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Fresnel drag in space–time-modulated metamaterials

Significance Space–time-dependent electromagnetic media, whose constitutive parameters are directionally biased in space and time, are a topic of current enormous interest across physics. Here we address a problem of fundamental relevance: the similarities and differences between such modulated materials and the classic problem of moving media. We establish that, surprisingly, the Fresnel drag effect of light in moving media, dictated by special relativity, is also present in modulated media, fully resolving this paradox with an analytical approach. We discuss how nonreciprocity can emerge at vanishing frequency. While we focus on electromagnetism, our findings can be extended to other wave systems. 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 traveling 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 to achieve these effects, and we present an equivalent transmission line model.