Determination of the effective parameters of a metamaterial by field summation method

A field summation method is used to determine the effective epsilon and mu of metamaterial structures. The numerical implementation of this method using commercial software is comprehensively described. The field summation method is shown to predict accurately the reflection and transmission coefficients of thin slabs of metamaterials. For thicker slabs, it is shown that any homogenization approach should be flawed. It is established that the limitations for the homogenization approach are not only simply related to the size of the patterns and unit cell but also to the resonance bandwidth of individual scatterers. To support this view, metamaterials made of patterns with limited conductivity are investigated. It is shown that a homogenization approach is adequate on composite made of patterns with larger resonance bandwidth. Field summation method provides good indications on the validity of a homogenization approach and then leads to satisfactory values for the effective epsilon and mu. (c) 2006 American Institute of Physics.