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Negative index metamaterials (NIMs) are artificial structures where the refractive index has a negative value over some frequency range[1]. This does not occur in any known natural materials, and thus is only achievable with engineered structures known as metamaterials. Metamaterial broadly refers to any synthetic material with unusual refractive properties, among other descriptions.
Metamaterials which exhibit a negative value for the refractive index (NIM) are often referred to by any of several names and terminologies: "left-handed media (LHM), backward wave media (BW media), media with negative refractive index, and double negative (DNG) metamaterials.[2]
Theoretical articles were published in 1996 and 1999 which showed that artificially fabricated materials could be constructed to purposely exhibit an effective permittivity and magnetic permeability, respectively. These papers, along with Veselago's 1967 theoretical analysis of the properties of negative index materials, provided the background to fabricate, for the first time, a metamaterial with simultaneous effective permittivity and magnetic permeability.[3][4](See below).
Essentially, a metamaterial developed to exhibit negative index behavior is typically formed from individual components. Each component responds independently to a radiated electromagnetic wave as it travels through the material. Each component has its own response to the electric and magnetic fields of the radiated source. Since these components are smaller than the radiated wavelength it is understood that a macroscopic view includes an effective value for both permittivity and permeability.[3]
In the year 2000 a team of UCSD researchers produced a new class of composite materials which exhibited unusual physical properties that were never before produced in nature. These materials obey the laws of physics, but behave differently from normal materials. In essence these negative index metamaterials were noted for having the ability to reverse many of the physical properties that govern the behavior of ordinary optical materials. One of those unusual properties is the capability to reverse, for the first time, the Snell's law of refraction. Until this year 2000 demonstration by the UCSD team, the material was unavailable. Advances during the 1990s in fabrication and computation capabilities allowed these first metamaterials to be constructed. Thus, testing the "new" metamaterial began for the effects described by Victor Veselago 30 years earlier, but only at first in the microwave frequency domain, and reversal of group velocity was explicitly announced in the related published paper (see ref # [5])....[3][4][6]
To date (March 2010) these materials have only been demonstrated at frequencies below the visible spectrum. In addition, NIMs are fabricated from opaque materials, and usually made of non-magnetic constituents. However, as an illustration – if these materials could be demonstrated at visible frequencies, and a flashlight is shined on a NIM slab, the material should focus the light at a point on the other side. This is not possible with a sheet of ordinary opaque material.[1][5][6]
When first demonstrated this composite material (NIM) was limited to transmitting microwave radiation at frequencies of 4 to 7 gigahertz. This is approximated to be the range of operating frequencies between household microwave ovens(3.3 GHz) and military radars (10 GHz). At demonstrated frequencies, pulses of electromagnetic radiation moving through the material in one direction are composed of constituent waves moving in the opposite direction.[5][6][7]
The metamaterial was constructed as a periodic array of copper conducting elements. The design was such that the cells, and the lattice spacing between the cells, were much smaller than the radiated electromagnetic wavelength. Hence, it behaves as an effective medium. The material has become notable because its range of (effective) permittivity εeff and permeability μeff values have exceeded those found in any ordinary material. Furthermore, the negative effective permeability evinced by this medium was and is the particularly notable characteristic because it has not been found in ordinary materials. In addition, the negative values for the magnetic component is directly related to its left-handed nomenclature and properties (discussed in a section below). The split-ring resonator (SRR), based on the prior 1999 theoretical article, is the tool employed to achieve negative permeability. This first composite metamaterial is then composed of split-ring resonators and electrical conducting posts.[5]
With antiferromagnets and certain types of insulating ferromagnets, effective negative magnetic permeability is achievable when polariton resonance exists. However, when negative electric permittivity occurs at the same time, negative magnetic permeability with low losses will not occur. The artificially fabricated split-ring resonator is a design that shows promise for solving this problem, e.g. dampen such high losses. It is possible to infer, from this first introduction of the metamaterial, that the losses incurred were smaller than antiferromagnetic or ferromagnetic materials.[5]
Negative permittivity εeff < 0 had already been discovered and realized in metals for frequencies all the way up to the plasma frequency, before the first metamaterial. There are two requirements to achieve a negative value for refraction. First, is to fabricate a material which can produce negative permeability μeff < 0. Second, negative values for both permittivity and permeability must occur simultaneously over a common range of frequencies.[1][3]
Therefore, for the first metamaterial, the nuts and bolts are one split-ring resonator electromagnetically combined with one (electric) conducting post. These are designed to resonate at designated frequencies to achieve the desired values. Looking at the make-up of the split ring, the associated magnetic field pattern from the SRR is dipolar. This dipolar behavior is notable because this means it mimics nature's atom, but on a much larger scale, such as in this case at 2.5 millimeters. Atoms exist on the scale of picometers.
