Resonance meets homogenization - Construction of meta-materials with astonishing properties
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Date
2016-10
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Abstract
Meta-materials are assemblies of small components. Even though the
single component consists of ordinary materials, the meta-material may
behave effectively in a way that is not known from ordinary materials. In
this text, we discuss some meta-materials that exhibit unusual properties
in the propagation of sound or light. The phenomena are based on
resonance effects in the small components. The small (sub-wavelength)
components can be resonant to the wave-length of an external field if
they incorporate singular features such as a high contrast or a singular
geometry. Homogenization theory allows to derive effective equations for
the macroscopic description of the meta-material and to verify its unusual
properties. We discuss three examples: Sound-absorbing materials,
optical materials with a negative index of refraction, perfect transmission
through grated metals.
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Meta-materials, resonance, homogenization, Helmholtz equation, Maxwell's equations, sound absorbers, negative index materials