Tunable Dispersion in Planar Arrays of Coalesced Resonators

Planar arrays of split-ring resonators are known to support the propagation of backward magnetoinductive waves due to the negative coupling coefficient between elements. In this work, it is shown that the dispersion character can be switched to a forward wave if the resonators are touching. In particular, when the shared side is capacitively loaded, the total coupling can be switched from negative to positive values, allowing for forward magnetoinductive waves to propagate on the structure. By varying the value of the capacitor in the shared side of square resonators, the sign and size of the total coupling can be further controlled. This is demonstrated in an 11-element array, where the magnetoinductive wave can switch between forward and backward propagation depending on the capacitance of the shared side. Furthermore, there is a critical value of capacitance where the coupling becomes almost zero, effectively cutting of wave propagation on the structure. Numerical simulations are used to study this behaviour.