The splits in the rings create a dynamic where the SRR unit cell can be made resonant at radiated wavelengths much larger than the diameter of the rings. If the rings were closed, a half wavelength boundary would be electromagnetically imposed as a requirement for resonance.[5]
The split in the second ring is oriented opposite the split in the first ring. It is there to generate a large capacitance, which occurs in the small gap. This capacitance substantially decreases the resonant frequency while concentrating the electric field. The individual SRR depicted on the right had a resonant frequency of 4.845 GHz, and the resonance curve, inset in the graph, is also shown. The radiative losses from absorption and reflection are noted to be small, because the unit dimensions are much smaller than the free space, radiated wavelength.[5]
When these units or cells, are combined into a periodic arrangement the magnetic coupling between the resonators is strengthened, and a strong magnetic coupling occurs. Properties unique in comparison to ordinary or conventional materials begin to emerge. For one thing, this periodic strong coupling creates a material which now has an effective magnetic permeability μeff in response to the radiated-incident magnetic field.[5]
Graphing the general dispersion curve, a region of propagation occurs from zero up to a lower band edge, followed by a gap, and then an upper passband. The presence of a 400 MHz gap between 4.2 GHz and 4.6 GHz implies a band of frequencies where μeff < 0 occurs.
Furthermore, when wires are added symmetrically between the split rings, a passband occurs within the previously forbidden band of the split ring dispersion curves. That this passband occurs within a previously forbidden region indicates that the negative ´εeff for this region has combined with the negative μeff to allow propagation. This fit with theoretical predictions. Mathematically, the dispersion relation leads to a band with negative group velocity everywhere, and a bandwidth that is independent of the plasma frequency, within the stated conditions.[5]
Mathematical modeling and experiment have both shown that periodically arrayed conducting elements (non-magnetic by nature) respond predominatly to the magnetic component of incident electromagnetic fields. The result is an effective medium and negative μeff over a band of frequencies. The permeability was verified to be the region of the forbidden band, where the gap in propagation occurred - from a finite section of material. This was combined with a negative permittivity material, εeff < 0, to form a “left-handed” medium, which formed a propagation band with negative group velocity where previously there was only attenuation. This validated predictions. In addition, a later work determined that this first metamaterial had a range of frequencies over which the refractive index was predicted to be negative for one direction of propagation (see ref # [1]). Other predicted electrodynamic effects were to be investigated in other research.[5]
From the conclusions in the above section a left-handed material (LHM) can be defined. It is a material which exhibits simultaneous negative values for permittivity, ε, and permeability, μ, in an overlapping frequency region. Since the values are derived from the effects of the composite medium system as a whole, these are defined as effective permittivity, εeff, and effective permeability, μeff. Real values are then derived to denote the value of negative index of refraction, and wave vectors. This means that in practice losses will occur for a given medium used to transmit electromagnetic radiation such as microwave, or infrared frequencies, or visible light - for example. In this instance, real values describe either the amplitude or the intensity of a transmitted wave relative to an incident wave, while ignoring the negligible loss values.[5][8]
In sections above, the first fabricated metamaterial was constructed with resonating elements, which exhibited one direction of incidence and polarization. In other words, this structure exhibited left-handed propagation in one dimension. This was discussed in relation to Veselago's seminal work 33 years earlier (1967). He predicted that intrinsic to a material which manifests negative values of effective permittivity and permeability, are several types of reversed physics phonomena. Hence, there was then a critical need for a higher dimensional LHMs to confirm Veselago's theory, as expected. The confirmation would include reversal of Snell's law (index of refraction), along with other reversed phenomena.
