On the possibility of superluminal energy propagation in a hyperbolic metamaterial of metal-dielectric layers

TL;DR

This paper rigorously proves that superluminal energy propagation cannot occur in hyperbolic metamaterials made of real dielectric and metallic layers, due to the dispersive nature of the medium and the constraints on group velocity.

Contribution

It provides a theoretical proof that superluminal energy propagation is impossible in dispersive hyperbolic metamaterials composed of real materials.

Findings

Group velocity in hyperbolic media is always less than the speed of light.

Numerical analysis shows wave packet velocity closely matches mode velocity.

Discrepancies arise with broad frequency spreads due to evanescent modes.

Abstract

The energy propagation of electromagnetic fields in the effective medium of a one-dimensional photonic crystal consisting of dielectric and metallic layers is investigated. We show that the medium behaves like Drude and Lorentz medium, respectively, when the electric field is parallel and perpendicular to the layers. For arbitrary time-varying electromagnetic fields in this medium, the energy density formula is derived. We prove rigorously that the group velocity of any propagating mode obeying the hyperbolic dispersion must be slower than the speed of light in vacuum, taking into account the frequency dependence of the permittivity tensor. That is, it is not possible to have superluminal propagation in this dispersive hyperbolic medium consisting of real dielectric and metallic material layers. The propagation velocity of a wave packet is also studied numerically. This packet velocity is very close to the velocity of the propagating mode having the central frequency and central wave vector of the wave packet. When the frequency spread of the wave packet is not narrow enough, small discrepancy between these two velocities manifests, which is caused by the non-penetration effect of the evanescent modes. This work reveals that no superluminal phenomenon can happen in a dispersive anisotropic metamaterial medium made of real materials.