Time-Dispersive Behaviour as a Feature of Critical Contrast Media

Abstract

Motivated by the urgent need to attribute a rigorous mathematical meaning to the term "metamaterial", we propose a novel approach to the homogenisation of critical-contrast composites. This is based on the asymptotic analysis of the Dirichlet-to-Neumann map on the interface between different components ("stiff" and "soft") of the medium, which leads to an asymptotic approximation of eigenmodes. This allows us to see that the presence of the soft component makes the stiff one behave as a class of time-dispersive media. By an inversion of this argument, we also offer a recipe for the construction of such media with prescribed dispersive properties from periodic composites.

arXiv comment24 pages, 6 fugures

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Cited by in corpus (5)

• Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I
• Functional model for boundary-value problems
• Linear Operators and Operator Functions Associated with Spectral Boundary Value Problems
• Scattering theory for a class of non-selfadjoint extensions of symmetric operators
• Operator-norm resolvent asymptotic analysis of continuous media with high-contrast inclusions