In the beginning of 2001 the exsitence of a higher dimensional structure was reported. It was two dimensional and demonstrated by both experiment and numerical confirmation. It was an LHM, a composite constructed of wire strips mounted behind the split-ring resonators (SRRs) in a periodic configuration. It was created for the express purpose of being suitable for further experiments to produce the Veselago predicted effects.[8]
Besides reversed values for index of refraction, Veselago predicted the occurrence of reversed Cherenkov radiation (also known simply as CR) in a left-handed medium. In 1934 Pavel Cherenkov discovered a coherent radiation (laser) that occurs when certain types of media are bombarded by fast moving electron beams. In 1937 a theory built around CR stated that when charged particles, such as electrons, travel through a medium at speeds faster than the speed of light only then will CR radiate. As the CR occurs, electromagnetic radiation is emitted in a cone shape, fanning out in the forward direction.
CR and the 1937 theory has led to a large array of applications in high energy physics. A notable application are the Cherenkov counters. These are used to determine various properties of a charged particle such as its velocity, charge, direction of motion, and energy. These properties are important in the identification of different particles. For example, the counters were applied in the discovery of the anti-proton and the J particle. Six large Chereknov counters were used in the discovery of the J particle.
It has been difficult to experimentally prove the reversed Cherenkov radiation.[9][10]
Theoretical work, along with numerical simulations, began early in the decade of the new millennium on the capabilities of the DNG slab for subwavelength focusing. The research began with Pendry's proposed "Perfect lens". Several research investigations that followed Pendry's concluded that the "Perfect lens" was possible in theory but not practical. One direction in subwavelegnth focusing proceeded with the use of negative index metamaterials, but based on the ehancements for imaging with surface plasmons. In another direction researchers explored paraxial approximations of DNG slabs.[2]
In a slab of conventional material, with an ordinary refractive index – a right-handed material (RHM) – the wave front is transmitted away from the source. In a NIM the wavefront travels toward the source. However, the magnitude and direction of the flow of energy essentially remains the same in both the ordinary material and the NIM. Since, the flow of energy remains the same in both materials (media) the impedance of the NIM matches the RHM. Hence, the sign of the intrinsic impedance is still positive in a NIM.[11][12]
Light incident on a left-handed material, or NIM, will bend to the same side as the incident beam, and for Snell’s law to hold, the refraction angle should be negative. In a passive metamaterial medium this determines a negative real and imaginary part of the refractive index.[2][11][12]
In 1968 Victor Veselago's paper showed that the opposite directions of EM plane waves and the flow of energy was derived from the individual Maxwell curl equations. In ordinary optical materials, the curl equation for the electric field show a "right hand rule" for the directions of the electric field E, the magnetic induction B, and wave propagation, which goes in the direction of wave vector k. However, the direction of energy flow formed by E × H is right-handed only when permeability is greater than zero. This means that when permeability is less than zero, e.g. negative, wave propagation is reversed (determined by k), and contrary to the direction of energy flow. Furthermore, the relations of vectors E, H, and k form a "left-handed" system – and it was Veselago who coined the term "left-handed" (LH) material, which is in wide use today (2010). He contended that an LH material has a negative refractive index and relied on the steady-state solutions of Maxwell's equations as a center for his argument.[13]
After a 30 year void, when LH materials were finally demonstrated, it could be said that that the designation of negative refractive index is unique to LH systems; even when compared to photonic crystals. Photonic crystals, like many other known systems, can exhibit unusual propagation behavior such as reversal of phase and group velocities. But, negative refraction does not occur in these systems, and not yet realistically in Photonic crystals.[13][14]
In 2001, a team of researchers constructed a prism composed of metamaterials (negative index metamaterials) to experimentally test for negative refractive index.[1][15][16][17][18][19][20]
