Negative-index metamaterial array configuration, which was constructed of copper split-ring resonators and wires mounted on interlocking sheets of fiberglass circuit board. The total array consists of 3 by 20×20 unit cells with overall dimensions of 10 mm × 100 mm × 100 mm (0.39 in × 3.94 in × 3.94 in).[1][2]
Metamaterials bend waves of all kinds. His metamaterials research is the most similar to that of David R. Smith, with whom he worked on the original split-ring resonators at UC San Diego 15 years ago. But Padilla is mostly focused on terahertz frequencies that lie between microwaves and infrared on the electromagnetic spectrum. Researchers are currently exploring the possibilities associated with an artificial type of matter called metamaterials. Naturally occurring matter exhibits behavior based on the molecules that make it up - the atomic material that composes the finished product determines what properties the product will have. For instance, take the relationship between wood and light.
A metamaterial (from the Greek word μετάmeta, meaning 'beyond' and the Latin word materia, meaning 'matter' or 'material') is a material engineered to have a property that is not found in naturally occurring materials.[3] They are made from assemblies of multiple elements fashioned from composite materials such as metals and plastics. The materials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Metamaterials derive their properties not from the properties of the base materials, but from their newly designed structures. Their precise shape, geometry, size, orientation and arrangement gives them their smart properties capable of manipulating electromagnetic waves: by blocking, absorbing, enhancing, or bending waves, to achieve benefits that go beyond what is possible with conventional materials.
Appropriately designed metamaterials can affect waves of electromagnetic radiation or sound in a manner not observed in bulk materials.[4][5][6] Those that exhibit a negative index of refraction for particular wavelengths have attracted significant research.[7][8][9] These materials are known as negative-index metamaterials.
Potential applications of metamaterials are diverse and include optical filters, medical devices, remote aerospace applications, sensor detection and infrastructure monitoring, smart solar power management, crowd control, radomes, high-frequency battlefield communication and lenses for high-gain antennas, improving ultrasonic sensors, and even shielding structures from earthquakes.[10][11][12][13] Metamaterials offer the potential to create superlenses. Such a lens could allow imaging below the diffraction limit that is the minimum resolution that can be achieved by conventional glass lenses. A form of 'invisibility' was demonstrated using gradient-index materials. Acoustic and seismic metamaterials are also research areas.[10][14]
Metamaterial research is interdisciplinary and involves such fields as electrical engineering, electromagnetics, classical optics, solid state physics, microwave and antenna engineering, optoelectronics, material sciences, nanoscience and semiconductor engineering.[5]
- 2Electromagnetic metamaterials
- 2.2Classification
- 3Other types
- 4Frequency bands
- 5Applications
- 7Institutional networks
History[edit]
Explorations of artificial materials for manipulating electromagnetic waves began at the end of the 19th century. Some of the earliest structures that may be considered metamaterials were studied by Jagadish Chandra Bose, who in 1898 researched substances with chiral properties. Karl Ferdinand Lindman studied wave interaction with metallic helices as artificial chiral media in the early twentieth century.
Winston E. Kock developed materials that had similar characteristics to metamaterials in the late 1940s. In the 1950s and 1960s, artificial dielectrics were studied for lightweight microwave antennas. Microwave radar absorbers were researched in the 1980s and 1990s as applications for artificial chiral media.[5]
Negative-index materials were first described theoretically by Victor Veselago in 1967.[15] He proved that such materials could transmit light. He showed that the phase velocity could be made anti-parallel to the direction of Poynting vector. This is contrary to wave propagation in naturally occurring materials.[9]
John Pendry was the first to identify a practical way to make a left-handed metamaterial, a material in which the right-hand rule is not followed.[15] Such a material allows an electromagnetic wave to convey energy (have a group velocity) against its phase velocity. Pendry's idea was that metallic wires aligned along the direction of a wave could provide negative permittivity (dielectric function ε < 0). Natural materials (such as ferroelectrics) display negative permittivity; the challenge was achieving negative permeability (µ < 0). In 1999 Pendry demonstrated that a split ring (C shape) with its axis placed along the direction of wave propagation could do so. In the same paper, he showed that a periodic array of wires and rings could give rise to a negative refractive index. Pendry also proposed a related negative-permeability design, the Swiss roll.
In 2000, Smith et al. reported the experimental demonstration of functioning electromagnetic metamaterials by horizontally stacking, periodically, split-ring resonators and thin wire structures. A method was provided in 2002 to realize negative-index metamaterials using artificial lumped-element loaded transmission lines in microstrip technology. In 2003, complex (both real and imaginary parts of) negative refractive index[16] and imaging by flat lens[17] using left handed metamaterials were demonstrated. By 2007, experiments that involved negative refractive index had been conducted by many groups.[4][13] At microwave frequencies, the first, imperfect invisibility cloak was realized in 2006.[18][19][20][21][22]
Electromagnetic metamaterials[edit]
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An electromagnetic metamaterial affects electromagnetic waves that impinge on or interact with its structural features, which are smaller than the wavelength. To behave as a homogeneous material accurately described by an effective refractive index, its features must be much smaller than the wavelength.[citation needed]
For microwave radiation, the features are on the order of millimeters. Microwave frequency metamaterials are usually constructed as arrays of electrically conductive elements (such as loops of wire) that have suitable inductive and capacitive characteristics. One microwave metamaterial uses the split-ring resonator.[6][7]
Photonic metamaterials, nanometer scale, manipulate light at optical frequencies. To date, subwavelength structures have shown only a few, questionable, results at visible wavelengths.[6][7]Photonic crystals and frequency-selective surfaces such as diffraction gratings, dielectric mirrors and optical coatings exhibit similarities to subwavelength structured metamaterials. However, these are usually considered distinct from subwavelength structures, as their features are structured for the wavelength at which they function and thus cannot be approximated as a homogeneous material.[citation needed] However, material structures such as photonic crystals are effective in the visible light spectrum. The middle of the visible spectrum has a wavelength of approximately 560 nm (for sunlight). Photonic crystal structures are generally half this size or smaller, that is <280 nm.[citation needed]
Plasmonic metamaterials utilize surface plasmons, which are packets of electrical charge that collectively oscillate at the surfaces of metals at optical frequencies.
Frequency selective surfaces (FSS) can exhibit subwavelength characteristics and are known variously as artificial magnetic conductors (AMC) or High Impedance Surfaces (HIS). FSS display inductive and capacitive characteristics that are directly related to their subwavelength structure.[23]
Negative refractive index[edit]
A comparison of refraction in a left-handed metamaterial to that in a normal material
Almost all materials encountered in optics, such as glass or water, have positive values for both permittivityε and permeabilityµ. However, metals such as silver and gold have negative permittivity at shorter wavelengths. A material such as a surface plasmon that has either (but not both) ε or µ negative is often opaque to electromagnetic radiation. However, anisotropic materials with only negative permittivity can produce negative refraction due to chirality.[citation needed]
Although the optical properties of a transparent material are fully specified by the parameters and , refractive index n is often used in practice, which can be determined from . All known non-metamaterial transparent materials possess positive and . By convention the positive square root is used for n.
