A novel multiscale model for micro-structured electromagnetic media

We present a novel multiscale formalism to characterize complex phenomena in electromagnetic media featuring micro-structures. By contrast to the conventional homogenization approaches, the proposed model is based on the variational framework given by the Method of Multiscale Virtual Power applied to Maxwell’s equations, which ensures energetic consistency between the macro- and micro-scales. From a set of well-defined minimal assumptions on the primal variables, the electromagnetic field and its curl, the formulation yields not only the micro-cell problem to be solved but also the homogenization formulae of the dual entities, as well as the homogenization of tangent operators that characterize, for instance, the effective electric permittivity and magnetic permeability. The proposed multiscale model is not restricted to periodic media, although it accounts for the periodicity assumption as a specific case. We apply the method in different cases of interest that range from low-frequency to high-frequency regimes to demonstrate the predictive and descriptive capabilities of the model in terms of effective electromagnetic properties.