A metamaterial (from the Ancient Greek word μετά meta, meaning "beyond" or "after", and the Latin word materia, meaning "matter" or "material") is a type of material engineered to have a property, typically rarely observed in naturally occurring materials, that is derived not from the properties of the base materials but from their newly designed structures. Metamaterials are usually fashioned from multiple materials, such as metals and plastics, and are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Their precise shape, geometry, dimensions, orientation, and arrangement give them their "smart" properties of manipulating Electromagnetism, acoustic, or even seismic 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. Those that exhibit a negative index of refraction for particular wavelengths have been the focus of a large amount of research. These materials are known as negative-index metamaterials.
Potential applications of metamaterials are diverse and include sports equipment, , , remote aerospace applications, sensor detection and infrastructure monitoring, smart solar power management, lasers, crowd control, , Battlespace and lenses for high-gain antennas, improving Level sensor, and even shielding structures from earthquakes.
Metamaterial research is interdisciplinary and involves such fields as electrical engineering, Electromagnetism, classical optics, solid state physics, microwave and antenna engineering, optoelectronics, , nanoscience and semiconductor engineering. Recent developments also show promise for metamaterials in optical computing, with metamaterial-based systems theoretically being able to perform certain tasks more efficiently than conventional computing.
In the late 1940s, Winston E. Kock from AT&T Bell Laboratories developed materials that had similar characteristics to metamaterials. In the 1950s and 1960s, artificial were studied for lightweight microwave antennas. Microwave radar absorbers were researched in the 1980s and 1990s as applications for artificial chiral media.Bowers J. A.; Hyde R. A. et al. "Evanescent electromagnetic wave conversion lenses I, II, III" US Patent and Trademark Office, Grant US-9081202-B2, 14 juli 2015,
Negative-index materials were first described theoretically by Victor Veselago in 1967. 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.
In 1995, John M. Guerra fabricated a sub-wavelength transparent grating (later called a photonic metamaterial) having 50 nm lines and spaces, and then coupled it with a standard oil immersion microscope objective (the combination later called a super-lens) to resolve a grating in a silicon wafer also having 50 nm lines and spaces. This super-resolved image was achieved with illumination having a wavelength of 650 nm in air.
In 2000, 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. Such a material allows an electromagnetic wave to convey energy (have a group velocity) against its phase velocity. Pendry hypothesized that metallic wires aligned along the direction of a wave could provide negative permittivity (dielectric function ε < 0). Natural materials (such as ferroelectricity) 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, David R. 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 indexAIP News, Number 628 #1, March 13 Physics Today, May 2003, Press conference at APS March Meeting, Austin, Texas, March 4, 2003, New Scientist, vol 177, p. 24. and imaging by flat lens using left handed metamaterials were demonstrated. By 2007, experiments that involved negative refractive index had been conducted by many groups. At microwave frequencies, the first, imperfect cloaking device was realized in 2006.
From the standpoint of governing equations, contemporary researchers can classify the realm of metamaterials into three primary branches: Electromagnetic/Optical wave metamaterials, other wave metamaterials, and diffusion metamaterials. These branches are characterized by their respective governing equations, which include Maxwell's equations (a wave equation describing transverse waves), other wave equations (for longitudinal and transverse waves), and diffusion equations (pertaining to diffusion processes). Crafted to govern a range of diffusion activities, diffusion metamaterials prioritize diffusion length as their central metric. This crucial parameter experiences temporal fluctuations while remaining immune to frequency variations. In contrast, wave metamaterials, designed to adjust various wave propagation paths, consider the wavelength of incoming waves as their essential metric. This wavelength remains constant over time, though it adjusts with frequency alterations. Fundamentally, the key metrics for diffusion and wave metamaterials present a stark divergence, underscoring a distinct complementary relationship between them. For comprehensive information, refer to Section I.B, "Evolution of metamaterial physics," in Ref.
