Hyperbolic metamaterials: nonlocal response regularizes broadband super-singularity

TL;DR

This paper investigates hyperbolic metamaterials using a hydrodynamic Drude model, revealing that nonlocal electron response regularizes the previously predicted broadband singularity, resulting in finite density of states enhancement.

Contribution

It introduces a nonlocal response model for hyperbolic metamaterials, showing how it modifies dispersion and density of states compared to local-response predictions.

Findings

Nonlocal response introduces a wavevector cutoff proportional to Fermi velocity.

Finite maximal density of states enhancement is predicted, avoiding super-singularity.

Unit cell size affects effective parameters even at deep sub-wavelength scales.

Abstract

We study metamaterials known as hyperbolic media that in the usual local-response approximation exhibit hyperbolic dispersion and an associated broadband singularity in the density of states. Instead, from the more microscopic hydrodynamic Drude theory we derive qualitatively different optical properties of these metamaterials, due to the free-electron nonlocal optical response of their metal constituents. We demonstrate that nonlocal response gives rise to a large-wavevector cutoff in the dispersion that is inversely proportional to the Fermi velocity of the electron gas, but also for small wavevectors we find differences for the hyperbolic dispersion. Moreover, the size of the unit cell influences effective parameters of the metamaterial even in the deep sub-wavelength regime. Finally, instead of the broadband super-singularity in the local density of states, we predict a large but finite maximal enhancement proportional to the inverse cube of the Fermi velocity.