However, some engineered metamaterials have and . Because the product is positive, n is real. Under such circumstances, it is necessary to take the negative square root for n.
Video representing negative refraction of light at uniform planar interface.
The foregoing considerations are simplistic for actual materials, which must have complex-valued and . The real parts of both and do not have to be negative for a passive material to display negative refraction.[24][25] Metamaterials with negative n have numerous interesting properties:[5][26]
- Snell's law (n1sinθ1 = n2sinθ2), but as n2 is negative, the rays are refracted on the same side of the normal on entering the material.
- Cherenkov radiation points the other way.[further explanation needed]
- The time-averaged Poynting vector is antiparallel to phase velocity. However, for waves (energy) to propagate, a –µ must be paired with a –ε in order to satisfy the wave number dependence on the material parameters .
Negative index of refraction derives mathematically from the vector triplet E, H and k.[5]
For plane waves propagating in electromagnetic metamaterials, the electric field, magnetic field and wave vector follow a left-hand rule, the reverse of the behavior of conventional optical materials.
Classification[edit]
Electromagnetic metamaterials are divided into different classes, as follows:[4][15][5][27]
Negative index[edit]
In negative-index metamaterials (NIM), both permittivity and permeability are negative, resulting in a negative index of refraction.[15] These are also known as double negative metamaterials or double negative materials (DNG). Other terms for NIMs include 'left-handed media', 'media with a negative refractive index', and 'backward-wave media'.[4]
In optical materials, if both permittivity ε and permeability µ are positive, wave propagation travels in the forward direction. If both ε and µ are negative, a backward wave is produced. If ε and µ have different polarities, waves do not propagate.
Mathematically, quadrant II and quadrant IV have coordinates (0,0) in a coordinate plane where ε is the horizontal axis, and µ is the vertical axis.[5]
To date, only metamaterials exhibit a negative index of refraction.[4][26][28]
Single negative[edit]
Single negative (SNG) metamaterials have either negative relative permittivity (εr) or negative relative permeability (µr), but not both.[15] They act as metamaterials when combined with a different, complementary SNG, jointly acting as a DNG.
Epsilon negative media (ENG) display a negative εr while µr is positive.[4][26][15] Many plasmas exhibit this characteristic. For example, noble metals such as gold or silver are ENG in the infrared and visible spectrums.
Mu-negative media (MNG) display a positive εr and negative µr.[4][26][15] Gyrotropic or gyromagnetic materials exhibit this characteristic. A gyrotropic material is one that has been altered by the presence of a quasistatic magnetic field, enabling a magneto-optic effect.[citation needed] A magneto-optic effect is a phenomenon in which an electromagnetic wave propagates through such a medium. In such a material, left- and right-rotating elliptical polarizations can propagate at different speeds. When light is transmitted through a layer of magneto-optic material, the result is called the Faraday effect: the polarization plane can be rotated, forming a Faraday rotator. The results of such a reflection are known as the magneto-optic Kerr effect (not to be confused with the nonlinearKerr effect). Two gyrotropic materials with reversed rotation directions of the two principal polarizations are called optical isomers.
Joining a slab of ENG material and slab of MNG material resulted in properties such as resonances, anomalous tunneling, transparency and zero reflection. Like negative-index materials, SNGs are innately dispersive, so their εr, µr and refraction index n, are a function of frequency.[26]
Bandgap[edit]
Electromagnetic bandgap metamaterials (EBG or EBM) control light propagation. This is accomplished either with photonic crystals (PC) or left-handed materials (LHM). PCs can prohibit light propagation altogether. Both classes can allow light to propagate in specific, designed directions and both can be designed with bandgaps at desired frequencies.[29][30] The period size of EBGs is an appreciable fraction of the wavelength, creating constructive and destructive interference.
PC are distinguished from sub-wavelength structures, such as tunable metamaterials, because the PC derives its properties from its bandgap characteristics. PCs are sized to match the wavelength of light, versus other metamaterials that expose sub-wavelength structure. Furthermore, PCs function by diffracting light. In contrast, metamaterial does not use diffraction.[31]
PCs have periodic inclusions that inhibit wave propagation due to the inclusions' destructive interference from scattering. The photonic bandgap property of PCs makes them the electromagnetic analog of electronic semi-conductor crystals.[32]
EBGs have the goal of creating high quality, low loss, periodic, dielectric structures. An EBG affects photons in the same way semiconductor materials affect electrons. PCs are the perfect bandgap material, because they allow no light propagation.[33] Each unit of the prescribed periodic structure acts like one atom, albeit of a much larger size.[4][33]
EBGs are designed to prevent the propagation of an allocated bandwidth of frequencies, for certain arrival angles and polarizations. Various geometries and structures have been proposed to fabricate EBG's special properties. In practice it is impossible to build a flawless EBG device.[4][5]
EBGs have been manufactured for frequencies ranging from a few gigahertz (GHz) to a few terahertz (THz), radio, microwave and mid-infrared frequency regions. EBG application developments include a transmission line, woodpiles made of square dielectric bars and several different types of low gain antennas.[4][5]
Double positive medium[edit]
Double positive mediums (DPS) do occur in nature, such as naturally occurring dielectrics. Permittivity and magnetic permeability are both positive and wave propagation is in the forward direction. Artificial materials have been fabricated which combine DPS, ENG and MNG properties.[4][15]
Bi-isotropic and bianisotropic[edit]
Categorizing metamaterials into double or single negative, or double positive, normally assumes that the metamaterial has independent electric and magnetic responses described by ε and µ. However, in many cases, the electric field causes magnetic polarization, while the magnetic field induces electrical polarization, known as magnetoelectric coupling. Such media are denoted as bi-isotropic. Media that exhibit magnetoelectric coupling and that are anisotropic (which is the case for many metamaterial structures[34]), are referred to as bi-anisotropic.[35][36]
Four material parameters are intrinsic to magnetoelectric coupling of bi-isotropic media. They are the electric (E) and magnetic (H) field strengths, and electric (D) and magnetic (B) flux densities. These parameters are ε, µ, κ and χ or permittivity, permeability, strength of chirality, and the Tellegen parameter respectively. In this type of media, material parameters do not vary with changes along a rotated coordinate system of measurements. In this sense they are invariant or scalar.[5]
The intrinsic magnetoelectric parameters, κ and χ, affect the phase of the wave. The effect of the chirality parameter is to split the refractive index. In isotropic media this results in wave propagation only if ε and µ have the same sign. In bi-isotropic media with χ assumed to be zero, and κ a non-zero value, different results appear. Either a backward wave or a forward wave can occur. Alternatively, two forward waves or two backward waves can occur, depending on the strength of the chirality parameter.
