Showing papers on "Metamaterial published in 2004"
TL;DR: Recent advances in metamaterials research are described and the potential that these materials may hold for realizing new and seemingly exotic electromagnetic phenomena is discussed.
Abstract: Recently, artificially constructed metamaterials have become of considerable interest, because these materials can exhibit electromagnetic characteristics unlike those of any conventional materials. Artificial magnetism and negative refractive index are two specific types of behavior that have been demonstrated over the past few years, illustrating the new physics and new applications possible when we expand our view as to what constitutes a material. In this review, we describe recent advances in metamaterials research and discuss the potential that these materials may hold for realizing new and seemingly exotic electromagnetic phenomena.
3,893 citations
TL;DR: In this article, an improved method to retrieve the effective constitutive parameters (permittivity and permeability) of a slab of metamaterial from the measurement of S parameters is proposed.
Abstract: We propose an improved method to retrieve the effective constitutive parameters (permittivity and permeability) of a slab of metamaterial from the measurement of S parameters. Improvements over existing methods include the determination of the first boundary and the thickness of the effective slab, the selection of the correct sign of effective impedance, and a mathematical method to choose the correct branch of the real part of the refractive index. The sensitivity of the effective constitutive parameters to the accuracy of the S parameters is also discussed. The method has been applied to various metamaterials and the successful retrieval results prove its effectiveness and robustness.
1,941 citations
TL;DR: The measured optical spectra of the nanofabricated gold structures come very close to the theoretical expectations and additional numerical simulations show that the structures exhibit a frequency range with negative permeability for a beam configuration in which the magnetic field couples to the LC resonance.
Abstract: An array of single nonmagnetic metallic split rings can be used to implement a magnetic resonance, which arises from an inductor-capacitor circuit (LC) resonance, at 100-terahertz frequency. The excitation of the LC resonance in the normal-incidence geometry used in our experiments occurs through the coupling of the electric field of the incident light to the capacitance. The measured optical spectra of the nanofabricated gold structures come very close to the theoretical expectations. Additional numerical simulations show that our structures exhibit a frequency range with negative permeability for a beam configuration in which the magnetic field couples to the LC resonance. Together with an electric response that has negative permittivity, this can lead to materials with a negative index of refraction.
1,448 citations
TL;DR: In this paper, the fundamental electromagnetic properties of left-handed metamaterials and the physical realization of these materials are reviewed based on a general transmission line (TL) approach.
Abstract: Metamaterials are artificial structures that can be designed to exhibit specific electromagnetic properties not commonly found in nature. Recently, metamaterials with simultaneously negative permittivity (/spl epsiv/) and permeability (/spl mu/), more commonly referred to as left-handed (LH) materials, have received substantial attention in the scientific and engineering communities. The unique properties of LHMs have allowed novel applications, concepts, and devices to be developed. In this article, the fundamental electromagnetic properties of LHMs and the physical realization of these materials are reviewed based on a general transmission line (TL) approach. The general TL approach provides insight into the physical phenomena of LHMs and provides an efficient design tool for LH applications. LHMs are considered to be a more general model of composite right/left hand (CRLH) structures, which also include right-handed (RH) effects that occur naturally in practical LHMs. Characterization, design, and implementation of one-dimensional and two-dimensional CRLH TLs are examined. In addition, microwave devices based on CRLH TLs and their applications are presented.
1,285 citations
TL;DR: The existence of acoustic metamaterial, in which both the effective density and bulk modulus are simultaneously negative, in the true and strict sense of an effective medium, is shown.
Abstract: We show here the existence of acoustic metamaterial, in which both the effective density and bulk modulus are simultaneously negative, in the true and strict sense of an effective medium. Our double-negative acoustic system is an acoustic analogue of Veselago's medium in electromagnetism, and shares many unique consequences, such as negative refractive index. The double negativity in acoustics is derived from low-frequency resonances, as in the case of electromagnetism, but the negative density and modulus are derived from a single resonance structure as distinct from electromagnetism in which the negative permeability and negative permittivity originates from different resonance mechanisms.
933 citations
TL;DR: A new particle, the complementary split rings resonator, is proposed for the design of metasurfaces with high frequency selectivity and planar metamaterials with a negative dielectric permittivity.
