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

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 perpendicu...

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Bibliographic Details
Published in:AIP advances 2018-01, Vol.8 (1), p.015106-015106-12
Main Authors: Luan, Pi-Gang, Wu, Jie-Luen
Format: Article
Language:English
Subjects:
Dependence
Dielectrics
Electromagnetic fields
Electromagnetism
Flux density
Group velocity
Metamaterials
Photonic crystals
Propagation
Propagation modes
Propagation velocity
Superluminal propagation
Velocity
Wave propagation
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Summary: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.
ISSN:2158-3226
2158-3226
DOI:10.1063/1.4997090