Singular Integral Formulations for Electrodynamic Analysis of Metamaterial-Inspired Antenna Array

In this letter, a set of singular integral formulations are derived to calculate the surface impedance matrix on the antenna array elements. The proposed mathematical model enables electrodynamic analysis of antenna arrays designed using metamaterial-inspired structures. The formulations allow the determination of the array's impedance, spatial, and polarization characteristics at significantly low computational cost compared to conventional electromagnetic (EM) solvers based on method-of-moments (MoM) numerical technique. The accuracy of the surface impedance results obtained from the theoretical formulations is verified using the full-wave EM software. It is shown that there is excellent agreement between the proposed formulations and EM software. The accuracy of the theoretical model presented is valid for single-layer structures.