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

Abstract

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.

Effective Medium Theory of Left-Handed Materials

“…The combined system of wires and SRRs exhibits synergy of the two components as a result of which its effective plasma frequency, ω ′ p , is much lower than the plasma frequency of the wires, ω p . There is also a significant amount of numerical work [10][11][12][13] in which the complex transmission and reflection amplitudes are calculated for a finite length of metamaterial. Using these data a retrieval procedure can then be applied to obtain the effective permittivity ǫ and permeability µ, under the assumption that the metamaterial can be treated as homogeneous.…”

Transmission properties of composite metamaterials in free space

“…All of these measurements were performed in a waveguide chamber which limited one of the dimensions of the LHM structures to a maximum of three cells. 16 Very recently, the fundamental properties of the LHMs were verified by the transfer matrix method ͑TMM͒, 17 ab initio, 18 the finite-element method, 19 and finite-difference-time-domain 20 simulations.…”

Enriching the Symmetry of Maxwell Equations through Unprecedented Magnetic Responses of Artificial Metamaterials and Their Revolutionary Applications

“…This set-up will increase the total capacitance value as C total = C gap + C parallel . In references [30][31][32][33][34][35][36][37][38][39], many researchers have systematically investigated the properties of SRR, such as the size and the shape of the SRRs, the size of the unit cell, dielectric properties of the substrate, complementary structures of SRR, and the orientation relative to incident waves in the microwave region.…”