Rigorous analysis of negative refractive index metamaterials using FDTD with embedded lumped elements

A methodology for the time-domain analysis of negative refractive index (NRI) media is proposed in this paper. Based on circuit models of NRI meta-materials and associated planar implementations that have been recently demonstrated, an extended FDTD approach is formulated, combining Maxwell's equations with lumped element voltage-current characteristics. Compared to previous FDTD modelling of NRI materials as negative dispersive index media, the proposed method presents the significant advantage of relying on simple and well-known mesh truncation method and not suffering from instabilities related to the Lorentz model poles. The analysis is accelerated by invoking periodic boundary conditions that allow for the simulation of a single unit cell as opposed to the whole grid. As a time-domain technique, the proposed one allows for the clarification of the transients involved with the evolution of backward waves and negative refraction in NRI meta-materials and the verification of the fact that causality is preserved throughout. Numerical results include validation against finite element analysis and converge studies that indicate the efficiency and computational speed of this method.