Analytical models for calculating the constitutive parameters of engineered complementary resonators

Analytical models for characterizing the effective permittivity of artificial complementary resonators are proposed. It is well-known that artificial magnetic materials can provide enhanced effective magnetic permeability, μ_eff, over a frequency band when exposed to an axial magnetic field H. Based on Babinet´s principle and duality, the complementary screen of the artificial magnetic materials are expected to respond to an axial electric field E. We demonstrate here through analytical models and full-wave numerical simulations that the electric permittivity of engineered complementary resonators is enhanced with negative real-part above resonance, due to an applied external E field, as opposed to artificial magnetic materials.