Homogenisation theory of space-time metamaterials: how synthetic motion drags light at low frequencies

Recently, time has emerged as a new degree of freedom for metamaterials, as variations of the electromagnetic parameters in time as well as in space allow for new pathways in wave control. In these time-dependent systems, energy is not necessarily conserved, and the linear bias imposed by travelling wave modulations permits non-reciprocal effects in the absence of external magnetic fields. I will present a theory of homogenisation of space-time metamaterials, which provides analytical expressions for the effective permittivity, permeability and magnetoelectric coupling in the long wavelength limit. From the derived parameters I will show how it is possible to bring nonreciprocity down to zero frequency if both the permittivity and permeability are modulated, and how the synthetic motion present in these systems enables a Fresnel drag effect of light without moving matter. Thus, giant magnetoelectric effects emerge without external magnetic biases or relativistically moving matter.