Hybrid Newmark-conformal FDTD modeling of thin spoof plasmonic metamaterials

The aim of this paper is to present a new efficient and accurate semi-implicit finite-difference time-domain (FDTD) method for modeling thin plasmonic metamaterials supporting spoof surface plasmons. The presented method is formulated by combining Yu-Mittra's conformal FDTD technique for dielectrics, the simplified conformal finite integration technique for perfectly electric conductors (PECs) and the Newmark-Beta method. The resultant scheme is magnetically implicit, has a more relaxed stability condition than that of Yee's FDTD scheme, and allows for accurate modeling of both PEC and dielectric curved surfaces. Energy conservation and stability of the presented scheme is theoretically proved with the energy inequality method. Its formulation can be generalized to a class of magnetically implicit FDTD schemes with weakly conditional and unconditional stability in a unified manner. The presented scheme is used to simulate thin structures supporting spoof surface plasmon polaritons and spoof localized surface plasmons, and also applied to recent plasmonic devices such as planar frequency splitter, ultrathin rainbow trapping device and compact planar metadisk with split-ring resonators. The accuracy and efficiency of the presented scheme are assessed in comparison with the conventional explicit and implicit FDTD methods, and their conformal variants.