Krylov subspace-based and MBF-based analysis of large finite arrays of silver nanorods in the presence of a scatterer

Metamaterials receive increasing attention at optical frequencies due to their potential for subwavelength imaging. Among the possible structures are dense, doubly periodic arrays of silver nanorods where image transmission is achieved via surface plasmon polaritons. However, the numerical simulation of such dense structures may require excessive computational resources without employing an efficient numerical approach. In this paper, the multiple-scattering based Macro Basis Function (MBF) method is applied to the shielded-block preconditioned matrix, which represents interactions between different elements of the array (subdomains). The “rule of thumb” that relates the number of MBFs generated on a subdomain to the number of iterations required by the Full Orthogonalization Method (FOM) for the same error level is investigated. For high levels of error, the number of MBFs are observed to be smaller than the number of iterations required. Conversely, for low levels of error, the FOM converges faster.