Mechanical motion and spatiotemporal modulation to realize non-reciprocal and active metamaterials

Non-static media have recently raised significant attention in the research community for their ability to break reciprocity without the use of magnetic fields. Different approaches to realize such media have been proposed in electromagnetics and acoustics, including mechanical motion and spatiotemporal modulation. Here, we connect these two approaches and show that they can both be derived from the same fundamental relativistic principles. We start our analysis with linear mechanical motion, and show that in the case of near-zero refractive index it is possible to achieve positive and negative refractive index for opposite propagation directions. Next, we show that a similar effect can be achieved with a moving Bragg grating, which can be realized through spatiotemporal modulation, thus avoiding any practically-challenging physical motion. We also show that similar remarks apply to the case of spinning ring resonators, which can form the basis of magnet-less acoustical and electromagnetic circulators. Finally, we discuss the consequences of the equivalence between physical motion and spatiotemporal modulation to applications beyond non-reciprocity, such as spontaneous light generation from dielectric or plasmonic slabs in relative motion with each other.