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Experimental determination and numerical simulation of the properties of negative index of refraction materials

R. B. Greegor, C. G. Parazzoli, K. Li, B. E. C. Koltenbah, and M. Tanielian

Open Access Open Access

Abstract

Negative index of refraction materials have been postulated for many years but have only recently been realized in practice. In the microwave region these materials are constructed of rings and wires deposited on a dielectric substrate to form a unit cell. We have constructed, experimentally characterized and simulated several of these structures operating in the 10 – 15 GHz range. Our simulations using Maxwell’s Equations solvers have included wire arrays, ring arrays and assemblies of unit cells comprised of rings and wires. We find good agreement between the numerical simulations and experimental measurements of the scattering parameters and index of refraction. The procedure was to first model ring and wire structures on the unit cell level to obtain scattering parameters from which effective ε, μ and n were retrieved. Next an assembled array of unit cells forming a 12° wedge was used for the Snell’s Law determination of the negative index of refraction. For the structure examined the computed value of n is within 20% of the one experimentally measured in the Snell’s Law experiment from 13.6 to 14.8 GHz.

©2003 Optical Society of America

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Figures (7)
Fig. 1.
Fig. 1. Unit cell showing electric / magnetic boundary conditions and the dimensions of the 901 structure used in the MWS simulations. Periodic boundary conditions were applied along the y-axis and z-axis when used. The direction of propagation of the electromagnetic field is along the x-axis, the electric field is oriented along the z-axis, the magnetic field along the y-axis. For the 901 structure C=0.025 cm, D=0.030 cm, G=0.046 cm, H=0.0254 cm, L=0.33cm, S=0.263 cm, T=17.0×10-4 cm and W=0.025 cm.

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Fig. 2.
Fig. 2. Comparison of experimental and simulated transmission Mod(S21), of wires and rings. Electric / magnetic boundary conditions were used in the simulations. (Top) Wire only structure 3 cells deep in propagation direction having an effective length of the wires Lw =12.5cm. (Bottom) SRR only structure, similar to the 901 structure without wire, 3 cells deep in the direction of propagation. In the MWS simulations the wire and ring conductivity was 5.8×107 (S/m) while the substrate dielectric constant εsub=3.7, and the loss tangent, tanδ=0.02.

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Fig. 3.
Fig. 3. Comparison of computed and measured Mod(S21) scattering parameters for a ring and wire structure. A Rogers 5880 substrate was used with Rohacell spacers and tape at the perimeter to hold the structure together. Periodic boundary conditions were used in the simulations. (a) 901 HWD structure showing additional wire in each unit cell. (b) Measured (blue) and computed (red) Mod(S21) scattering parameter for 3 cells in propagation direction..

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Fig. 4.
Fig. 4. Simulated losses at the pass-band peak for the 901 HWD structure. The thickness of the PC board was 0.025 cm. The nominal conductivity of Cu was given to the rings and wires. The dimensions of the 901 structure is given in Fig. 1.

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Fig. 5.
Fig. 5. Simulated transmission in the 901 HWD structure for (a) various adhesive loss tangents and (b) various metallic conductivities. The solid vertical bar indicates the conductivity of copper.

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Fig. 6.
Fig. 6. Surface plots of measured normalized peak amplitude of electric field component Ez (r, f) for the Teflon and 901 HWD NIM wedge. Note that the electric field refracted by the Teflon wedge peaks at a positive refractive angle of 17° (corresponding to an index of refraction of 1.4) and is independent of frequency. The electric field refracted by the NIM wedge however, peaks at negative refractive angles that are a function of the frequency

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Fig. 7.
Fig. 7. Experimentally measured (data points) and simulated (solid line) dispersion relation of the index of refraction for the 901 HWD structure with substrate ε=2.2 and no adhesive used in the construction process. The measured and simulated values agree within 20%. The measured values were obtained from the Snell’s Law experiment and the simulated values were obtained from the simulated scattering parameters using retrieval procedures. Periodic boundary conditions were used in the simulations.

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