In the general case, the constitutive relations for bi-anisotropic materials read where and are the permittivity and the permeability tensors, respectively, whereas and are the two magneto-electric tensors. If the medium is reciprocal, permittivity and permeability are symmetric tensors, and , where is the chiral tensor describing chiral electromagnetic and reciprocal magneto-electric response. The chiral tensor can be expressed as , where is the trace of , I is the identity matrix, N is a symmetric trace-free tensor, and J is an antisymmetric tensor. Such decomposition allows us to classify the reciprocal bianisotropic response and we can identify the following three main classes: (i) chiral media (), (ii) pseudochiral media (), (iii) omega media (). Generally the chiral and/or bianisotropic electromagnetic response is a consequence of 3D geometrical chirality: 3D chiral metamaterials are composed by embedding 3D chiral structures in a host medium and they show chirality-related polarization effects such as optical activity and circular dichroism. The concept of 2D chirality also exists and a planar object is said to be chiral if it cannot be superposed onto its mirror image unless it is lifted from the plane. On the other hand, bianisotropic response can arise from geometrical achiral structures possessing neither 2D nor 3D intrinsic chirality. Plum et al.[37] investigated extrinsic chiral metamaterials where the magneto-electric coupling results from the geometric chirality of the whole structure and the effect is driven by the radiation wave vector contributing to the overall chiral asymmetry (extrinsic electromagnetic chiralilty). Rizza et al.[38] suggested 1D chiral metamaterials where the effective chiral tensor is not vanishing if the system is geometrically one-dimensional chiral (the mirror image of the entire structure cannot be superposed onto it by using translations without rotations).
Chiral[edit]
Chiral metamaterials are constructed from chiral materials in which the effective parameter k is non-zero. This is a potential source of confusion as the metamaterial literature includes two conflicting uses of the terms left- and right-handed. The first refers to one of the two circularly polarized waves that are the propagating modes in chiral media. The second relates to the triplet of electric field, magnetic field and Poynting vector that arise in negative refractive index media, which in most cases are not chiral.
Wave propagation properties in chiral metamaterials demonstrate that negative refraction can be realized in metamaterials with a strong chirality and positive ε and μ.[39][40] This is because the refractive index has distinct values for left and right, given by
It can be seen that a negative index will occur for one polarization if κ > √εrµr. In this case, it is not necessary that either or both εr and µr be negative for backward wave propagation.[5]
FSS based[edit]
Frequency selective surface-based metamaterials block signals in one waveband and pass those at another waveband. They have become an alternative to fixed frequency metamaterials. They allow for optional changes of frequencies in a single medium, rather than the restrictive limitations of a fixed frequency response.[41]
Other types[edit]
Elastic[edit]
These metamaterials use different parameters to achieve a negative index of refraction in materials that are not electromagnetic. Furthermore, 'a new design for elastic metamaterials that can behave either as liquids or solids over a limited frequency range may enable new applications based on the control of acoustic, elastic and seismic waves.'[42] They are also called mechanical metamaterials.[citation needed]
Acoustic[edit]
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Acoustic metamaterials control, direct and manipulate sound in the form of sonic, infrasonic or ultrasonic waves in gases, liquids and solids. As with electromagnetic waves, sonic waves can exhibit negative refraction.[14]
Control of sound waves is mostly accomplished through the bulk modulusβ, mass densityρ and chirality. The bulk modulus and density are analogs of permittivity and permeability in electromagnetic metamaterials. Related to this is the mechanics of sound wave propagation in a lattice structure. Also materials have mass and intrinsic degrees of stiffness. Together, these form a resonant system and the mechanical (sonic) resonance may be excited by appropriate sonic frequencies (for example audible pulses).
Structural[edit]
Structural metamaterials provide properties such as crushability and light weight. Using projection micro-stereolithography, microlattices can be created using forms much like trusses and girders. Materials four orders of magnitude stiffer than conventional aerogel, but with the same density have been created. Such materials can withstand a load of at least 160,000 times their own weight by over-constraining the materials.[43][44]
A ceramic nanotruss metamaterial can be flattened and revert to its original state.[45]
Nonlinear[edit]
Metamaterials may be fabricated that include some form of nonlinear media, whose properties change with the power of the incident wave. Nonlinear media are essential for nonlinear optics. Most optical materials have a relatively weak response, meaning that their properties change by only a small amount for large changes in the intensity of the electromagnetic field. The local electromagnetic fields of the inclusions in nonlinear metamaterials can be much larger than the average value of the field. Besides, remarkable nonlinear effects have been predicted and observed if the metamaterial effective dielectric permittivity is very small (epsilon-near-zero media).[46][47][48] In addition, exotic properties such as a negative refractive index, create opportunities to tailor the phase matching conditions that must be satisfied in any nonlinear optical structure.
Hall metamaterials[edit]
In 2009, Marc Briane and Graeme Milton[49] proved mathematically that one can in principle invert the sign of a 3 materials based composite in 3D made out of only positive or negative sign Hall coefficient materials. Later in 2015 Muamer Kadic et al.[50] showed that a simple perforation of isotropic material can lead to its change of sign of the Hall coefficient. This theoretical claim was finally experimentally demonstrated by Christian Kern et al.[51]
In 2015, it was also demonstrated by Christian Kern et al. that an anisotropic perforation of a single material can lead to a yet more unusual effect namely the parallel Hall effect.[52] This means that the induced electric field inside a conducting media is no longer orthogonal to the current and the magnetic field but is actually parallel to the latest.
Thermo-electric metamaterials[edit]
Frequency bands[edit]
Terahertz[edit]
Terahertz metamaterials interact at terahertz frequencies, usually defined as 0.1 to 10 THz. Terahertz radiation lies at the far end of the infrared band, just after the end of the microwave band. This corresponds to millimeter and submillimeter wavelengths between the 3 mm (EHF band) and 0.03 mm (long-wavelength edge of far-infrared light).
Photonic[edit]
Photonic metamaterial interact with optical frequencies (mid-infrared). The sub-wavelength period distinguishes them from photonic band gap structures.[53][54]
Tunable[edit]
Tunable metamaterials allow arbitrary adjustments to frequency changes in the refractive index. A tunable metamaterial expands beyond the bandwidth limitations in left-handed materials by constructing various types of metamaterials.
Plasmonic[edit]
Plasmonic metamaterials exploit surface plasmons, which are produced from the interaction of light with metal-dielectrics. Under specific conditions, the incident light couples with the surface plasmons to create self-sustaining, propagating electromagnetic waves known as surface plasmon polaritons.
Applications[edit]
Metamaterials are under consideration for many applications.[55] Metamaterial antennas are commercially available.
In 2007, one researcher stated that for metamaterial applications to be realized, energy loss must be reduced, materials must be extended into three-dimensional isotropic materials and production techniques must be industrialized.[56]
Antennas[edit]
Metamaterial antennas are a class of antennas that use metamaterials to improve performance.[13][15][57][58] Demonstrations showed that metamaterials could enhance an antenna's radiated power.[13][59] Materials that can attain negative permeability allow for properties such as small antenna size, high directivity and tunable frequency.[13][15]
Absorber[edit]
A metamaterial absorber manipulates the loss components of metamaterials' permittivity and magnetic permeability, to absorb large amounts of electromagnetic radiation. This is a useful feature for photodetection[60][61] and solar photovoltaic applications.[62] Loss components are also relevant in applications of negative refractive index (photonic metamaterials, antenna systems) or transformation optics (metamaterial cloaking, celestial mechanics), but often are not utilized in these applications.
