Dynamical Drexhage Effect: Amplified Emission in Time-Varying Electromagnetic Environments

We investigate the effect of nonrelativistic motion on the emission dynamics of a dipole emitter moving next to a reflective interface. Within the macroscopic quantum electrodynamics formalism, we obtain an equation of motion for the dipole amplitude in terms of a general dyadic Green's function. We then focus on the dynamical Drexhage effect, where, at short dipole-surface distances, the dipole behaves as a parametric oscillator featuring time-dependent damping and Lamb shifts, both arising from position modulation. Importantly, sinusoidal trajectories with specific modulation amplitudes and frequencies lead to the parametric amplification of the dipole amplitude and radiation. A perturbative Mathieu equation model yields permittivity-dependent amplification thresholds, while Floquet analysis reveals the key role of the dynamical Lamb shift and the absence of amplification for certain epsilon-near-zero materials, regardless of the amplitude of modulation. Our findings open avenues for the dynamic control of the light-matter interaction in nanophotonic environments.