Magnetically Implicit Single-Field FDTD Scheme Based on the Newmark-Beta Method

A single-field finite-difference time-domain (FDTD) scheme based on the wave equation of magnetic field and the Newmark-beta method is formulated. The resulting scheme has a directionally implicit time updating of magnetic field component only. Its numerical stability and numerical dispersion property are analyzed with the Fourier method. The stability condition of the presented scheme is relaxed than that of the traditional explicit FDTD. This scheme is used to simulate a terahertz (THz) frequency splitter based on the propagation of spoof surface plasmon polaritons and a rainbow trapping device with graded metallic grating structures. With the upper limit of the relaxed stability condition, it is shown to be faster than the explicit FDTD, the fully implicit Crank–Nicolson FDTD, and the semi-implicit mixed Newmark-leapfrog FDTD schemes.