Fast Eigensolver for plasmonic metasurfaces

Alexander O. Korotkevich, University of New Mexico, Landau Institute of Theoretical Physics
Xingjie Ni, Purdue University, Birck Nanotechnology Center
Alexander V. Kildishev, Purdue University, Birck Nanotechnology Center

Abstract

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. (C) 2014 Optical Society of America

Discipline(s)

Nanoscience and Nanotechnology