Hybrid sub-gridding ADE-FDTD method of modeling periodic metallic nanoparticle arrays

In this paper, a modified sub-gridding scheme that hybridizes the conventional finite-difference time-domain (FDTD) method and the unconditionally stable locally one-dimensional (LOD) FDTD is developed for analyzing the periodic metallic nanoparticle arrays. The dispersion of the metal, caused by the evanescent wave propagating along the metal-dielectric interface, is expressed by the Drude model and solved with a generalized auxiliary differential equation (ADE) technique. In the sub-gridding scheme, the ADE-FDTD is applied to the global coarse grids while the ADE-LOD-FDTD is applied to the local fine grids. The time step sizes in the fine-grid region and coarse-grid region can be synchronized, and thus obviating the temporal interpolation of the fields in the time-marching process. Numerical examples about extraordinary optical transmission through the periodic metallic nanoparticle array are provided to show the accuracy and efficiency of the proposed method.