A recently published theory has suggested that a cloak of invisibility is in principle possible, at least over a narrow frequency band. We describe here the first practical realization of such a cloak; in our demonstration, a copper cylinder was “hidden” inside a cloak constructed according to the previous theoretical prescription. The cloak was constructed with the use of artificially structured metamaterials, designed for operation over a band of microwave frequencies. The cloak decreased scattering from the hidden object while at the same time reducing its shadow, so that the cloak and object combined began to resemble empty space.
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Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the calculation of these material properties for coordinate transformations that describe spaces with spherical or cylindrical holes in them. The resulting material properties can then implement invisibility cloaks in flat space. We also describe a method for performing geometric ray tracing in these materials which are both inhomogeneous and anisotropic in their electric permittivity and magnetic permeability.
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Pendry et al. have reported electromagnetically anisotropic and inhomogeneous shells that, in theory, completely shield an interior structure of arbitrary size from electromagnetic fields without perturbing the external fields. Neither the coordinate transformation-based analytical formulation nor the supporting ray-tracing simulation indicate how material perturbations and full-wave effects might affect the solution. We report fully electromagnetic simulations of the cylindrical version of this cloaking structure using ideal and nonideal
but physically realizable electromagnetic parameters that show that the low-reflection and power-flow bending properties of the electromagnetic cloaking structure are not especially sensitive to modest permittivity and permeability variations. The cloaking performance degrades smoothly with increasing loss, and effective lowreflection shielding can be achieved with a cylindrical shell composed of an eight– (homogeneous) layer approximation of the ideal continuous medium. An imperfect but simpler version of the cloaking material is derived and is shown to reproduce the ray bending of the ideal material in a manner that may be easier to experimentally realize.
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We perform an experimental study of the phase and amplitude of microwaves interacting with and scattered by two-dimensional negative index metamaterials. The measurements are performed in a parallel plate waveguide apparatus at X-band frequencies (8-12 GHz), thus constraining the electromagnetic fields to two dimensions. A detection antenna is fixed to one of the plates, while a second plate with a fixed source antenna or waveguide is translated relative to the first plate. The detection antenna is inserted into, but not protruding below, the stationary plate so that fields internal to the metamaterial samples can be mapped. From the measured mappings of the electric field, the interplay between the microstructure of the metamaterial lattice and the macroscopic averaged response is revealed. For example, the mapped phase fronts within a metamaterial having a negative refractive index are consistent with a macroscopic phase—in accordance with the effective medium predictions—which travels in a direction opposite to the direction of propagation. The field maps are in excellent agreement with finite element numerical simulations performed assuming homogeneous metamaterial structures.
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We explore the electromagnetic characterization of a planar artificial magnetic metamaterial. Because the composite structure is two- rather than three-dimensional, it does not form a medium with assignable bulk properties, such as the electric permittivity and magnetic permeability. However, we find that it is possible to characterize the expected bulk response of a structure composed of repeated layers of metamaterial planes, from a reflectance measurement of a single metamaterial surface made at an oblique angle. We present an analytical theory that relates the reflectance of a single plane to the expected bulk permeability and permeability of the composite, as well as supporting experiments and numerical simulations. Our results show that the recent use of reflectance measurements to characterize planar split ring resonator samples can reveal the presence of circulating currents in a sample—the precursor to artificial magnetism—but are insufficient to provide quantitative results unless the symmetry of the underlying metamaterial elements is carefully specified.
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A medium that exhibits artificial magnetism can be formed by assembling an array of split ring resonators (SRRs)—planar conducting elements that exhibit a resonant response to electromagnetic radiation. The SRR exhibits a large magnetic dipole moment when excited by a magnetic field directed along its axis. However, the SRR also exhibits an electric response that can be quite large depending on the symmetry of the SRR and the orientation of the SRR with respect to the electric component of the field. So, while the SRR medium can be considered as having a predominantly magnetic response for certain orientations with respect to the incident wave, it is generally the case that the SRR exhibits magnetoelectric coupling, and hence a medium of SRRs arranged so as to break mirror symmetry about one of the axes will exhibit bianisotropy. We present here a method of directly calculating the magnetoelectric coupling terms using averages over the fields computed from full-wave finite-element based numerical simulations. We confirm the predicted bianisotropy of a fabricated SRR medium by measuring the cross polarization of a microwave beam transmitted through the sample. We also demonstrate that the magnetoelectric coupling that gives rise to the bianisotropic response is suppressed by symmetrizing the SRR composite structure and provide measurements comparing the cross polarization of the symmetric and asymmetric structures.
