Fast Eigensolver for plasmonic metasurfaces

Finding the wavevectors (eigenvalues) and wavefronts (eigenvectors) in nanostructured metasurfaces is cast as a problem of finding the complex roots of a non-linear equation. A new algorithm is introduced for solving this problem; example eigenvalues are obtained and compared against the results from a popular, yet much more computationally expensive method built on a matrix eigenvalue problem. In contrast to the conventional solvers, the proposed method always returns a set of 'exact' individual eigenvalues. First, by using the Lehmer-Schur algorithm, we isolate individual complex roots from each other, then use a zero-polishing method applied at the very final stage of ultimate eigenvalue localization. Exceptional computational performance, scalability, and accuracy are demonstrated.