Propagation property analysis of metamaterial constructed by conductive SRRs and wires using the MGS-based algorithm

An efficient numerical algorithm based on the modified Gram-Schmidt (MGS) procedure is developed in this paper to solve the electrical-field integral equation for characterizing metamaterials. The method of moments (MoM) with rooftop basis functions is implemented in the integral-equation solver. The MGS-based algorithm is implemented into the solver for decomposing the local MoM dense matrix without prior knowledge of the matrix elements. Although each element of the metamaterials is electrically small in size, the number of elements is very large so that the number of unknowns for characterizing the metamaterials is very large. Even so, this algorithm in the MoM solver has demonstrated via examples to be efficient and accurate. Numerical results on the number N of unknowns show that the CPU time per iteration and the memory requirements are both reduced from O(N²) to O(N^1.5). After implementing this algorithm in the solver, propagation characteristics are finally presented when electromagnetic waves pass through a metamaterial prism that is synthesized using square split-ring resonators and wires in free space.