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Engineered materials composed of designed inclusions can exhibit exotic and unique electromagnetic properties not inherent in the individual constituent components. These artificially structured composites, known as metamaterials, have the potential to fill critical voids in the electromagnetic spectrum where material response is limited and enable the construction of novel devices. Recently, metamaterials that display negative refractive index – a property not found in any known naturally occurring material – have drawn significant scientific interest, underscoring the remarkable potential of metamaterials to facilitate new developments in electromagnetism.
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Built from “metamaterials” with bizarre, controversial optical properties, a superlens could produce images that include details finer than the wavelength of light that is used.
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Using the freedom of design that metamaterials provide, we show how electromagnetic fields can be redirected at will and propose a design strategy. The conserved fields—electric displacement field D, magnetic induction field B, and Poynting vector S—are all displaced in a consistent manner. A simple illustration is given of the cloaking of a proscribed volume of space to exclude completely all electromagnetic fields. Our work has relevance to exotic lens design and to the cloaking of objects from electromagnetic fields.
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We review both the theoretical electromagnetic response and the spectroscopic measurements of metamaterials. To critically examine published results for metamaterial structures operating in the range from terahertz to optical frequencies, we focus on protocols allowing one to extract the optical constants from experimental observables. We discuss the complexity of this task when applied to metamaterials exhibiting electric, magnetic, and magneto-optical response. The general theory of the electromagnetic response of such systems is presented and methods are described. Finally, we briefly overview possible solutions for implementing metamaterials with tunable resonant behavior. (read more)

Over the past several years, metamaterials have been introduced and rapidly been adopted as a means of achieving unique electromagnetic material response. In metamaterials, artificially structured—often periodically positioned—inclusions replace the atoms and molecules of conventional materials. The scale of these inclusions is smaller than that of the electromagnetic wavelength of interest, so that a homogenized description applies. We present a homogenization technique in which macroscopic fields are determined via averaging the local fields obtained from a full-wave electromagnetic simulation or analytical calculation. The field-averaging method can be applied to homogenize any periodic structure with unit cells having inclusions of arbitrary geometry and material. By analyzing the dispersion diagrams and retrieved parameters found by field averaging, we review the properties of several basic metamaterial structures. (read more)

Metamaterial structures designed to have simultaneously negative permittivity and permeability are known as left-handed materials. Their complexity and our understanding of their properties have advanced rapidly to the point where direct applications are now viable. We present a radial gradient-index lens with an index of refraction ranging from −-2.67 (edge) to -−0.97 (center). Experimentally, we find that the lens can produce field intensities at the focus that are greater than that of the incident plane wave. These results are obtained at 10.3 GHz and in excellent agreement with full-wave simulations. We also demonstrate an advanced fabrication technique using conventional printed circuit board technology which offers significant design, mechanical, and cost advantages over other microwave lens constructions.
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We present simulations of plasmonic transmission lines consisting of planar metal strips embedded in isotropic dielectric media, with a particular emphasis on the long-range surface plasmon polariton (SPP) modes that can be supported in such structures. Our computational method is based on analyzing the eigenfrequencies corresponding to the wave equation subject to a mixture of periodic, electric and magnetic boundary conditions. We demonstrate the accuracy of our approach through comparisons with previously reported simulations based on the semi-analytical method-of-lines.We apply our method to study a variety of aspects of long-range SPPs, including tradeoffs between mode confinement and propagation distance, the modeling of bent waveguides and the effect of disorder and periodicity on the long-ranging modes.
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A lithographically patterned inductive-capacitive resonator is described that has a strong electric response. This resonator can be used to construct metamaterials with desired positive or negative permittivity. Such materials provide an alternative to wire media, and have the benefit of not requiring continuous current paths between unit cells. A planar medium composed of these resonators was simulated, fabricated, and measured in the microwave frequency range.
