of the dipole, demonstrating the potential impact of a time-modulated environment.