Accurate analytical model of coupled omega particles for metamaterial design

We propose an analytical model of the bi-omega particle consisting of two opposite-oriented and spaced omega resonators. Properly placing the two omega particles very close to each other, the coupling effect between them contributes to shift down the resonant frequency, achieving a simple and deeply electrically small inclusion for the design of metamaterials with negative permeability working in the microwave frequency range. The proposed model, based on the small antenna theory, takes into account all the coupling effects that comes into play when the distance between the two omegas is very small. The results of the analytical model are compared to the numerical ones, showing a very good agreement.