Eur. Phys. J. B (2018) 91: 146
https://doi.org/10.1140/epjb/e2018-90207-5

Regular Article

Microscopic theory of refractive index applied to metamaterials: effective current response tensor corresponding to standard relation n² = ε_effμ_eff

¹ Institute for Theoretical Solid State Physics, RWTH Aachen University, Otto-Blumenthal-Straße, 52074 Aachen, Germany
² Institute for Theoretical Physics, TU Bergakademie Freiberg, Leipziger Straße 23, 09596 Freiberg, Germany

^a e-mail: schober@physik.rwth-aachen.de

Received: 26 March 2018
Received in final form: 30 April 2018
Published online: 4 July 2018

Abstract

In this article, we first derive the wavevector- and frequency-dependent, microscopic current response tensor which corresponds to the “macroscopic” ansatz D = ε₀ε_effE and B = μ₀μ_effH with wavevector- and frequency-independent, “effective” material constants ε_eff and μ_eff. 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 = ε_effμ_eff 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, ε_T(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.