Composite right/left‐handed extended equivalent circuit (CRLH‐EEC) FDTD: stability and dispersion analysis with examples

Abstract

AbstractA composite right/left‐handed (CRLH) extended equivalent circuit (EEC) FDTD method with a stability criterion based on a Liapunov discrete energy function is presented and applied to investigate several transient and refractive phenomena occurring at the interface between a CRLH metamaterial (MTM) and a purely right‐handed (PRH) structure. This formulation consists in an extension of the equivalent circuit (EC) Yee scheme including a left‐handed (LH) series capacitance and shunt inductance in addition to the canonical right‐handed (RH) series inductance and shunt capacitance, so as to model general CRLH transmission line (TL) MTMs. This CRLH‐EEC FDTD scheme is shown to represent a convenient numerical scheme, with remarkable formulation compactness and high computational efficiency, for the analysis of any type of MTM structure. Moreover, this scheme, coupled with a Y‐matrix representation of the EEC Yee cell, is shown to rigorously restore the dispersion/attenuation relation of CRLH MTMs. Transient solutions for the propagation of a modulated Gaussian pulse through a PRH–CRLH interface highlights interesting effects such as space‐domain compression, infinite phase velocity modulation and the well‐known backward wave effect. Frequency‐domain analysis of the fields radiated by dipoles through the Veselago–Pendry lens shows how focusing is affected both qualitatively and quantitatively by the orientation of the dipoles. Copyright © 2006 John Wiley & Sons, Ltd.