Electromagnetic Field Quantization in Time-Dependent Linear Media

We present a quantization scheme for the electromagnetic field in time-dependent homogeneous nondispersive conducting and nonconducting linear media without sources. Using the Coulomb gauge, we demonstrate this quantization can be mapped into a damped (attenuated) time-dependent quantum harmonic oscillator. Remarkably, we find that the time dependence of the permittivity, for ε>0, gives rise to an attenuation of the radiation field. Afterwards, we obtain the exact wave functions for this problem and consider an exponential time accretion of the permittivity as a particular case.