Eigenpulses of dispersive time-varying media

TL;DR

This paper introduces a compact operator-based theory for analyzing dispersive, time-varying media, revealing eigenfunctions as invariant pulses and identifying poles as bound states, advancing understanding of wave-material interactions.

Contribution

It presents a novel operator framework for dispersive, time-varying media, linking eigenfunctions to invariant pulses and poles to bound states, improving analysis methods.

Findings

Eigenfunctions correspond to non-changing spectral pulses.

Poles of operators indicate non-time harmonic bound states.

The approach compares favorably with existing techniques.

Abstract

We develop a compact theory that can be applied to a variety of time-varying dispersive materials. The continuous wave reflection and transmission coefficients are replaced with equivalent operator expressions. In addition to comparing this approach to existing numerical and analytical techniques, we find that the eigenfunctions of these operators represent pulses that do not change their spectra after interaction with the time-varying, dispersive material. In addition, the poles of these operators represent the non-time harmonic bound states of the system.