Electromagnetic wave propagation in spatially homogeneous yet smoothly time-varying dielectric media

- Wave transformation in smoothly time-varying dielectric media is considered.
- Analytically exact solutions to time-dependent Maxwell׳s equations are found.
- Amplification and attenuation of waves in non-stationary media is demonstrated.
- Energy exchange between waves and non-stationary media leads to frequency conversion.

We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a finite period τ, as a phenomenologically realistic and sigmoidal change of the dielectric permittivity, an analytically exact solution to Maxwell׳s equations is derived for the electric displacement in terms of hypergeometric functions. Using this solution, we show the possibility of amplification and attenuation of waves and associate this with the decrease and increase of the time-dependent permittivity. We demonstrate, moreover, that such an energy exchange between waves and non-stationary media leads to the transformation (or conversion) of frequencies. Our results may pave the way towards controllable light-matter interaction in time-varying structures.