Frequency-Dependent Homogenization: Application to Metamaterials

A new approach to homogenization of spatially periodic composite materials is proposed, in which the frequency of the excitation is an essential parameter. An analysis of the "cell problem", by which effective homogeneous parameters εeff and μeff are obtained, show they can have negative real part, which is one of the interesting emergent properties of some (so-called "left-handed") metamaterials. The method can be used to design such materials, by numerical shape optimization.