Effective Maxwell’s equations in general periodic microstructures
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Date
2017-03-15
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Abstract
We study the time harmonic Maxwell equations in a meta-material
consisting of perfect conductors and void space. The meta-material is assumed to
be periodic with period η > 0; we study the behaviour of solutions ( E^η ,H^η ) in the
limit η → 0 and derive an effective system. In geometries with a non-trivial topology,
the limit system implies that certain components of the effective fields vanish.
We identify the corresponding effective system and can predict, from topological
properties of the meta-material, whether or not it permits the propagation of waves.
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Keywords
Maxwell’s equations, homogenization, diffraction, periodic structure, meta-material