Electromagnetic radiation in a time-varying background medium

TL;DR

This paper derives analytical solutions for electromagnetic radiation in homogeneous media with time-varying permittivity and permeability, revealing spectral shifts, modulation, and scattering effects caused by the medium's temporal changes.

Contribution

It provides explicit formulas for electromagnetic radiation in time-varying media with arbitrary pulsed sources, including cases of constant and varying impedance, highlighting new spectral and scattering phenomena.

Findings

Spectral shifts and spatio-temporal modulation occur due to medium variations.

Explicit radiation formulas are derived for specific time-dependence cases.

Time-varying media can cause causal echoes in the received electromagnetic signals.

Abstract

Analytical solutions are presented for the electromagnetic radiation by an arbitrary pulsed source into a homogeneous time-varying background medium. In the constant-impedance case an explicit radiation formula is obtained for the synchronous permittivity and permeability described by any positive function of time. As might be expected, such a medium introduces significant spectral shifts and spatio-temporal modulation, which are analized here for the linear and exponential time-variations of the medium parameters. In the varying-impedance case the solution is obtained for the fourth-order polynomial time-dependence of the permittivity. In addition to the spectral shifts and modulation this spatially homogeneous medium scatters the field introducing causal echoes at the receiver location.