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A gradient index (GRIN) lens using a negative index of refraction material (NIM) has been designed and tested. The GRIN lens was fabricated using a NIM slab with a variable index of refraction perpendicular to the propagation direction. Ray tracing calculations based on the isotropic Eikonal equation determined the index of refraction gradient required for a given focal length. An electromagnetic code was then used to design the required ring and wire unit cells. Finally, the index of refraction was approximated using ten discrete steps in an effective medium simulation for the GRIN lens that agreed with the experimental measurements.
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None.
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We derive a general expression for the material properties of a compensating bilayer, which is a pair of material layers which transfer the field distribution from one side of the bilayer to the other with resolution limited only by the deviation of the material properties from specified values. One of the layers can be free space, a special case of which is the perfect lens, but the layers need not have equal thickness. Compensating a thick layer of free space with a thin layer creates a focusing device with increased working distance, and employs an anisotropic material. It is also possible to achieve compensation of materials with property tensors that are neither positive nor negative definite. In this case, we refer to such media as indefinite, and we analyse, in detail, bilayers of these media which support coupling of internal propagating waves to incident waves of any transverse wave vector. In this case, we find that the enhanced spatial resolution provided by large transverse wave vectors is far less sensitive to loss than that of the perfect lens.
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We study the frequency dependence of the effective electromagnetic parameters of left-handed and related metamaterials of the split ring resonator and wire type. We show that the reduced translational symmetry speriodic structured inherent to these metamaterials influences their effective electromagnetic response. To anticipate this periodicity, we formulate a periodic effective medium model which enables us to distinguish the resonant behavior of electromagnetic parameters from effects of the periodicity of the structure. We use this model for the analysis of numerical data for the transmission and reflection of periodic arrays of split ring resonators, thin metallic wires, cut wires, as well as the left-handed structures. The present method enables us to identify the origin of the previously observed resonance-antiresonance coupling as well as the occurrence of negative imaginary parts in the effective permittivities and permeabilities of those materials. Our analysis shows that the periodicity of the structure can be neglected only for the wavelength of the electromagnetic wave larger than 30 space periods of the investigated structure.
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We study the surface plasmons (SPs) that exist at the interface between air and a metamaterial constructed of split ring resonators (SRRs). The SRR metamaterial possesses a frequency band in the microwave regime (12.5–14 GHz) over which the permeability is negative. We apply an attenuated total reflection technique in the Otto configuration in which a beam of microwaves is reflected from a higher dielectric (polycarbonate) prism to excite and probe the surface plasmons. The resulting evanescent microwave fields on the transmission side of the prism couple to SPs on the metamaterial and are indicated by a dip in the reflected power. The experimental data are compared with analytic solutions in which the metamaterial slab is approximated as an infinite half space, for which the frequency-dependent permeability sand permittivityd is derived from finiteelement simulations on an SRR structure with the same parameters as those measured.
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None.
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We discuss the validity of standard retrieval methods that assign bulk electromagnetic properties, such as the electric permittivity (epsilon) and the magnetic permeability (mu), from calculations of the scattering (S-) parameters for finite-thickness samples. S-parameter retrieval methods have recently become the principal means of characterizing artificially structured metamaterials, which, by nature, are inherently inhomogeneous. While the unit cell of a metamaterial can be made considerably smaller than the free space wavelength, there remains a significant variation of the phase across the unit cell at operational frequencies in nearly all metamaterial structures reported to date. In this respect, metamaterials do not rigorously satisfy an effective medium limit and are closer conceptually to photonic crystals. Nevertheless, we show here that a modification of the standard S-parameter retrieval procedure yields physically reasonable values for the retrieved electromagnetic parameters, even when there is significant inhomogeneity within the unit cell of the structure. We thus distinguish a metamaterial regime, as opposed to the effective medium or photonic crystal regimes, in which a refractive index can be rigorously established but where the wave impedance can only be approximately defined. We present numerical simulations on typical metamaterial structures to illustrate the modified retrieval algorithm and the impact on the retrieved material parameters. We find that no changes to the standard retrieval procedures are necessary when the inhomogeneous unit cell is symmetric along the propagation axis; however, when the unit cell does not possess this symmetry, a modified procedure—in which a periodic structure is assumed—is required to obtain meaningful electromagnetic material parameters.
