Analytical models for predicting the effective permittivity of complementary metamaterial structures

We present an analytical formula to calculate the resultant effective permittivity of a metamaterial medium composed of unit cells with complementary structures. Complementary metamaterial can be considered to be the complementary screen of artificial magnetic materials. Based on Babinet's principle and duality, complementary metamaterial provides a negative effective permittivity in the vicinity of its resonance frequency. The developed formula is general and predicts the effective permittivity for a specific topology. The derived model validated by comparison to results obtained using full-wave simulation.