Schweizer, Ben2017-03-062017-03-062016-10http://hdl.handle.net/2003/3584010.17877/DE290R-17864Meta-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.enMeta-materialsresonancehomogenizationHelmholtz equationMaxwell's equationssound absorbersnegative index materials610preprint