FDTD-PLRC Technique for Modeling of Anisotropic-Dispersive Media and Metamaterial Devices

The goal of this paper is to develop a versatile computational engine based on the finite-difference time-domain (FDTD) technique to comprehensively demonstrate the broadband behaviors of devices designed utilizing anisotropic-dispersive metamaterials. In this regard, the frequency-dependent behavior of dispersive materials is incorporated into the FDTD equations with the use of a piecewise linear recursive convolution (PLRC) approach. The FDTD domain is effectively terminated utilizing convolutional perfectly matched layered (CPML) absorbing walls, which are derived from the complex frequency-shifted (CFS) formulation. The CPML has the advantage that it operates only on the filed intensities and has nothing to do with the and constitutive relationships. The CPML is also highly absorptive to both propagating and evanescent waves. Therefore, it would be of great interest for terminating metamaterials having complex constitutive parameters. The developed method is also capable of characterizing periodic configurations illuminated by normal incident plane waves. The FDTD engine is successfully validated through the analyses of several complex metamaterials. The design and characterization of novel devices such as a patch antenna printed on metasubstrate with anisotropic
epsiv
(omega) -
mu
(omega)parameters, an electrically small antenna embedded in negative permittivity resonator, and an anisotropic-dispersive self-biased hexagonal ferrite-coupled line (FCL) circulator are highlighted.