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

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 μeff and an effective electrical permittivity εeff, 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 (SRRs), 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.