Propagation through metamaterial temporal slabs: transmission, reflection and special cases

TL;DR

This paper investigates how electromagnetic waves interact with time-varying metamaterials structured as temporal slabs, deriving scattering coefficients and demonstrating control over wave response through application time, enabling novel temporal devices.

Contribution

It extends the analysis of time discontinuities to finite temporal slabs, deriving scattering coefficients and showing how response can be controlled via application time.

Findings

Scattering coefficients depend on refractive indices and application time.

Temporal slabs can be used to design devices like temporal matching networks and Bragg gratings.

Response of the temporal slab is controllable through the application time.

Abstract

Time-varying metamaterials are artificial materials whose electromagnetic properties change over time. Similar to a spatial medium discontinuity, a sudden change in time of the metamaterial refractive index induces the generation of a reflected and refracted light waves. The relationship between the incident and emerging fields at one temporal interface has been subject of investigation in earlier studies. Here, we extend the study to a temporal slab, i.e., a uniform homogeneous medium that is present in the whole space for a limited time. The scattering coefficients have been derived as a function of the refractive indices and application time, demonstrating that the response of the temporal slab can be controlled through the application time, which acts similarly to the electrical thickness of conventional spatial slabs. The results reported in this letter pave the way to novel devices based on temporal discontinuities, such as temporal matching networks, Bragg grating, dielectric mirrors, which exhibit zero space occupancy by exploiting the time dimension, instead of the spatial one.