Superlens[edit]
A superlens is a two or three-dimensional device that uses metamaterials, usually with negative refraction properties, to achieve resolution beyond the diffraction limit (ideally, infinite resolution). Such a behaviour is enabled by the capability of double-negative materials to yield negative phase velocity. The diffraction limit is inherent in conventional optical devices or lenses.[63][64]
Cloaking devices[edit]
Metamaterials are a potential basis for a practical cloaking device. The proof of principle was demonstrated on October 19, 2006. No practical cloaks are publicly known to exist.[65][66][67][68][69][70]
RCS (Radar Cross Section) reducing metamaterials[edit]
Conventionally, the RCS has been reduced either by Radar absorbent material (RAM) or by purpose shaping of the targets such that the scattered energy can be redirected away from the source. While RAMs have narrow frequency band functionality, purpose shaping limits the aerodynamic performance of the target. More recently, metamaterials or metasurfaces are synthesized that can redirect the scattered energy away from the source using either array theory[71][72][73] or generalized Snell's law.[74][75] This has led to aerodynamically favorable shapes for the targets with the reduced RCS.
Seismic protection[edit]
Seismic metamaterials counteract the adverse effects of seismic waves on man-made structures.[10][76][77]
Sound filtering[edit]
Metamaterials textured with nanoscale wrinkles could control sound or light signals, such as changing a material's color or improving ultrasound resolution. Uses include nondestructive material testing, medical diagnostics and sound suppression. The materials can be made through a high-precision, multi-layer deposition process. The thickness of each layer can be controlled within a fraction of a wavelength. The material is then compressed, creating precise wrinkles whose spacing can cause scattering of selected frequencies.[78][79]
Theoretical models[edit]
All materials are made of atoms, which are dipoles. These dipoles modify light velocity by a factor n (the refractive index). In a split ring resonator the ring and wire units act as atomic dipoles: the wire acts as a ferroelectric atom, while the ring acts as an inductorL, while the open section acts as a capacitorC. The ring as a whole acts as an LC circuit. When the electromagnetic field passes through the ring, an induced current is created. The generated field is perpendicular to the light's magnetic field. The magnetic resonance results in a negative permeability; the refraction index is negative as well. (The lens is not truly flat, since the structure's capacitance imposes a slope for the electric induction.)
Several (mathematical) material models frequency response in DNGs. One of these is the Lorentz model, which describes electron motion in terms of a driven-damped, harmonic oscillator. The Debye relaxation model applies when the acceleration component of the Lorentz mathematical model is small compared to the other components of the equation. The Drude model applies when the restoring force component is negligible and the coupling coefficient is generally the plasma frequency. Other component distinctions call for the use of one of these models, depending on its polarity or purpose.[4]
Three-dimensional composites of metal/non-metallic inclusions periodically/randomly embedded in a low permittivity matrix are usually modeled by analytical methods, including mixing formulas and scattering-matrix based methods. The particle is modeled by either an electric dipole parallel to the electric field or a pair of crossed electric and magnetic dipoles parallel to the electric and magnetic fields, respectively, of the applied wave. These dipoles are the leading terms in the multipole series. They are the only existing ones for a homogeneous sphere, whose polarizability can be easily obtained from the Mie scattering coefficients. In general, this procedure is known as the 'point-dipole approximation', which is a good approximation for metamaterials consisting of composites of electrically small spheres. Merits of these methods include low calculation cost and mathematical simplicity.[80][81]
Other first principles techniques for analyzing triply-periodic electromagnetic media may be found in Computing photonic band structure
Institutional networks[edit]
MURI[edit]
The Multidisciplinary University Research Initiative (MURI) encompasses dozens of Universities and a few government organizations. Participating universities include UC Berkeley, UC Los Angeles, UC San Diego, Massachusetts Institute of Technology, and Imperial College in London. The sponsors are Office of Naval Research and the Defense Advanced Research Project Agency.[82]
MURI supports research that intersects more than one traditional science and engineering discipline to accelerate both research and translation to applications. As of 2009, 69 academic institutions were expected to participate in 41 research efforts.[83]
Metamorphose[edit]
The Virtual Institute for Artificial Electromagnetic Materials and Metamaterials 'Metamorphose VI AISBL' is an international association to promote artificial electromagnetic materials and metamaterials. It organizes scientific conferences, supports specialized journals, creates and manages research programs, provides training programs (including PhD and training programs for industrial partners); and technology transfer to European Industry.[84][85]
See also[edit]
- Artificial dielectrics—macroscopic analogues of naturally occurring dielectrics that came into use with the radar microwave technologies developed between the 1940s and 1970s.
- METATOY (Metamaterial for rays)—composed of super-wavelength structures, such as small arrays of prisms and lenses and can operate over a broad band of frequencies
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External links[edit]
- Media related to Metamaterials at Wikimedia Commons
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A tunable metamaterial is a metamaterial with a variable response to an incident electromagnetic wave. This includes remotely controlling how an incident electromagnetic wave (EM wave) interacts with a metamaterial. This means the capability to determine whether the EM wave is transmitted, reflected, or absorbed. In general, the lattice structure of the tunable metamaterial is adjustable in real time, making it possible to reconfigure a metamaterial device during operation. It encompasses developments beyond the bandwidth limitations in left-handed materials by constructing various types of metamaterials. The ongoing research in this domain includes electromagnetic materials that are very meta which mean good and has a band gap metamaterials (EBG), also known as photonic band gap (PBG), and negative refractive index material (NIM).[1][2][3]
- 2Tuning strategies for split ring resonators
- 3Tunable NIMs using ferrite material
- 4Liquid crystal tuning for metamaterials
- 8Frequency selective surface based metamaterials
Overview[edit]
Since natural materials exhibit very weak coupling through the magnetic component of the electromagnetic wave, artificial materials that exhibit a strong magnetic coupling are being researched and fabricated. These artificial materials are known as metamaterials. The first of these were fabricated (in the lab) with an inherent, limited, response to only a narrow frequency band at any given time. Its main purpose was to practically demonstrate metamaterials. The resonant nature of metamaterials results in frequency dispersion and narrow bandwidth operation where the center frequency is fixed by the geometry and dimensions of the rudimentary elements comprising the metamaterial composite. These were followed by demonstrations of metamaterials that were tunable only by changing the geometry and/or position of their components. These have been followed by metamaterials that are tunable in wider frequency ranges along with strategies for varying the frequencies of a single medium (metamaterial). This is in contrast to the fixed frequency metamaterial, which is determined by the imbued parameters during fabrication.[3][4]
Tuning strategies for split ring resonators[edit]
Metamaterial-based devices could come to include filters, modulators, amplifiers, transistors, and resonators, among others. The usefulness of such a device could be extended tremendously if the metamaterial’s response characteristics can be dynamically tuned. Control of the effective electromagnetic parameters of a metamaterial is possible through externally tunable components.
