SUMMARYA conformal finite-difference time-domain algorithm for the solution of electrodynamic problems in general perfectly conducting 3D geometries is presented. Unlike previous conformal approaches it has the second-order convergence without the need to reduce the maximal stable time step of conventional staircase approach. A novel proof for the local error rate for general geometries is given, and the method is verified and compared to other approaches by means of several numerical 2D examples.

Effective electric permittivity and magnetic permeability for metamaterial structures are extracted from 3D field simulation data. The equivalent representation of the metamaterial is a homogeneous slab described with parameterized dispersive Drude and Lorentz models. The parameters of dispersive models are obtained by optimization. Proposed approach is applied to the extraction of effective material parameters for double negative metamaterial cells. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 285–288, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22105

In this paper we present a reformulation of the FDTD algorithm on nonorthogonal grids, which was originally proposed by Holland in 1983. Based on the matrix-vector notation of the Finite Integration Technique (FIT), the new formulation allows to study a special type of instability, which is due to the spatial discretization and independent of the choice of the timestep. It is shown, that this type of instability can be avoided by a symmetric evaluation of the metric coefflcients of the nonorthogonal grid. Two numerical examples demonstrate the stability properties and the high accuracy of the new method.

Using numerical simulation techniques, the transmission and reflection coefficients, or S parameters, for left-handed metamaterials are calculated. Metamaterials consist of a lattice of conducting, nonmagnetic elements that can be described by an effective magnetic permeability eff and an effective electrical permittivity eff , both of which can exhibit values not found in naturally occurring materials. Because the electromagnetic fields in conducting metamaterials can be localized to regions much smaller than the incident wavelength, it can be difficult to perform accurate numerical simulations. The metamaterials simulated here, for example, are based on arrays of split ring resonators ͑SRRs͒, which produce enhanced and highly localized electric fields within the gaps of the elements in response to applied time dependent fields. To obtain greater numerical accuracy we utilize the newly developed commercially available code MICROWAVE STUDIO, which is based on the finite integration technique with the perfect boundary approximation. The simulation results are in agreement with published experimental results for the frequencies and bandwidths of the propagation and stop bands associated with the various structures. We further analyze the properties of an individual SRR, and find the dependence of the resonant frequency on the SRR radius, ring thickness, inner/outer radial gap, azimuthal gap, electrical permittivity, and magnetic permeability of the components' materials. Comparison with previously published analytical estimates shows only approximate agreement with the simulation results.

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