A frequency-dependent LOD-FDTD method with the ADE technique for extraordinary optical transmission analyses

In this paper, a generalized auxiliary differential equation (ADE) technique is utilized to develop a frequency-dependent locally one-dimensional finite-difference time-domain (LOD-FDTD) method for the extraordinary optical transmission (EOT) analyses of periodic metal gratings. The LOD-FDTD method is an unconditionally stable method which is not restricted by the Courant-Friedrich-Lewy (CFL) stability condition, and a large time step could be utilized in the time marching procedure. Surface plasmon polaritons (SPPs) are the evanescent waves propagating along the interface between a metal and a dielectric. The dispersions of the metal are expressed by the Drude model, which is solved with the ADE technique in LOD-FDTD. The implementation of an efficient perfectly matched layer (PML) and periodic boundary conditions (PBC) in ADE-LOD-FDTD is discussed and demonstrated. Simultaneously, the incident waves are successfully introduced into the computational area through the total field/scattering field (TF/SF) boundaries. With the proposed ADE-LOD-FDTD method, which is easy to implement for the analysis of SPPs, the transmission resonances of periodic metal gratings with sub-wavelength slits are investigated in the visible and near infrared regions. Two numerical examples with different sub-wavelength slits in each period are discussed in this paper. The numerical results from our proposed ADE-LOD-FDTD method agree well with those from the traditional explicit ADE-FDTD method and the computation time of ADE-LOD-FDTD is largely reduced. The simulation results showed that the Fabry-Pérot (FP)-like behavior is not the only mechanism affecting the EOT phenomenon and the surface of the metal film also plays an important role of SPPs at the same time.