Dispersive Contour-Path MNL-FDTD Scheme for Fast Analysis of Waveguide Metamaterials

A semi-implicit dispersive thin-wire finite-difference time-domain (FDTD) scheme is proposed for fast analysis of waveguide metamaterials. The proposed scheme is based on combining the Newmark-beta method with Mäkinen's improved thin-wire FDTD model based on the contour-path integral of Maxwell's equations around a wire corrected with scaling factors and Wait's surface-impedance boundary condition for thin wires of finite conductivity. Its stability condition is determined by only the two meshes in the transverse plane to the wire axis. This feature allows using larger mesh steps than a wire radius without time step reducing. In order to verify the scheme, we demonstrate four device applications: plasmonic parallel-plate waveguide filled with only positive dielectrics, edge Fabry-Pérot resonator, waveguide metatronic high-pass filter, and coaxial-to-waveguide matching with an epsilon-near-zero narrow channel. Its stability, accuracy, and computational efficiency are assessed in comparison with the standard FDTD explicit scheme, analytical solutions, and existing experimental data.