Single element control[edit]
Studies have examined the ability to control the response of individual particles using tunable devices such as varactor diodes, semiconductor materials, and barium strontium titanate (BST) thin films.[5]
For example, H. T. Chen, in 2008, were able to fabricate a repeating split-ring resonator (SRR) cell with semiconductor material aligning the gaps. This initial step in metamaterial research expanded the spectral range of operation for a given, specific, metamaterial device. Also this opened the door for implementing new device concepts. The importance of incorporating the semiconductor material this way is noted because of the higher frequency ranges at which this metamaterial operates. It is suitable at terahertz (THz) and higher frequencies, where the entire metamaterial composite may have more than 104 unit cells, along with bulk-vertical integration of the tuning elements. Strategies employed for tuning at lower frequencies would not be possible because of the number of unit cells involved. The semiconductor material, such as silicon, is controlled by photoexcitation. This in turn controls, or alters, the effective size of the capacitor and tunes the capacitance. The whole structure is not just semiconductor material. This was termed a 'hybrid', because the semiconductor material was fused with dielectric material; a silicon-on-sapphire (SOS) wafer. Wafers were then stacked - fabricating a whole structure.[6] A. Degiron et al., appear to have used a similar strategy in 2007. [note 1]
Multi-element control[edit]
A multielement tunable magnetic medium was reported by Zhao et al. This structure immersed SRRs in liquid crystals, and achieved a 2% tunable range.[note 2]
BST-loaded SRRs comprising tunable metamaterial, encapsulates all of the tunability within the SRR circuit.[5]
In a section below, a research team reported a tunable negative index medium using copper wires and ferrite sheets. The negative permeability behavior appears to be dependent on the location and bandwidth of the ferrimagnetic resonance, a break from wholly non-magnetic materials, which produces a notable negative index band. A coil or permanent magnetic is needed to supply the magnetic field bias for tuning.
Electrical tuning[edit]
Electrical tuning for tunable metamaterials.[6]
Magnetostatic control[edit]
Magnetostatic control for tunable metamaterials.[6]
Optical pumping[edit]
Optical pumping for tunable metamaterials.[6]
Tunable NIMs using ferrite material[edit]
Yttrium iron garnet (YIG) films allow for a continuously tunable negative permeability, which results in a tunable frequency range over the higher frequency side of the ferromagnetic resonance of the YIG. Complementary negative permittivity is achieved using a single periodic array of copper wires. Eight wires were spaced 1 mm apart and a ferromagnetic film of a multi-layered YIG at 400 mm thickness was placed in a K band waveguide. The YIG film was applied to both sides of a gadolinium gallium garnet substrate of 0.5 mm thickness. Ferromagnetic resonance was induced when the external H magnetic field was applied along the X axis.[3]
The external magnetic field was generated with an electromagnet. Pairs of E–H tuners were connected before and after the waveguide containing the NIM composite. The tunability was demonstrated from 18 to 23 GHz. Theoretical analysis, which followed, closely matched the experimental results.[3]
An air gap was built into the structure between the array of copper wires and the YIG. This reduces coupling with the ferrite, YIG material. When negative permeability is achieved across a range of frequencies, the interaction of the ferrite with the wires in close proximity, reduces the net current flow in the wires. This is the same as moving toward positive permittivity. This would be an undesired result as the material would no longer be a NIM. The separation also reduces the effective loss of the dielectric, induced by the interaction of the wire's self-field with permeability. Furthermore, there are two sources of conduction in the copper wire. First, the electric field in a (microwave) waveguide creates a current in the wire. Second, any arbitrary magnetic field created by the ferrite when it moves into a perpendicular configuration induces a current. Additionally, at frequencies where µ is negative, the induced microwave magnetic field is opposite to the field excited in a TE10 mode of propagation in a waveguide. Hence, the induced current is opposite to the current resulting from the electric field in a waveguide.[3]
Metamaterial phase shifter[edit]
In aerospace applications (for example) negative index metamaterials are likely candidates for tunable, compact and lightweight phase shifters. Because the designated metamaterials can handle the appropriate power levels, have strong dispersion characteristics, and are tunable in the microwave range these show potential to be desirable phase shifters.[7]
The YIG negative index metamaterial is a composite which actually utilizes ferrite material. As a metamaterial, the ferrite produces a resonant, (real) magnetic permeabilityμ' that is large enough to be comparable to the conventional ferrite phase shifter. The advantage of using a ferrite NIM material for phase shifter application is that it allows use of a ferrite in the negative magnetic permeability region near the FMR (ferromagnetic resonance frequency) when is relatively high and still maintains low losses. Near the FMR frequency, the magnitude of μ' is larger than that at frequencies away from it. Assuming the loss factor to be about the same for the NIM and the conventional ferrite phase shifter, we would expect a much improved performance using the NIM composite, since the phase shifts would be significantly higher owing to higher differential μ'.[7]
Liquid crystal tuning for metamaterials[edit]
Liquid crystal metamaterial tunable in the near-infrared[edit]
Tuning in the near infrared range is accomplished by adjusting the permittivity of an attached nematic liquid crystal. The liquid crystal material appears to be used as both a substrate and a jacket for a negative index metamaterial. The metamaterial can be tuned from negative index values, to zero index, to positive index values. In addition, negative index values can be increased or decreased by this method.[8][9]
Tunability of wire-grid metamaterial immersed into nematic liquid crystal[edit]
Sub-wavelength metal arrays, essentially another form of metamaterial, usually operate in the microwave and optical frequencies. A liquid crystal is both transparent and anisotropic at those frequencies. In addition, a liquid crystal has the inherent properties to be both intrinsically tunable and provide tuning for the metal arrays. This method of tuning a type of metamaterial can be readily used as electrodes for applying switching voltages.[10]
Tuning NIMs with liquid crystals[edit]
Areas of active research in optical materials are metamaterials that are capable of negative values for index of refraction (NIMs), and metamaterials that are capable of zero index of refraction (ZIMs). Complicated steps required to fabricate these nano-scale metamaterials have led to the desire for fabricated, tunable structures capable of the prescribed spectral ranges or resonances.