Abstract: The electromagnetic theory of diffraction and the Babinet principle are applied to the design of artificial metasurfaces and metamaterials. A new particle, the complementary split rings resonator, is proposed for the design of metasurfaces with high frequency selectivity and planar metamaterials with a negative dielectric permittivity. Applications in the fields of frequency selective surfaces and polarizers, as well as in microwave antennas and filter design, can be envisaged. The tunability of all these devices by an applied dc voltage is also achievable if these particles are etched on the appropriate substrate.
854 citations
TL;DR: This investigation details the properties of a passive, dispersive metamaterial that is matched to free space and has an index of refraction equal to zero, and shows that in both the source and scattering configurations the electromagnetic fields in a matched zero-index medium take on a static character in space, yet remain dynamic in time.
Abstract: Planar metamaterials that exhibit a zero index of refraction have been realized experimentally by several research groups. Their existence stimulated the present investigation, which details the properties of a passive, dispersive metamaterial that is matched to free space and has an index of refraction equal to zero. Thus, unlike previous zero-index investigations, both the permittivity and permeability are zero here at a specified frequency. One-, two-, and three-dimensional source problems are treated analytically. The one- and two-dimensional source problem results are confirmed numerically with finite difference time domain (FDTD) simulations. The FDTD simulator is also used to treat the corresponding one- and two-dimensional scattering problems. It is shown that in both the source and scattering configurations the electromagnetic fields in a matched zero-index medium take on a static character in space, yet remain dynamic in time, in such a manner that the underlying physics remains associated with propagating fields. Zero phase variation at various points in the zero-index medium is demonstrated once steady-state conditions are obtained. These behaviors are used to illustrate why a zero-index metamaterial, such as a zero-index electromagnetic band-gap structured medium, significantly narrows the far-field pattern associated with an antenna located within it. They are also used to show how a matched zero-index slab could be used to transform curved wave fronts into planar ones.
613 citations
TL;DR: In this paper, a woodpile EBG made up of magneto-dielectric material is proposed for the design of novel EM structures with applications in the VHF-UHF bands.
Abstract: In this paper, the unique features of periodic magneto-dielectric meta-materials in electromagnetics are addressed. These materials, which are arranged in periodic configurations, are applied for the design of novel EM structures with applications in the VHF-UHF bands. The utility of these materials is demonstrated by considering two challenging problems, namely, design of miniaturized electromagnetic band-gap (EBG) structures and antennas in the VHF-UHF bands. A woodpile EBG made up of magneto-dielectric material is proposed. It is shown that the magneto-dielectric woodpile not only exhibits band-gap rejection values much higher than the ordinary dielectric woodpile, but also for the same physical dimensions it shows a rejection band at a much lower frequency. The higher rejection is a result of higher effective impedance contrasts between consecutive layers of the magneto-dielectric woodpile structure. Composite magneto-dielectrics are also shown to provide certain advantages when used as substrates for planar antennas. These substrates are used to miniaturize antennas while maintaining a relatively high bandwidth and efficiency. An artificial anisotropic meta-substrate having /spl mu//sub r/>/spl epsiv//sub r/, made up of layered magneto-dielectric and dielectric materials is designed to maximize the bandwidth of a miniaturized patch antenna. Analytical and numerical approaches, based on the anisotropic effective medium theory (AEMT) and the finite-difference time-domain (FDTD) technique, are applied to carry out the analyzes and fully characterize the performance of finite and infinite periodic magneto-dielectric meta-materials integrated into the EBG and antenna designs.
473 citations
TL;DR: In this article, a spiral resonator (SR) was introduced as a useful artificial atom for artificial magnetic media design and fabrication, and a simple theoretical model which provides the most relevant properties and parameters of the SR was presented.
Abstract: A metallic planar particle, that will be called spiral resonator (SR), is introduced as a useful artificial atom for artificial magnetic media design and fabrication. A simple theoretical model which provides the most relevant properties and parameters of the SR is presented. The model is validated by both electromagnetic simulation and experiments. The applications of SR's include artificial negative magnetic permeability media (NMPM) and left-handed-media (LHM) design. The main advantages of SR's for such purpose are small electrical size at resonance, absence of magnetoelectric coupling (thus avoiding bianisotropic effects in the continuous medium made of these particles), and easy fabrication. Experimental confirmation of NMPM and LHM behavior using SR's is also reported.
