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# From Positive- to Negative-Index Materials: Transitional Phenomena

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From Positive- to Negative-Index Materials: Transitional Phenomena
Ildar Gabitov, University of Arizona, Tucson.
We study electrodynamics of newly-fabricated metamaterials with a negative index of
refraction. One of the most remarkable phenomena that take place at a positive-negative
index material interface is that the right-handed triplet of vectors consisting of the
electric and magnetic fields and the wave vector (E,H, k ) undergoes a discontinuous
change. From a topological viewpoint, a left-handed triplet cannot be transformed into a
right-handed triplet by a continuous transformation. However, $\epsilon$ and $\mu$ can
be changed from positive to negative values as continuous functions of the coordinate in
the direction normal to the interface. The fact that continuously changing material
characteristics can lead to a topologically critical phenomenon must be reflected in the
transitional characteristics of the electromagnetic waves traversing the interface. We
developed a mathematical model and investigated electromagnetic field propagation
through a transition layer between positive-index and negative-index materials with
linearly changing dielectric permittivity and magnetic permeability. We show that
components of electromagnetic waves may exhibit singular behavior in the vicinity of the
point where both dielectric permittivity and magnetic permeability vanish. Also, the
phase velocity is found to be discontinuous and tends to infinity near the same point even
at normal incidence.

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