Homogenisation Theory of Space-Time Metamaterials

TL;DR

This paper develops a comprehensive homogenisation framework for space-time metamaterials, deriving exact effective parameters and Fresnel drag effects, applicable across frequencies under specific conditions.

Contribution

It introduces a general homogenisation theory for space-time metamaterials, providing analytical formulas for effective parameters and demonstrating exactness under certain conditions.

Findings

Exact formulas for effective permittivity, permeability, and magnetoelectric coupling.

Homogenisation theory is exact at all frequencies without back-reflections.

Derived precise Fresnel drag expressions for light in modulated media.

Abstract

We present a general framework for the homogenisation theory of space-time metamaterials. By mapping to a frame co-moving with the space-time modulation, we derive analytical formulae for the effective material parameters for travelling wave modulations in the low frequency limit: electric permittivity, magnetic permeability and magnetoelectric coupling. Remarkably, we show that the theory is exact at all frequencies in the absence of back-reflections, and exact at low frequencies when that condition is relaxed. This allows us to derive exact formulae for the Fresnel drag experienced by light travelling through travelling-wave modulations of electromagnetic media.