The Elusive Drude-Born-Fedorov Model for Chiral Electromagnetic Media

TL;DR

This paper investigates the time-dependent Drude-Born-Fedorov model for chiral media using a Hilbert space approach, addressing gaps in understanding its behavior beyond the time-harmonic case.

Contribution

It develops a solution theory for the time-dependent Drude-Born-Fedorov model using Sobolev lattices, advancing the mathematical understanding of chiral electromagnetic media.

Findings

Established a Hilbert space framework for the model

Provided existence and uniqueness results for solutions

Extended analysis beyond time-harmonic assumptions

Abstract

Electro-magnetic wave propagation in more complex linear materials such as bi-anisotropic media have come to a considerable attention within the last fifteen to twenty years. The Drude-Born-Fedorov model has been extensively studied mostly in the time-harmonic case as a model for chiral media. In the physically relevant time-dependent case the record is much less convincing. In this paper we focus on this case and analyze the Drude-Born-Fedorov model in the light of recently developed Hilbert space approach to evolutionary problems. The solution theory will be developed in the framework of extrapolation spaces (Sobolev lattices).