A negative index meta-material for Maxwell´s equations
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Date
2015-07-29
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Abstract
We derive the homogenization limit for time harmonic Maxwell's equations
in a periodic geometry with periodicity length η > 0. The considered
meta-material has a singular sub-structure: the permittivity coefficient in
the inclusions scales like η⁻² and a part of the substructure (corresponding
to wires in the related experiments) occupies only a volume fraction of order
η²; the fact that the wires are connected across the periodicity cells leads
to contributions in the effective system. In the limit η → 0, we obtain a
standard Maxwell system with a frequency dependent effective permeability
μ^eff (ω) and a frequency independent effective permittivity ε^eff. Our formulas
for these coefficients show that both coefficients can have a negative real
part, the meta-material can act like a negative index material. The magnetic
activity μ^eff≠1 is obtained through dielectric resonances as in previous publications.
The wires are thin enough to be magnetically invisible, but, due
to their connectedness property, they contribute to the effective permittivity.
This contribution can be negative due to a negative permittivity in the wires.
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Keywords
Maxwell´s equations, negative index material, homogenization