28 research outputs found
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 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.Comment: 17 pages, 7 figure
Power loss and electromagnetic energy density in a dispersive metamaterial medium
The power loss and electromagnetic energy density of a metamaterial
consisting of arrays of wires and split-ring resonators (SRRs) are
investigated. We show that a field energy density formula can be derived
consistently from both the electrodynamic (ED) approach and the equivalent
circuit (EC) approach. The derivations are based on the knowledge of the
dynamical equations of the electric and magnetic dipoles in the medium and the
correct form of the power loss. We discuss the role of power loss in
determining the form of energy density and explain why the power loss should be
identified first in the ED derivation. When the power loss is negligible and
the field is harmonic, our energy density formula reduces to the result of
Landau's classical formula. For the general case with finite power loss, our
investigation resolves the apparent contradiction between the previous results
derived by the EC and ED approaches.Comment: 10 pages, 1 figure, Submitted to Phys. Rev.