On homogenization approaches for manipulation with fields inside and outside metamaterials

Application of metamaterial in realistic devices requires reliable approaches for effective material parameters. We demonstrate that a general homogenization procedure is non-versatile relative to the approach associated with the device functionality either inside or outside the structure. We exemplify it with internal and external treatments for the effective permittivity of a metamaterial in a lens consisting of dielectric rods. The dependence of the focal length on the permittivity and frequency of the incident field is determined, and the composite metalens with an ordinary lens are compared. The focal length is the same for both lens types. The approaches are compared to obtain effective permittivity values. The results show that different methods of homogenization are to be considered for a property description depending on the needs.