Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries

Abstract

Abstract. The accuracy of finite-difference time-domain (FDTD) modelling of left-handed metamaterials (LHMs) is dramatically improved by using an averaging technique along the boundaries of LHM slabs. The material frequency dispersion of LHMs is taken into account using auxiliary differential equation (ADE) based dispersive FDTD methods. The dispersive FDTD method with averaged permittivity along the material boundaries is implemented for a two-dimensional (2-D) transverse electric (TE) case. A mismatch between analytical and numerical material parameters (e.g. permittivity and permeability) introduced by the time discretisation in FDTD is demonstrated. The expression of numerical permittivity is formulated and it is suggested to use corrected permittivity in FDTD simulations in order to model LHM slabs with their desired parameters. The influence of switching time of source on the oscillation of field intensity is analysed. It is shown that there exists an optimum value which leads to fast convergence in simulations.2

A Radially-Dependent Dispersive Finite-Difference Time-Domain Method for the Evaluation of Electromagnetic Cloaks

“…Thus, the conventional FDTD method cannot correctly simulate materials with the properties of ε r , µ r , ε z , µ z and new dispersive FDTD techniques have to be employed, like in the case of the left-handed metamaterials (LHMs) [37]. The parameters are mapped with dispersive material models and more precisely with the well-known and widely used Drude model:…”

“…Hence, for the proposed dispersive FDTD method a spatial resolution of ∆x < λ/10 is not sufficient unlike the conventional dielectric material simulations in which it is the required value [36]. From a previous analysis of left-handed metamaterials (LHMs) [37], it was found that spurious resonances are caused due to coarse time discretisation which leads to numerical errors and inaccurate modeling results. It was proposed that a spatial resolution of ∆x < λ/80 is essential for accurate simulations.…”

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

“…In the spatial grid, , , and are collocated with the corresponding field components, as done in [33], as opposed to being at the center of the Yee cell, as done in [31]. As discussed elsewhere [33] and [34], numerical mismatching effects (spurious surface plasmon) that may occur at double-negative interfaces need to be properly addressed. This can be achieved by using either an arithmetic mean of the material permittivity [34] or a current averaging technique [33] at the interfaces.…”

“…As discussed elsewhere [33] and [34], numerical mismatching effects (spurious surface plasmon) that may occur at double-negative interfaces need to be properly addressed. This can be achieved by using either an arithmetic mean of the material permittivity [34] or a current averaging technique [33] at the interfaces. In this work, we use the latter technique at the interfaces.…”

“…For these examples, we choose and a 30-cycle smooth ramp function ( ) in the time-domain excitation. The time marching is performed until to sufficiently perform the process of the (slow) growth of evanescent waves and thus obtain steady-state responses [12], [34]. Fig.…”