433 citations
TL;DR: The simple pattern of the inclusion, the wide left-handed frequency band exhibited, and the low losses measured indicate the superiority of this inclusion in the realization of left- handed metamaterials.
Abstract: We analyze an $\mathsf{S}$-shaped inclusion for the realization of metamaterials exhibiting left-handed properties. Unlike most of the conventional inclusions used so far that are composed of two separate geometries---typically a split ring and a rod---the inclusion proposed in this paper is made of only one $\mathsf{S}$-shaped element which yields an overlapping negative permittivity and negative permeability response over a frequency band of about $2.6\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. By adopting this geometry, we manage to lower the negative permittivity frequency band down to the level of the negative permeability frequency band, thus allowing the overlapping to occur. Therefore, the structure works as a stand alone and does not require the use of an additional rod. A theoretical analysis is carried out to study this inclusion and numerical simulations, as well as a Snell refraction experiment, clearly show that the material indeed exhibits a negative index of refraction at some frequencies. The simple pattern of the inclusion, the wide left-handed frequency band exhibited, and the low losses measured indicate the superiority of this inclusion in the realization of left-handed metamaterials.
407 citations
TL;DR: In this paper, the authors analyzed the transmission and reflection data obtained through transfer matrix calculations on metamaterials of finite lengths, to determine their effective permittivity and permeability.
Abstract: We analyze the transmission and reflection data obtained through transfer matrix calculations on metamaterials of finite lengths, to determine their effective permittivity $ϵ$ and permeability $\ensuremath{\mu}$. Our study concerns metamaterial structures composed of periodic arrangements of wires, cut wires, split ring resonators (SRRs), closed SRRs, and both wires and SRRs. We find that the SRRs have a strong electric response, equivalent to that of cut wires, which dominates the behavior of left-handed materials (LHM). Analytical expressions for the effective parameters of the different structures are given, which can be used to explain the transmission characteristics of LHMs. Of particular relevance is the criterion introduced by our studies to identify if an experimental transmission peak is left or right handed.
TL;DR: In this article, the authors discussed linear and nonlinear optical wave propagation in a left-handed medium (LHM) or medium of negative refraction (NRM) and used the approach of characterizing the medium response totally by a generalized electric polarization (with a dielectric permittivity {tilde {var_epsilon}}(w, {rvec k})) that can be decomposed into a curl and a non-curl part.
Abstract: We discuss linear and nonlinear optical wave propagation in a left-handed medium (LHM) or medium of negative refraction (NRM). We use the approach of characterizing the medium response totally by a generalized electric polarization (with a dielectric permittivity {tilde {var_epsilon}}(w, {rvec k})) that can be decomposed into a curl and a non-curl part. The description has a one-to-one correspondence with the usual approach characterizing the LHM response with a dielectric permittivity {var_epsilon}<0 and a magnetic permeability {mu}<0. The latter approach is less physically transparent in the optical frequency region because the usual definition of magnetization loses its physical meaning. Linear wave propagation in LHM or NRM is characterized by negative refraction and negative group velocity that could be clearly manifested by ultra-short pulse propagation in such a medium. Nonlinear optical effects in LHM can be predicted from the same calculations adopted for ordinary media using our general approach.
TL;DR: In this article, the results of theoretical analysis for guided modes in parallel-plate waveguides filled with pairs of parallel layers made of any two of the following materials are presented: (1) a material with negative real permittivity, but positive real permeability (epsilon-negative); (2) amaterial with negativereal permeability and positive real permitivity (mu-negative), and (3) a conventional material with both negative real and permeability, double-negative, in a given range of frequency.
Abstract: Here we present the results of our theoretical analysis for guided modes in parallel-plate waveguides filled with pairs of parallel layers made of any two of the following materials: (1) a material with negative real permittivity, but positive real permeability (epsilon-negative); (2) a material with negative real permeability, but positive real permittivity (mu-negative); (3) a material with both negative real permittivity and permeability (double-negative); and (4) a conventional material with both positive real permittivity and permeability (double-positive) in a given range of frequency. Salient properties of these guided modes are studied in terms of how these materials and their parameters are chosen to be paired, and are then compared and contrasted with those of the guided modes in conventional waveguides. Special features such as monomodality in thick waveguides and presence of TE modes with no-cutoff thickness in thin parallel-plate waveguides are highlighted and discussed. Physical insights and intuitive justifications for the mathematical findings are also presented.
