Microscopic theory of refractive index applied to metamaterials: Effective current response tensor corresponding to standard relation $n^2={\epsilon }_{\mathrm{eff}}{\mu }_{\mathrm{eff}}$

Abstract

In this article, we first derive the wavevector- and frequency-dependent, microscopic current response tensor which corresponds to the "macroscopic" ansatz $\vec{D}={\epsilon }_0{\epsilon }_{\mathrm{eff}}\vec{E}$ and $\vec{B}={\mu }_0{\mu }_{\mathrm{eff}}\vec{H}$ with wavevector- and frequency-independent, "effective" material constants ${\epsilon }_{\mathrm{eff}}$ and ${\mu }_{\mathrm{eff}}$. 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 $n^2={\epsilon }_{\mathrm{eff}}{\mu }_{\mathrm{eff}}$ 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, ${\epsilon }_{\mathrm{T}}(\vec{k},\omega )=0$. 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.

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Cited by in corpus (2)

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• General form of the full electromagnetic Green function in materials physics