Domain Decomposition CN-FDTD Method for Analyzing Dispersive Metallic Gratings

Abstract

In this paper, an efficient domain decomposition (DD) technique is originally introduced into the unconditionally stable Crank–Nicolson finite-difference time-domain (CN-FDTD) method for analyzing the extraordinary optical transmission (EOT) phenomenon of periodic metallic gratings. Being caused by the evanescent waves propagating along the metal-dielectric interface in the visible and near infrared regions, the dispersion of the considered metal in this case is expressed by the Drude model and solved with a generalized auxiliary differential equation (ADE) technique. The periodic boundary condition is applied to the two-dimensional periodic metallic grating structures due to their periodicity. Then, the standard unsplit-field perfectly matched layer is derived as the absorbing boundary condition for CN-FDTD based on the ADE concept. In DD structures, the whole computational domain is divided into several subdomains to reduce the matrix size and save calculating time. Furthermore, the reverse Cuthill–Mckee scheme for the lower–upper decomposition is applied to the subdomain matrices individually to improve the efficiency of DD-CN-FDTD. Finally, two numerical examples are calculated and the physical mechanism of the EOT phenomenon is investigated. The results from the proposed method demonstrate its accuracy and efficiency for the nanostructures.