Subcell Method for Modeling Metallic Resonators in Metamaterials

This paper describes a subcell modeling technique for metallic resonators where the actual metal traces are replaced by a thin wire having equivalent magnetic and electric radii, as well as an impedance per unit length. The formulas for these quantities in the case of rectangular traces are given. In addition, the gap of a split-ring resonator is replaced by a lumped load. The response of the resonator can then be modeled using thin-wire algorithms in an integral equation code. It is demonstrated that the number of unknowns and runtime can be reduced by factors of a thousand using the subcell models. This is particularly important in cases where metamaterial designs with tapered properties are encountered and periodic boundary conditions are not applicable, because with this simplification larger numbers of resonator cells can be handled.