The most commonly applied scheme to achieve these effects is electro-optical tuning. Here the change in refractive index is proportional to either the applied electric field, or is proportional to the square modulus of the electric field. These are the Pockels effect and Kerr effect, respectively. However, to achieve these effects electrodes must be built-in during the fabrication process. This introduces problematic complexity into material formation techniques. Another alternative is to employ a nonlinear optical material as one of the constituents of this system, and depend on the optical field intensity to modify the refractive index, or magnetic parameters.[11]
Liquid crystal tuning of silicon-on-ring-resonators[edit]
Ring resonators are optical devices designed to show resonance for specific wavelengths. In silicon-on-insulator layered structures, they can be very small, exhibit a high Q factor and have low losses that make them efficient wavelength-filters. The goal is to achieve a tunable refractive index over a larger bandwidth.[12]
Structural tunability in metamaterials[edit]
A novel approach is proposed for efficient tuning of the transmission characteristics of metamaterials through a continuous adjustment of the lattice structure, and is confirmed experimentally in the microwave range.[13]
Hybrid metamaterial composites[edit]
Metamaterials were originally researched as a passive response material. The passive response was and still is determined by the patterning of the metamaterial elements. In other words, the majority of research has focused on the passive properties of the novel transmission, e.g., the size and shape of the inclusions, the effects of metal film thickness, hole geometry, periodicity, with passive responses such as a negative electric response, negative index or gradient index etc. In addition, the resonant response can be significantly affected by depositing a dielectric layer on metal hole arrays and by doping a semiconductor substrate. The result is significant shifting of the resonance frequency. However, even these last two methods are part of the passive material research.[14]
Electromagnetic metamaterials can be viewed as structured composites with patterned metallic subwavelength inclusions. As mesoscopic physical systems, these are built starting from the unit cell level. These unit cells are designed to yield prescribed electromagnetic properties. A characteristic of this type of metamaterial is that the individual components have a resonant (coupling) response to the electric, magnetic or both components of the electromagnetic radiation of the source. The EM metamaterial as an artificially designed transmission medium, has so far delivered desired responses at frequencies from the microwave through to the near visible.[6]
The introduction of a natural semiconductor material within or as part of each metamaterial cell results in a new design flexibility. The incorporation, application, and location of semiconductor material is strategically planned so as to be strongly coupled at the resonance frequency of the metamaterial elements. The hybrid metamaterial composite is still a passive material. However, the coupling with the semiconductor material then allows for external stimulus and control of the hybrid system as a whole, which produces alterations in the passive metamaterial response. External excitation is produced in the form, for example, photoconductivity, nonlinearity, or gain in the semiconductor material.[6]
Tunable spectral range via electric field control[edit]
Terahertz (THz) metamaterials can show a tunable spectral range, where the magnetic permeability reaches negative values. These values were established both theoretically and experimentally. The demonstrated principle represents a step forward toward a metamaterial with negative refractive index capable of covering continuously a broad range of THz frequencies and opens a path for the active manipulation of millimeter and submillimeter beams.[15]
Frequency selective surface based metamaterials[edit]
Frequency selective surfaces (FSS) has become an alternative to the fixed frequency metamaterial where static geometries and spacings of unit cells determine the frequency response of a given metamaterial. Because arrayed unit cells maintain static positions throughout operation, a new set of geometrical shapes and spacings would have to be embedded in a newly fabricated material for each different radiated frequency and response. Instead, FSS based metamaterials allow for optional changes of frequencies in a single medium (metamaterial) rather than a restriction to a fixed frequency response.[4]
Frequency selective surfaces can be fabricated as planar 2-dimensional periodic arrays of metallic elements with specific geometrical shapes, or can be periodic apertures in a metallic screen. The transmission and reflection coefficients for these surfaces are dependent on the frequency of operation and may also depend on the polarization and the angle of the transmitted electromagnetic wave striking the material or angle of incidence. The versatility of these structures are shown when having frequency bands at which a given FSS is completely opaque (stop-bands) and other bands at which the same surface allows wave transmission.[16]
An example of where this alternative is highly advantageous is in deep space or with a satellite or telescope in orbit. The expense of regular space missions to access a single piece of equipment for tuning and maintenance would be prohibitive. Remote tuning, in this case, is advantageous.[4]
FSS was first developed to control the transmission and reflection characteristics of an incident radiation wave. This has resulted in smaller cell size along with increases in bandwidth and the capability to shift frequencies in real time for artificial materials.[4]
This type of structure can be used to create a metamaterial surface with the intended application of artificial magnetic conductors or applications for boundary conditions. Another application is as stop band device for surface wave propagation along the interface. This is because surface waves are a created as a consequence of an interface between two media having dissimilar refractive indices. Depending on the application of the system that includes the two media, there may be a need to attenuate surface waves or utilize them.[17]
An FSS based metamaterial employs a (miniature) model of equivalent LC circuitry. At low frequencies the physics of the interactions is essentially defined by the LC model analysis and numerical simulation. This is also known as the static LC model. At higher frequencies the static LC concepts become unavailable. This is due to dependence on phasing. When the FSS is engineered for electromagnetic band gap (EBG) characteristics, the FSS is designed to enlarge its stop band properties in relation to dispersive, surface wave (SW) frequencies (microwave and radio frequencies). Furthermore, as an EBG it is designed to reduce its dependence on the propagating direction of the surface wave traveling across the surface (interface).[17]
Artificial magnetic conductors and High impedance surfaces[edit]
A type of FSS based metamaterial has the interchangeable nomenclature Artificial Magnetic Conductor (AMC) or High Impedance Surface (HIS). The HIS, or AMC, is an artificial, metallic, electromagnetic structure. The structure is designed to be selective in supporting surface wave currents, different from conventional metallic conductors. It has applications for microwave circuits and antennas.[18][19][20]
As an antenna ground plane it suppresses the propagation of surface waves, and deployed as an improvement over the flat metal sheet as a ground plane, or reflector. Hence, this strategy tends to upgrade the performance of the selected antenna.[18][19][20]
Strong surface waves of sufficient strength, which propagate on the metal ground plane will reach the edge and propagate into free space. This creates a multi-path interference. In contrast the HIS surface suppresses the propagation of surface waves. Furthermore, control of the radio frequency or microwave radiation pattern is efficiently increased, and mutual coupling between antennas is also reduced.[18][19][20]
When employing conventional ground planes as the experimental control, the HIS surface exhibits a smoother radiation pattern, an increase in the gain of the main lobe, a decrease in undesirable return radiation, and a decrease in mutual coupling.[18]
Description[edit]
An HIS, or AMC, can be described as a type of electromagnetic band gap (EBG) material or a type of synthetic composite that is intentionally structured with a magnetic conductor surface for an allotted, but defined range of frequencies. AMC, or HIS structures often emerge from an engineered periodic dielectric base along with metallization patterns designed for microwave and radio frequencies. The metalization pattern is usually determined by the intended application of the AMC or HIS structure. Furthermore, two inherent notable properties, which cannot be found in natural materials, have led to a significant number of microwave circuit applications.[19][20]
First, AMC or HIS surfaces are designed to have an allotted set of frequencies over which electromagnetic surface waves and currents will not be allowed to propagate. These materials are then both beneficial and practical as antenna ground planes, small flat signal processing filters, or filters as part of waveguide structures. For example, AMC surfaces as antenna ground planes are able to effectively attenuate undesirable wave fluctuations, or undulations, while producing good radiation patterns. This is because the material can suppress surface wave propagation within the prescribed range of forbidden frequencies.
