Analytical model of connected bi-omega: robust particle for the selective power transmission through sub-wavelength apertures

In this paper, we present a new analytical model of the connected bi-omega structure consisting of two bi-omega particles connected together through their arms. A single bi-omega particle consists of a pair of regular equal omegas with mirror symmetry. Assuming the individual bi-omega particle electrically small, the equivalent circuit is derived, in order to predict its resonant frequency. Then, two bi-omega particles are connected together, obtaining a symmetric structure that supports two fundamental modes, with even and odd symmetries, respectively. The proposed analytical model, then, is used to develop a procedure allowing the design of the particle for a desired resonant frequency. The effectiveness of the proposed analytical model and design guidelines is confirmed by proper comparisons to full-wave numerical and experimental results. We also demonstrate through a proper set of experiments that the resonant frequencies of the connected bi-omega particle depend only on the geometrical and electrical parameters of the omegas and are rather insensitive to the practical scenario where the particle itself is actually used, e.g. in free-space, rectangular waveguide or across an aperture in a metallic screen.