Fresnel drag in space–time-modulated metamaterials

Abstract

A moving medium drags light along with it as measured by Fizeau and explained by Einstein's theory of special relativity. Here we show that the same effect can be obtained in a situation where there is no physical motion of the medium. Modulations of both the permittivity and permeability, phased in space and time in the form of travelling waves, are the basis of our model. Space-time metamaterials are represented by effective bianisotropic parameters, which can in turn be mapped to a moving homogeneous medium. Hence these metamaterials mimic a relativistic effect without the need for any actual material motion. We discuss how both the permittivity and permeability need to be modulated in order to achieve these effects, and we present an equivalent transmission line model.

Temporal aiming

“…Metamaterials and metasurfaces have so far been studied mostly in the time-harmonic scenario, where wave propagation is controlled by engineering geometries and materials in the spatial region, i.e., spatial inhomogeneity, in which the wave is travelling. Recently, the temporal modulation of metamaterials has also gained growing attention within the scientific community [37][38][39][40][41][42][43][44] , as changing the electromagnetic properties (ε, µ) of metamaterials both in space (x, y, z) and time (t) can offer full fourdimensional spatiotemporal control of wave-matter interactions. It is important to highlight that the interaction of electromagnetic waves in a time-modulated medium has been of great interest in the scientific community for several decades, where, for instance, in the last century, it was considered a time-dependent relative permittivity ε r (t) that is rapidly changed in time from one positive value ε r1 (greater than unity) to a different greater-than-unity positive value ε r2 40,41 .…”

Effective medium concept in temporal metamaterials

“…However, to further control wave propagation at will, there is another dimension, time (t), that can be manipulated in addition to these three dimensions. Space-time metamaterials have been studied since several decades ago [32,33] and they have recently been used for exciting applications [34,35] such as inverse prism [36], frequency conversion [37], nonreciprocity [38][39][40], temporal band-gap, and time reversal [41][42][43][44][45][46][47][48]. The idea of "time crystals" has also been introduced and developed [49][50][51][52].…”

Metamaterials with high degrees of freedom: space, time, and more

“…The research on time-varying electromagnetic platforms has a long history dating back to 1950s, when one of the early works, by Morgenthaler [17], explored theoretically what would happen to a monochromatic electromagnetic wave in a medium when the medium's phase velocity is rapidly changed in time. In the past decades, there have been numerous efforts in investigating various phenomena related to the temporal variation of electromagnetic media, providing temporal boundaries [18], temporal holography [19], Doppler cloaking [20], temporal band gaps [21][22][23], temporal effective medium concept [24], temporal impedance matching [25,26], Fresnel drag in spatiotemporal metamaterials [27], spacetime cloaks [28,29], modeling time and causality with metamaterials [30,31], rapidly growing plasma and accelerating reference frame [32], and exceptional points in timevarying media [33], just to name a few.…”