Magnetoinductive waves in 2D periodic arrays of split ring resonators

Magnetoinductive waves in arrays of split ring resonators (SRRs) have been previously investigated. Here we characterize modes with real and complex wavenumber in two dimensional periodic arrays of SRRs. Each SRR is modeled as a single magnetic dipole, and the retrieval of the complex modal wavenumbers is performed by computing the complex zeroes of the homogeneous scalar equation characterizing the field in the array. The required periodic Green's function is analytically continued into the complex wavenumber space by using the Ewald method. The proposed method allows for the description of each complex mode when varying frequency, complementing previous investigations. In particular, we analyze proper and improper, bound and leaky, magnetoinductive waves.