Microscopic theory of refractive index applied to metamaterials: effective current response tensor corresponding to standard relation n 2 = ε eff μ eff

Abstract

In this article, we first derive the wavevector- and frequency-dependent, microscopic current response tensor which corresponds to the “macroscopic” ansatz D = ε0εeffE and B = μ0μeffH with wavevector- and frequency-independent, “effective” material constants εeff and μeff. We then deduce the electromagnetic and optical properties of this effective material model by employing exact, microscopic response relations. In particular, we argue that for recovering the standard relation n2 = εeffμeff between the refractive index and the effective material constants, it is imperative to start from the microscopic wave equation in terms of the transverse dielectric function, εT(k, ω) = 0. On the phenomenological side, our result is especially relevant for metamaterials research, which draws directly on the standard relation for the refractive index in terms of effective material constants. Since for a wide class of materials the current response tensor can be calculated from first principles and compared to the model expression derived here, this work also paves the way for a systematic search for new metamaterials.