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Metamaterials—artificially structured materials with tailored electromagnetic response—can be designed to have properties difficult or impossible to achieve with traditional materials fabrication methods. Here we present a structured metamaterial, based on conducting split ring resonators sSRRsd, which has an effective index of refraction with a constant spatial gradient. We experimentally confirm the gradient by measuring the deflection of a microwave beam by a planar slab of the composite metamaterial over a range of microwave frequencies. The gradient index metamaterial may prove an advantageous alternative approach to the development of gradient index lenses and similar optics, especially at higher frequencies. In particular, the gradient index metamaterial we propose may be suited for terahertz applications, where the magnetic resonant response of SRRs has recently been demonstrated.
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The diffraction of electromagnetic plane waves by a rectangular grating formed by discrete steps in the interface of a homogeneous, isotropic, linear, negative phase-velocity (negative index) material with free space is studied using the semi-analytic Cmethod. When a nonspecular diffracted order is of the propagating type, coupling to that order is significantly larger for a negative index material than for a conventional material. The computed coupling strengths reported here are in agreement with recent experiments, and illustrate the role of evanescent fields localized at the grating interface in producing this enhanced coupling.
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We examine the Seidel aberrations of thin spherical lenses composed of media with refractive index not restricted to be positive. We find that consideration of this expanded parameter space allows for the reduction or elimination of more aberrations than is possible with only positive index media. In particular, we find that spherical lenses possessing real aplanatic focal points are possible only with a negative index. We perform ray tracing, using a custom code that relies only on Maxwell’s equations and conservation of energy, that confirms the results of the aberration calculations.
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We show by numerical simulation as well as by measurements on negative index metamaterial wedge samples, that the unavoidable stepping of the refraction interface—due to the finite unit-cell size inherent to metamaterials—can give rise to a well-defined diffracted beam in addition to the negatively refracted beam. The direction of the diffracted beam is consistent with elementary diffraction theory; however, the coupling to this higher order beam is much larger than would be the case for a positive index material. The results confirm recent theoretical predictions of enhanced diffraction for negative index grating surfaces.
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We have designed, produced, and experimentally characterized 2.7 mm thick composite panels having negative refractive index between 8.4 and 9.2 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.
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Materials engineered to have negative permittivity and permeability demonstrate exotic behavior, from a negative refractive index to subwavelength focusing.
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None.
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Artificial electromagnetic structures have significantly broadened the range of wave propagation phenomena available. In particular, it has been shown that metamaterials can be constructed for which the index-of-refraction is negative over a finite band of frequencies. In this paper, we present the design, fabrication and characterization of a metamaterial that exhibits negative refraction. The metamaterial design we explore is anisotropic in the plane of propagation. Based on our analysis and supporting simulations and measurements, we demonstrate that for the geometry considered, the anisotropic metamaterial has the identical negative refraction properties as would an isotropic negative index metamaterial.
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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.
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Negative-index materials are being used to make lenses with perfect image reconstruction.
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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 21 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.
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We describe an angle resolved microwave spectrometer ~ARMS! based on a planar waveguide scattering chamber, capable of acquiring the angular distribution of TE polarized microwaves scattered from samples centered within the chamber. The spacing between the upper and lower conducting circular plates is 0.4 in. (~1 cm), which, with the associated X-band waveguide adapters, fixes the frequency of operation of the ARMS to be optimally within the X-band frequency range ~8–12 GHz!. Microwave energy can be injected either as an apertured beam via an extended arm connected to the chamber, or via an antenna located in the center of the chamber. Power is detected at a waveguide adapter located on the periphery of the chamber, attached to a rotating arm that has an angular range of 180°. A computer controlled stepper motor attached to the rotating arm facilitates angular scanning with the data acquired at every angle in an automated fashion. The ARMS has excellent reproducibility and signal-to-noise characteristics, making it ideal for characterizing the refraction properties of metamaterial samples, or as a probe of the interaction between antennas and metamaterial substrates.
