Boundary conditions for quadrupolar metamaterials

Abstract

One of the long-standing problems in effective medium theories is using the knowledge of the bulk material response to predict the behavior of the electromagnetic fields at the material boundaries. Here, using a first principles approach, we derive the boundary conditions satisfied by the macroscopic fields at interfaces between reciprocal metamaterials with a quadrupolar-type response. Our analysis reveals that in addition to the usual Maxwellian-type boundary conditions for the tangential fields, in general—to ensure the conservation of the power flow and Lorentz reciprocity—it is necessary to enforce an additional boundary condition (ABC) at an interface between a quadrupolar material and a standard dielectric. It is shown that the ABC is related to the emergence of an additional wave in the bulk quadrupolar medium.