Second, AMC surfaces have very high surface impedance within a specific frequency range, where the tangential magnetic field is small, even with a large electric field along the surface. Therefore, an AMC surface can have a reflection coefficient of +1.[19][20]
In addition, the reflection phase of incident light is part of the AMC and HIS tool box.[note 3] The phase of the reflected electric field has normal incidence the same phase of the electric field impinging at the interface of the reflecting surface. The variation of the reflection phase is continuous between +180◦ to −180◦ relative to the frequency. Zero is crossed at one frequency, where resonance occurs. A notable characteristic is that the useful bandwidth of an AMC is generally defined as +90◦ to −90◦ on either side of the central frequency.[21] Thus, due to this unusual boundary condition, in contrast to the case of a conventional metal ground plane, an AMC surface can function as a new type of ground plane for low-profile wire antennas (wireless communication systems). For example, even though a horizontal wire antenna is extremely close to an AMC surface, the current on the antenna and its image current on the ground plane are in-phase, rather than out-of phase, thereby strengthening the radiation.[20][21]
AMC as an FSS band gap[edit]
Top image - circuit board. The structure consists of a lattice of metal plates, connected to a solid metal sheet by vertical conducting vias. :Bottom image - Looking down on top of the high-impedance surface, showing a triangular lattice of hexagonal metal plates. The configuration creates a capacitive and inductive surface. It can be utilized as band gap material at prescribed frequencies. It is also designed to enhance antenna operation as a novel periodic material.[19]
Frequency selective surfaces (FSS) materials can be utilized as band gap material in the surface wave domain, at microwave and radio frequency wavelengths. Support of surface waves is a given property of metals. These are propagating electromagnetic waves that are bound to the interface between the metal surface and the air. Surface plasmons occur at optical frequencies, but at microwave frequencies, they are the normal currents that occur on any electrical conductor.[17][19] At radio frequencies, the fields associated with surface waves can extend thousands of wavelengths into the surrounding space, and they are often best described as surface currents. They can be modeled from the viewpoint of an effective dielectric constant, or an effective surface impedance.[19]
For example, a flat metal sheet always has low surface impedance. However, by incorporating a special texture on a conducting surface, a specially designed geometry, it is possible to engineer a high surface impedance and alter its electromagnetic-radio-frequency properties. The protrusions are arranged in a two dimensional lattice structure, and can be visualized as thumbtacks protruding from the surface.[19]
Because the protrusions are fractionally smaller than the operating wavelength, the structure can be described using an effective medium model, and the electromagnetic properties can be described using lumped-circuit elements (capacitors and inductors). They behave as a network of parallel resonant LC circuits, which act as a two-dimensional electric filter to block the flow of currents along the sheet.[19]
This structure can then serve as an artificial magnetic conductor (AMC), because of its high surface impedance within a certain frequency range. In addition, as an artificial magnetic conductor it has a forbidden frequency band, over which surface waves and currents cannot propagate. Therefore, AMC surfaces have good radiation patterns without unwanted ripples based on suppressing the surface wave propagation within the band gap frequency range.[20]
The surface impedance is derived from the ratio of the electric field at the surface to the magnetic field at the surface, which extends far into the metal beyond the skin depth. When a texture is applied to the metal surface, the surface impedance is altered, and its surface wave properties are changed. At low frequencies, it is inductive, and supports transverse-magnetic (TM) waves. At high frequencies, it is capacitive, and supports transverse electric (TE) waves. Near the LCresonance frequency, the surface impedance is very high. In this region, waves are not bound to the surface. Instead, they radiate into the surrounding space.[19][23]
A high-impedance surface was fabricated as a printed circuit board. The structure consists of a triangular lattice of hexagonal metal plates, connected to a solid metal sheet by vertical conducting vias.[19]
Uniplanar compact photonic-bandgap[edit]
The uniplanar compact photonic-bandgap (UC-PBG) is proposed, simulated, and then constructed in the lab to overcome elucidated limitations of planar circuit technology. Like photonic bandgap structures it is etched into the ground plane of the microstrip line. The geometry is square metal pads. Each metal pad has four connecting branches forming a distributed LC circuit.[24][25]
See also[edit]
- Academic journals
- Metamaterials books
Notes[edit]
- ^A. Degiron, J. J. Mock, and D. R. Smith, Opt. Express 15, 3 (2007).
- ^Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, Appl. Phys. Lett. 90, 011112 (2007)
- ^When light goes from one medium (n-1) to another (n-2), the reflected light at that interface undergoes a phase change as follows: if n-1 < n-2 there is a 180 degree phase change. However, if n-1 > n-2: no phase change.
References[edit]
- ^Lapine, Mikhail (2009). 'Tunable metamaterials: the key step to practical application'(Online web page). SPIE Newsroom. doi:10.1117/2.1200910.1827.
- ^'Tunable metamaterials imply the ability to continuously change their properties through an external influence or signal with the intrinsic mechanism of tunability.'
- Lapine, Mikhail; Powell, David; Gorkunov, Maxim; Shadrivov, Ilya; Marqués, Ricardo; Kivshar, Yuri (2009). 'Structural tunability in metamaterials'(PDF). Applied Physics Letters. 95 (8): 084105. arXiv:0907.2303. Bibcode:2009ApPhL..95h4105L. doi:10.1063/1.3211920. Free PDF download.
- ^ abcdeHe, Yongxue; Peng He; Soack Dae Yoon; P.V. Parimic; F.J. Rachford; V.G. Harris; C. Vittoria (June 2007). 'Tunable NIM using yttrium iron garnet'(PDF). Journal of Magnetism and Magnetic Materials. 313 (1): 187–191. Bibcode:2007JMMM..313..187H. doi:10.1016/j.jmmm.2006.12.031.
- ^ abcdCapolino, Filippo (October 2009). Theory and Phenomena of Metamaterials. Taylor & Francis. pp. 32–1, Chapter 32. ISBN978-1-4200-5425-5.
- ^ abHand, Thomas H.; Cummer, Steven A. (2008-03-15). 'Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings'. Journal of Applied Physics. 103 (6): 066105–066105–3. Bibcode:2008JAP...103f6105H. doi:10.1063/1.2898575. ISSN0021-8979.
- ^ abcdefChen, Hou-Tong; O'Hara, John F.; Azad, Abul K.; Taylor, Antoinette J.; Averitt, Richard D.; Shrekenhamer, David B.; Padilla, Willie J. (May 2008). 'Experimental demonstration of frequency-agile terahertz metamaterials'(PDF). Nature Photonics. 2 (5): 295. CiteSeerX10.1.1.738.111. doi:10.1038/nphoton.2008.52. Retrieved 2009-11-01.
- ^ abHe, P.; P.V. Parimi; Y. He; V.G. Harris; C. Vittoria (2007). 'Tunable negative refractive index metamaterial phase shifter'(PDF). Electronics Letters. 43 (25): 1440. doi:10.1049/el:20072451. Retrieved 2009-09-28.
- ^Werner, Douglas H.; Do-Hoon Kwon; Iam-Choon Khoo; Alexander V. Kildishev; Vladimir M. Shalaev (2007-03-19). 'Liquid crystal clad near-infrared metamaterials with tunable negative-zero-positive refractive indices'(PDF). Optics Express. 15 (6): 3342–3347. Bibcode:2007OExpr..15.3342W. doi:10.1364/OE.15.003342. PMID19532575.