According to Snell's law, when refraction of light is measured or observed for ordinary materials surrounded by air, the value is always greater than one, n > 1. A refracted ray entering a material from air will be bent towards, but never end up on the same side as the normal. In addition, the science and practice of optical lensing and imaging is based on the knowledge that any material with a refractive index different from its environment will alter the direction of incoming rays which do not arrive in a straight line in relation to the interface (of the material surface and air). Also, lenses have been designed focus and steer the various spectra of light (EM radiation) in frequency ranges from radio to the visible spectra. Furthermore, all known natural occurring materials demonstrate refractive indices that are positive. However, a theoretical work in 1967 showed that a refractive index with negative values is possible and that this does not violate the laws of physics. As discussed previously (above), the first metamaterial had a range of frequencies over which the refractive index was predicted to be negative for one direction of propagation were reported in May of the year 2000.[1][17][21]
The first fabricated metamaterial is used as a basis for a U.S. patent, number 6791432. The nomenclature for this patent is "Left handed composite media" and David Smith, Sheldon Schultz, Norman Kroll, Richard A. Shelby are listed as the inventors. The paper, eventually published in Physical Review Letters (Vol 84 p. 8184 2000), was one of the works cited for this invention.
The invention achieves simulataneous negative permittivity and permeability over a common band of frequencies. The material can integrate media which is already composite or continuous, but which will produce negative permittivity and permeability within the same spectrum of frequencies. Different types of continuous or composite may be deemed appropriate when combined for the desired effect. However, the inclusion of a periodic array of conducting elements is preferred. The array scatters electromagnetic radiation at wavelengths longer than the size of the element and lattice spacing. The array is then viewed as an effective medium.[22]
The history of metamaterials, dates to the 1940s in that some notable pioneering researchers, W. E. Kock and Sergei Schelkunoff proposed periodic artificial structures. Schelkunoff achieved notability for contributions to Antenna theory and electromagnetic wave propagation.
W. E. Kock proposed microwave lense for antenna systems. In addition, he conducted analytical studies regarding the response of customized metallic particles to a quasi-static electromagnetic radiation. As with the current large group of researchers, discovering the behavior of metamaterials, Kock discovered behaviors in artificial materials that parallel metamaterials.
He employed particles, which would be of varying geometric shape; spheres, discs, ellipsoids and prolate or oblate spheroids, and would be either isolated or set in a repeating pattern as part of an array configuration. Metamaterial researchers avail themeselves to this same technique to create a metamaterial, resulting in, among other things, a dielectric behavior.
He was able to determine that such particles behave as a dielectric medium. Metamaterials are a type of dielectric medium. Furthermore, the permittivity ε and permeability μ of these particles can be purposely tuned, but not independently. With metamaterials, local values for both ε and μ are designed as part of the fabrication process, or analytically designed in theoretical studies. However, these inclusions are independently tuned for metmaterials.
He was able to see that any value for ε and μ, arbitrarily large or small, can be achieved, and that this included the possibility of negative values for these paramters. This is one of the notable characteristics of modern metamaterials. Also, paralleling metamaterials, the optical properties of the medium depended solely on the particles’ geometrical set up, rather than on their own intrinsic behavior. His work also anticipated the split-ring resonator, a fabricated periodic structure that is a common work horse for metamaterials.
A noteworthy path is one that Kock did not take. He did not investigate simultaneous occureance of negative values of ε and μ, as was one of the first achievements defining modern metamaterials. This was because research in artificial materials was oriented toward other goals, such creating plasma media at RF or microwave frequencies related to the overarching needs of NASA and the space program at the time.[23][24][25][26]
Propagation of a Gaussian Light Pulse through an Anomalous Dispersion Medium.[27][28] However the speed of transmitting information is always limited to c.[27][29]
The research in the field of Metamaterials has diffused out into the American government science research departments, including the US Naval Air Systems Command, US Air Force, and US Army. Many scientific institutions are involved including:
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