This chapter focuses on acoustic, electromagnetic, elastic and piezo-electric wave
propagation through heterogenous layers. The motivation is provided by the demand for a
better understanding of meta-materials and their possible construction. We stress the analogies
between the mathematical treatment of phononic, photonic and elastic meta-materials.
Moreover, we treat the cloaking problem in more detail from an analytical and simulation
oriented point of view. The novelty in the approach presented here is with the interlinked
homogenization- and optimization procedure.