TL;DR: In this article, the negative refraction of microwaves in a metallic photonic crystal prism was shown to correspond to left-handed electromagnetism that arises due to the dispersion characteristics of waves in a periodic medium.
Abstract: We demonstrate the negative refraction of microwaves in a metallic photonic crystal prism. The spectral response of the photonic crystal prism, which manifests both positive and negative refraction, is in complete agreement with band-structure calculations and numerical simulations. The validity of Snell's law with a negative refractive index is confirmed experimentally and theoretically. The negative refraction observed corresponds to left-handed electromagnetism that arises due to the dispersion characteristics of waves in a periodic medium. This mechanism for negative refraction is different from that in metamaterials.
Patent•
08 Mar 2004TL;DR: In this article, an efficient, low-loss, low sidelobe, high dynamic range phased-array radar antenna system was proposed that uses metamaterials, which are manmade composite materials having a negative index of refraction, to create a biconcave lens architecture.
Abstract: An efficient, low-loss, low sidelobe, high dynamic range phased-array radar antenna system is disclosed that uses metamaterials, which are manmade composite materials having a negative index of refraction, to create a biconcave lens architecture (instead of the aforementioned biconvex lens) for focusing the microwaves transmitted by the antenna. Accordingly, the sidelobes of the antenna are reduced. Attenuation across microstrip transmission lines may be reduced by using low loss transmission lines that are suspended above a ground plane a predetermined distance in a way such they are not in contact with a solid substrate. By suspending the microstrip transmission lines in this manner, dielectric signal loss is reduced significantly, thus resulting in a less-attenuated signal at its destination.
TL;DR: In this article, a detailed analysis of the refraction and reflection behavior of electromagnetic waves at an interface between an indefinite medium and vacuum is presented, and it is shown that certain classes of indefinite media have identical refractive properties as isotropic negative index materials.
Abstract: Initial experiments on wedge samples composed of isotropic metamaterials with simultaneously negative permittivity and permeability have indicated that electromagnetic radiation can be negatively refracted. In more recently reported experiments [Phys. Rev. Lett. 90, 1074011 (2003)], indefinite metamaterial samples, for which the permittivity and permeability tensors are negative along only certain of the principal axes of the metamaterial, have also been used to demonstrate negative refraction. We present here a detailed analysis of the refraction and reflection behavior of electromagnetic waves at an interface between an indefinite medium and vacuum. We conclude that certain classes of indefinite media have identical refractive properties as isotropic negative index materials. However, there are limits to this correspondence, and other complicating phenomena may occur when indefinite media are substituted for isotropic negative index materials. We illustrate the results of our analysis with finite-element-based numerical simulations on planar slabs and wedges of negative index and indefinite media.
TL;DR: In this article, a one-dimensional metamaterial was realized using three connected Ω rings printed back-to-back and reversed on two sides of a dielectric substrate, yielding concordant results of the presence of a left-handed frequency band.
Abstract: A one-dimensional metamaterial is realized using three connected Ω rings printed back-to-back and reversed on two sides of a dielectric substrate. Both transmission and prism experiments are reported, yielding concordant results of the presence of a left-handed frequency band. Experiments show reduced losses and an enlarged left-handed frequency band.
TL;DR: In this article, a metamaterial composed of split ring resonators, designed to provide a permeability equal to −1 along the longitudinal axis, was shown to redirect s-polarized electromagnetic waves from a nearby source to a partial focus.
Abstract: Negative refraction can occur at the interface between vacuum and an indefinite medium—an anisotropic medium for which not all elements of the permittivity and permeability tensors have the same sign. We show experimentally and via simulations that a metamaterial composed of split ring resonators, designed to provide a permeability equal to −1 along the longitudinal axis, will redirect s-polarized electromagnetic waves from a nearby source to a partial focus. The dispersion characteristics of indefinite media prohibit the possibility of true aplanatic points for a planar slab; however, by contouring the surfaces aplanatic points may be realized, as well as other geometrical optical behavior.
TL;DR: In this article, a metamaterial surface composed of a periodic arrangement of Hilbert curve inclusions above a conducting ground plane is analyzed numerically and is shown to possess the properties of a high impedance surface by investigating the phase and magnitude of the reflection coefficient, /spl Gamma/, for a plane wave of normal incidence.