- ^Chettiar, Uday K.; Kildishev, Alexander V.; Klar, Thomas A.; Shalaev, Vladimir M. (2006). 'Negative index metamaterial combining magnetic resonators with metal films'(PDF). Optics Express. 14 (17): 7872–7. arXiv:physics/0606129. Bibcode:2006OExpr..14.7872C. doi:10.1364/OE.14.007872. PMID19529154.
- ^Gorkunov, M. V.; M. A. Osipov (2008-02-05). 'Tunability of wire-grid metamaterial immersed into nematic liquid crystal'. J. Appl. Phys Communications. 103 (3): 036101–036101–3. arXiv:0708.4286. Bibcode:2008JAP...103c6101G. doi:10.1063/1.2837099.
- ^Wang, Xiande; et al. (2007). 'Tunable optical negative-index metamaterials employing anisotropic liquid crystals'(PDF). Applied Physics Letters. 91 (14): 143122. Bibcode:2007ApPhL..91n3122W. doi:10.1063/1.2795345. Retrieved 2009-10-02.
- ^Wout, De Cort; Beeckman, Jeroen; James, Richard; Fernández, F. Anibal; Baets, Roel; Neyts, Kristiaan; et al. (2009-06-29). 'Tuning of silicon-on-insulator ring resonators with liquid crystal cladding using the longitudinal field component'(PDF). Optics Letters. 34 (13): 2054–6. Bibcode:2009OptL...34.2054D. CiteSeerX10.1.1.701.4072. doi:10.1364/OL.34.002054. PMID19571997. Retrieved 2009-10-11.
- ^Lapine, Mikhail; Powell, David; Gorkunov, Maxim; Shadrivov, Ilya; Marqués, Ricardo; Kivshar, Yuri; et al. (2009-08-27). 'Structural tunability in metamaterials'. Appl. Phys. Lett. 95 (8): 084105. arXiv:0907.2303. Bibcode:2009ApPhL..95h4105L. doi:10.1063/1.3211920.
- ^Chen, Hou-Tong; Lu, Hong; Azad, Abul K.; Averitt, Richard D.; Gossard, Arthur C.; Trugman, Stuart A.; O'Hara, John F.; Taylor, Antoinette J. (2008-05-12). 'Electronic control of extraordinary terahertz transmission through subwavelength metal hole arrays'. Optics Express. 16 (11): 7641–7648. arXiv:0804.2942. Bibcode:2008OExpr..16.7641C. doi:10.1364/OE.16.007641. PMID18545471.
- ^Němec, H.; Kužel, P.; Kadlec, F.; Kadlec, C.; Yahiaoui, R.; Mounaix, P.; et al. (2009-06-24). 'Tunable terahertz metamaterials with negative permeability'. Physical Review B. 79 (24): 241108(R)(2009). Bibcode:2009PhRvB..79x1108N. doi:10.1103/PhysRevB.79.241108.
- ^Alù, Andrea; Nader Engheta (2005). 'Evanescent Growth and Tunneling Through Stacks of Frequency-Selective Surfaces'. IEEE Antennas and Wireless Propagation Letters. 4 (1): 417–420. arXiv:cond-mat/0408384. Bibcode:2005IAWPL...4..417A. doi:10.1109/LAWP.2005.859381.
- ^ abcNader, Engheta; Richard W. Ziolkowski (June 2006). Metamaterials: Physics and Engineering Explorations. Wiley & Sons. pp. 351 Chap. 13. ISBN978-0-471-76102-0.
- ^ abcdFriedrich, Nancy (May 2007). 'High-Impedance Electromagnetic Surface improves antenna performance'. Microwaves & RF magazine. pp. 62 (1 page). Retrieved 2010-08-23. See: 'Application of High Impedance Electromagnetic Surface to Archimedean Planner Spiral Antenna,' Microwave and Optical Technology Letters, January 2007, p. 129.
- ^ abcdefghijklSievenpiper, D.; Zhang, Lijun; Broas, R. F. J.; Alexopolous, N. G.; Yablonovitch, E. (1999). 'High-impedance electromagnetic surfaces with a forbidden frequency band'. IEEE Transactions on Microwave Theory and Techniques. 47 (11): 2059–2074. Bibcode:1999ITMTT..47.2059S. doi:10.1109/22.798001. ISSN0018-9480.
- ^ abcdefgSohn, J. R.; Kim, Ki Young; Tae, Heung-Sik; Lee, H. J.; et al. (2006). 'Comparative study on various artificial magnetic conductors for low-profile antenna'(PDF). Progress in Electromagnetics Research. 61: 27–37. doi:10.2528/PIER06011701. Archived from the original(PDF) on September 6, 2006. Retrieved 2009-11-13.
- ^ abCosta, F.; Genovesi, S.; Monorchio, A. (2009). 'On the Bandwidth of High-Impedance Frequency Selective Surfaces'. IEEE Antennas and Wireless Propagation Letters. 8: 1341–1344. arXiv:1001.0523. Bibcode:2009IAWPL...8.1341C. doi:10.1109/LAWP.2009.2038346. Free PDF download.
- ^McVay, J.; Engheta, N.; Hoorfar, A. (2004). 'High impedance metamaterial surfaces using Hilbert-curve inclusions'(PDF). IEEE Microwave and Wireless Components Letters. 14 (3): 130–132. doi:10.1109/LMWC.2003.822571. Archived from the original(PDF) on 2012-03-24. Free PDF download.
- ^Sievenpiper, D.; Zhang, L.; Yablonovitch, E. (1999). High-impedance electromagnetic ground planes. 1999 IEEE MTT-S International Microwave Symposium Digest (Cat. No.99CH36282). 4. pp. 1529–1532. doi:10.1109/MWSYM.1999.780247. ISBN978-0-7803-5135-6.
- ^Fei-Ran Yang; Kuang-Ping Ma; Yongxi Qian; Itoh, T. (1999). 'A uniplanar compact photonic-bandgap (UC-PBG) structure and its applications for microwave circuit'(PDF). IEEE Transactions on Microwave Theory and Techniques. 47 (8): 1509. Bibcode:1999ITMTT..47.1509Y. doi:10.1109/22.780402. Archived from the original(PDF) on March 24, 2012.
- ^Yongxi Qian; Itoh, T. (1999). 'Microwave applications of photonic band-gap (PBG) structures'(PDF). 1999 Asia Pacific Microwave Conference. APMC'99. Microwaves Enter the 21st Century. Conference Proceedings (Cat. No.99TH8473). 2. pp. 315–318. doi:10.1109/APMC.1999.829858. ISBN978-0-7803-5761-7. Archived from the original(PDF) on 2012-10-08.
External links[edit]
- MURI project:Tunable, reconfigurable, optical NIMs with low losses
- Ph.D. dissertation - Dan. Sievenpiper, “High-impedance electromagnetic surfaces,” Dept. Elect. Eng., Univ. California at Los Angeles, Los Angeles, CA, 1999
- Modulating and tuning the response of metamaterials at the unit cell level Optics Express Vol. 15, Iss. 3, pp. 1115–1127 (2007)
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