Field Averaging Techniques in Electromagnetic Problems

In this work we present two field averaging techniques for structured electromagnetic materials. One is concerned with 3D-periodic composite media, while the other one is concerned with 2D-periodic planar structures. In the first case, the field averaging is prescribed by the integral form of Maxwell’s equations and is carried out along the paths laying at the boundaries of the unit cell. In the second case, the integration regions are prescribed by the Generalized Sheet Transition Conditions. Both techniques are useful in homogenization of structured materials such as metamaterials and metasurfaces, for the extraction of their effective material parameters and surface susceptibilities, respectively.