Abstract: A metamaterial surface, composed of a periodic arrangement of Hilbert Curve inclusions above a conducting ground plane, is analyzed numerically and is shown to possess the properties of a high impedance surface by investigating the phase and magnitude of the reflection coefficient, /spl Gamma/, for a plane wave of normal incidence. A parametric study is presented with respect to the iteration order of the Hilbert curve, the surface height above the ground plane, and the separation distance between the neighboring Hilbert elements within the surface array.
TL;DR: In this paper, a nanostructured metallic photonic crystal metamaterial is described and characterized, which is magnetically active in the near-infrared region of the spectrum.
Abstract: We describe and characterize a nanostructured metallic photonic crystal metamaterial which is magnetically active in the near-infrared region of the spectrum. The periodic array of modified split-ring resonator structures is numerically demonstrated to have a negative effective permeability at telecommunications wavelengths. Local electric fields in the structure can be many orders of magnitude larger than in free space thus allowing for enhanced nonlinear effects. We have derived an expression for the change in the resonance frequency of the structure due to the Kerr nonlinear index change and estimate a characteristic magnetic field strength for the observation of bistable behavior.
01 Jan 2004
TL;DR: True left-handed (LH) behavior in a composite metamaterial consisting of a periodically arranged split ring resonator (SRR) and wire structures is reported and it is confirmed experimentally that the effective plasma frequency of the LH material composed of SRRs and wires is lower than the plasma Frequency of the wires.
Abstract: We report true left-handed (LH) behavior in a composite metamaterial consisting of a periodically arranged split ring resonator (SRR) and wire structures. We demonstrate the magnetic resonance of the SRR structure by comparing the transmission spectra of SRRs with those of closed SRRs. We have confirmed experimentally that the effective plasma frequency of the LH material composed of SRRs and wires is lower than the plasma frequency of the wires. A well-defined LH transmission band with a peak value of 21.2 dB 20.3 dB cm was obtained. The experimental results agree extremely well with the theoretical calculations. © 2004 Optical Society of America OCIS codes: 120.7000, 260.2110.
TL;DR: In this paper, a left-handed metamaterial consisting of a periodically arranged split ring resonator (SRR) and wire structures was analyzed and the experimental results agree extremely well with the theoretical calculations.
Abstract: We report true left-handed (LH) behavior in a composite metamaterial consisting of a periodically arranged split ring resonator (SRR) and wire structures. We demonstrate the magnetic resonance of the SRR structure by comparing the transmission spectra of SRRs with those of closed SRRs. We have confirmed experimentally that the effective plasma frequency of the LH material composed of SRRs and wires is lower than the plasma frequency of the wires. A well-defined LH transmission band with a peak value of -1.2 dB (-0.3 dB/cm) was obtained. The experimental results agree extremely well with the theoretical calculations.
TL;DR: In this article, an array factor approach of leaky-wave antennas is proposed for efficient and fast computation of the radiation patterns of complex metamaterial LW structures of arbitrary length from the analysis of a single periodic unit cell.
Abstract: An array factor approach of leaky-wave (LW) antennas is proposed for efficient and fast computation of the radiation patterns of complex metamaterial LW structures of arbitrary length from the analysis of a single periodic unit cell. This approach is demonstrated in one-dimensional and two-dimensional composite right/left-handed (CRLH) LW antennas.
TL;DR: In this paper, the authors present experimental measurements at microwave frequencies of a double band left-handed metamaterial, composed of an extended version of the S-shaped resonators that exhibit simultaneously a negative permittivity and a negative permeability response at comparable frequencies.
Abstract: We present experimental measurements at microwave frequencies of a double band left-handed metamaterial. The sample of metamaterial is composed of an extended version of the S-shaped resonators that exhibit simultaneously a negative permittivity and a negative permeability response at comparable frequencies. The experimental results clearly show that there exist two frequency bands where the refraction index is negative. The double left-handed passbands are due to the multiple capacitances and inductances induced in the structure, which can be further tuned to realize a metamaterial with multiple (more than two) left-handed frequency bands.
TL;DR: In this paper, a two-dimensional photonic crystal composed of polaritonic materials behaves as an effective medium with negative permeability in the micron wavelength range, due to the large values of e(ω) attained near the transverse phonon frequency ωT.
