Ab initio numerical simulation of left-handed metamaterials: Comparison ofcalculations and experiments

Using numerical simulation techniques, the transmission and reflection coef ficients, or S parameters, for left-handed metamaterials are calculated. Me tamaterials consist of a lattice of conducting, nonmagnetic elements that c an be described by an effective magnetic permeability mu (eff) and an effec tive electrical permittivity epsilon (eff), both of which can exhibit value s not found in naturally occurring materials. Because the electromagnetic f ields in conducting metamaterials can be localized to regions much smaller than the incident wavelength, it can be difficult to perform accurate numer ical simulations. The metamaterials simulated here, for example, are based on arrays of split ring resonators (SRRs), which produce enhanced and highl y localized electric fields within the gaps of the elements in response to applied time dependent fields. To obtain greater numerical accuracy we util ize the newly developed commercially available code MICROWAVE STUDIO, which is based on the finite integration technique with the perfect boundary app roximation. The simulation results are in agreement with published experime ntal results for the frequencies and bandwidths of the propagation and stop bands associated with the various structures. We further analyze the prope rties of an individual SRR, and find the dependence of the resonant frequen cy on the SRR radius, ring thickness, inner/outer radial gap, azimuthal gap , electrical permittivity, and magnetic permeability of the components' mat erials. Comparison with previously published analytical estimates shows onl y approximate agreement with the simulation results. (C) 2001 American Inst itute of Physics.