Efficient Frequency-Dependent Newmark-Beta-FDTD Method for Periodic Grating Calculation

In this paper, the Newmark-Beta algorithm is introduced into the finite-difference time-domain (FDTD) method in dispersion media, resulting in an unconditionally stable method for periodic metallic grating analysis. The proposed method eliminates the Courant-Friedrich-Levy constraint and improves the simulation efficiency for multiscale problems. The dispersion of the metal, which is caused by the evanescent waves propagating along the interface between the metal and dielectric materials in the visible and near-infrared regions, is solved with a generalized auxiliary differential equation (ADE) technique. The extraordinary optical transmission through a periodic metallic grating with different number and different size of the perpendicular bump is also investigated. Compared with the traditional ADE-FDTD method and ADE alternating-direction-implicit FDTD method, the results from the proposed method show its accuracy and efficiency.