Abstract: We find that a two-dimensional photonic crystal composed of polaritonic materials behaves as an effective medium with negative permeability in the micron wavelength range. The resonance in μeff is due to the large values of e(ω) attained near the transverse phonon frequency ωT. The minimal wavelength for achieving an effective permeability less than −1 in a LiTaO3 crystal, obtained by optimizing the rod size and the lattice constant, is around 12μm, a range previously inaccessible using dielectric metamaterials. For certain dissipation levels, we find that other polaritonic media also exhibit a resonant effect with μeff<−1 for wavelengths ranging from 2 to ∼100μm.
TL;DR: In this article, an equivalent circuit consisting of bulk and distributed elements is derived for describing the properties of a potential metamaterial element capable of providing negative effective permeability, which is called the singly split double ring (SSDR).
Abstract: An equivalent circuit, consisting of bulk and distributed elements, is derived for describing the properties of a potential metamaterial element capable of providing negative effective permeability. It is the singly split double ring (SSDR), a special case of the split ring resonator (J. B. Pendry et al., IEEE Trans. Microwave Theory Tech. 47, 2075 (1999)), obtained when the gap capacitance in the inner ring is infinitely large. The variables are the inter-ring voltage and the currents flowing in the inner and outer rings. The excitation is assumed in the form of a spatially constant temporally varying magnetic field. The functions, showing the angular variation of the variables, are found by solving a set of differential equations with boundary conditions imposed at the position of the split. It is shown from the analytical solution that the SSDR can have resonant frequencies in the full spectrum from very low to very high frequencies. It is pointed out in particular that whenever the mean diameter of th...
TL;DR: In this paper, a coupled-line coupler comprising a microstrip line, edge-coupled to a negative-refractive-index line, exhibits co-directional phase but contradirectional Poynting vectors on the lines, leading to backward coupling.
Abstract: A coupled-line coupler comprising a microstrip line, edge-coupled to a negative-refractive-index line, exhibits co-directional phase but contra-directional Poynting vectors on the lines, leading to backward coupling. A key feature of this coupler is that it can support complex coupled modes. The resulting exponential field decay enables enhanced coupling with moderate line lengths and spacing. An example 3 dB device has been implemented and tested at 3 GHz.
TL;DR: In this paper, a slab waveguide structure that guides visible light in an air core was designed and analyzed using metal-dielectric nanostructures, which showed intriguing optical properties including total external reflection.
Abstract: Metamaterials composed of metal-dielectric nanostructures can be engineered to have the real part of the effective refractive index less than unity at optical wavelengths. These materials show intriguing optical properties including total external reflection. We utilize this effect to design and analyze slab waveguide structures that guide visible light in an air core.
TL;DR: In this article, a power/ground planes design for eliminating the ground bounce noise (GBN) in high-speed digital circuits is proposed by using low-period photonic bandgap (PBG) structure.
Abstract: A novel power/ground planes design for eliminating the ground bounce noise (GBN) in high-speed digital circuits is proposed by using low-period photonic bandgap (PBG) structure. Keeping solid for the ground plane and designing low-period PBG pattern on the power plane, the proposed structure omni-directionally behaves highly efficient suppression of GBN (over 50 dB) within broadband frequency range from 1 GHz to 4 GHz. Although the power plane has low-period perforation, the proposed structure still performs with relatively low radiation within the stopband compared with the solid power/ground planes. The low radiation and high suppression of the GBN for the proposed structure are checked both experimentally and numerically. Good consistency is seen.
TL;DR: In this article, the authors have designed, produced, and experimentally characterized $2.7\phantom{\rule{0.3em}{0ex}}\mathrm{mm} thick composite panels having negative refractive index between 8.4 and 9.3m.
Abstract: We have designed, produced, and experimentally characterized $2.7\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ thick composite panels having negative refractive index between 8.4 and $9.2\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. The composite metamaterial is fabricated using conventional commercial multilayer circuit-board lithography; three-dimensional physical (as opposed to electromagnetic) structure is introduced by the use of vias to form sections of the scattering elements in the direction perpendicular to the circuit board surfaces. From scattering parameter measurements, we show that the complex permittivity, permeability, index, and impedance of the composite can be unambiguously determined. The measurements enable the quantitative determination of the negative index band and associated losses. The extracted material parameters are shown to be in excellent agreement with simulation results.