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

TL;DR

This paper derives an exact analytical solution for electromagnetic wave propagation in media with smoothly varying dielectric permittivity, revealing wave amplification, attenuation, and frequency transformation possibilities in time-varying structures.

Contribution

It provides the first exact solution to Maxwell's equations for smoothly time-varying dielectric media, enabling analysis of wave amplification, attenuation, and frequency conversion.

Findings

Wave amplification and attenuation are possible through permittivity changes.

Frequency transformation occurs due to energy exchange with the medium.

Analytical solutions are expressed in hypergeometric functions.

Abstract

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 {\tau}, 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.