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We show that magnetic response at terahertz frequencies can be achieved in a planar structure composed of nonmagnetic conductive resonant elements. The effect is realized over a large bandwidth and can be tuned throughout the terahertz frequency regime by scaling the dimensions of the structure. We suggest that artificial magnetic structures, or hybrid structures that combine natural and artificial magnetic materials, can play a key role in terahertz devices.
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We present experimental scattering data at microwave frequencies on a structured metamaterial that exhibits a frequency band where the effective index of refraction (n) is negative. The material consists of a two-dimensional array of repeated unit cells of copper strips and split ring resonators on interlocking strips of standard circuit board material. By measuring the scattering angle of the transmitted beam through a prism fabricated from this material, we determine the effective n, appropriate to Snell’s law. These experiments directly confirm the predictions of Maxwell’s equations that n is given by the negative square root of [the product of the permittivity and the permeability] for the frequencies where both the permittivity and the permeability are negative. Configurations of geometrical optical designs are now possible that could not be realized by positive index materials.
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We present experimental data, numerical simulations, and analytical transfer-matrix calculations for a two-dimensionally isotropic, left-handed metamaterial (LHM) at X-band microwave frequencies. A LHM is one that has a frequency band with simultaneously negative [effective permittivity] and [effective permeability], thereby having real values of index of refraction and wave vectors, and exhibiting extended wave propagation over that band. Our physical demonstration of a two-dimensional isotropic LHM will now permit experiments to verify some of the explicit predictions of reversed electromagnetic-wave properties including negative index of refraction as analyzed by Veselago [Usp. Fiz. Nauk 92, 517 (1964), Sov. Phys. Usp. 10, 509 (1968)].
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The response of a material to electromagnetic radiation can be entirely characterized by the material parameters: the electrical permittivity, and the magnetic permeability. The range of possible values for the material parameters, as dictated by fundamental considerations such as causality or thermodynamics, extends beyond that found in naturally occurring materials. We thus seek to extend the material parameter space by creating electromagnetic metamaterials—ordered composite materials that display electromagnetic properties beyond those found in naturally occurring materials. Recently, we have demonstrated a metamaterial made of a repeated lattice of conducting, nonmagnetic elements that exhibits an effective [permeability] and an effective [permittivity], both of which are simultaneously negative over a band of frequencies. Such a medium has been termed Left-Handed, as the electric field (E), magnetic intensity (H) and propagation vector (k) are related by a left-hand rule. We introduce the reader to the expected properties predicted by Maxwell’s equations for Left-Handed media, and describe our recent numerical and experimentalwork in developing and analyzing this new metamaterial.
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Recently, an electromagnetic metamaterial was fabricated and demonstrated to exhibit a ‘‘left-handed’’ (LH) propagation band at microwave frequencies. A LH metamaterial is one characterized by material constants—the permeability and permittivity—which are simultaneously negative, a situation never observed in naturally occurring materials or composites. While the presence of the propagation band was shown to be an inherent demonstration of left handedness, actual numerical values for the material constants were not obtained. In the present work, using appropriate averages to define the macroscopic fields, we extract quantitative values for the effective permeability and permittivity from finite-difference simulations using three different approaches.
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The real part of the refractive index n(omega) of a nearly transparent and passive medium is usually taken to have only positive values. Through an analysis of a current source radiating into a 1D “left-handed” material (LHM)—where the permittivity and permeability are simultaneously less than zero—we determine the analytic structure of n(omega), demonstrating frequency regions where the sign of Re[n(omega)] must, in fact, be negative. The regime of negative index, made relevant by a recent demonstration of an effective LHM, leads to unusual electromagnetic wave propagation and merits further exploration.
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We demonstrate a composite medium, based on a periodic array of interspaced conducting nonmagnetic split ring resonators and continuous wires, that exhibits a frequency region in the microwave regime with simultaneously negative values of effective permeability and permittivity. This structure forms a “left-handed” medium, for which it has been predicted that such phenomena as the Doppler effect, Cherenkov radiation, and even Snell’s law are inverted. It is now possible through microwave experiments to test for these effects using this new metamaterial.
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