The unusual properties of metamaterials arise from the resonant response of each constituent element rather than their spatial arrangement into a lattice. It allows considering the local effective material parameters (permittivity and permeability). The resonance effect related to the mutual arrangement of elements is responsible for Bragg scattering, which underlies the physics of photonic crystals, another class of electromagnetic materials. Unlike the local resonances, Bragg scattering and corresponding Bragg stop-band have a low-frequency limit determined by the lattice spacing. The subwavelength approximation ensures that the Bragg stop-bands with the strong spatial dispersion effects are at higher frequencies and can be neglected. The criterion for shifting the local resonance below the lower Bragg stop-band make it possible to build a photonic phase transition diagram in a parameter space, for example, size and permittivity of the constituent element. Such diagram displays the domain of structure parameters allowing the metamaterial properties observation in the electromagnetic material.
For microwave, the features are on the order of . Microwave frequency metamaterials are usually constructed as arrays of electrically conductive elements (such as loops of wire) that have suitable inductor and capacitor characteristics. Many microwave metamaterials use split-ring resonators.
Photonic metamaterials are structured on the nanometers scale and manipulate light at optical frequencies. Photonic crystals and frequency-selective surfaces such as diffraction gratings, dielectric mirrors and exhibit similarities to subwavelength structured metamaterials. However, these are usually considered distinct from metamaterials, as their function arises from diffraction or interference and thus cannot be approximated as a homogeneous material. However, material structures such as photonic crystals are effective in the visible light. 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.
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.
Electromagnetic metamaterials can be divided into different classes, as follows:
Assuming a material well-approximated by a real permittivity and permeability, the relationship between permittivity , permeability and refractive index n is given by . All known non-metamaterial transparent materials (glass, water, ...) 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 number. Under such circumstances, it is necessary to take the negative square root for n. When both and are positive (negative), waves travel in the forward ( backward) direction. Electromagnetic waves cannot propagate in materials with and of opposite sign as the refractive index becomes Imaginary number. Such materials are opaque for electromagnetic radiation and examples include surface plasmon materials such as metals (gold, silver, ...).
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.Voznesenskaya, A. and Kabanova, D. (2012) "Analysis of Ray Tracing Through Optical Systems with Metamaterial Elements", Scientific and Technical Journal of Information Technologies, Mechanics and Optics, Volume 5, Number 12, p. 5. Indeed, a negative refractive index for circularly polarized waves can also arise from chirality. Metamaterials with negative n have numerous interesting properties:
Negative index of refraction derives mathematically from the vector triplet E, H and k.
For 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.
To date, only metamaterials exhibit a negative index of refraction.
Epsilon negative media (ENG) display a negative εr while μr is positive. Many plasmas exhibit this characteristic. For example, noble metals such as gold or silver are ENG in the infrared and .
Mu-negative media (MNG) display a positive εr and negative μr. 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. 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 nonlinear optics Kerr effect). Two gyrotropic materials with reversed rotation directions of the two principal polarizations are called .
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.
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.
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.
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. Each unit of the prescribed periodic structure acts like one atom, albeit of a much larger size.
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.
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.
Four material parameters are intrinsic to magnetoelectric coupling of bi-isotropic media. They are the Electric field and Magnetic field field strengths, and Electric flux and magnetic flux 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.
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 a 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 planar 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. 2D-chiral metamaterials that are anisotropic and lossy have been observed to exhibit directionally asymmetric transmission (reflection, absorption) of circularly polarized waves due to circular conversion dichroism.
On the other hand, bianisotropic response can arise from geometrical achiral structures possessing neither 2D nor 3D intrinsic chirality. Plum and colleagues investigated magneto-electric coupling due to extrinsic chirality, where the arrangement of a (achiral) structure together with the radiation wave vector is different from its mirror image, and observed large, tuneable linear optical activity, nonlinear optical activity, specular optical activity and circular conversion dichroism. Rizza et al. 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).
3D-chiral metamaterials are constructed from chiral materials or resonators in which the effective chirality parameter is non-zero.
Wave propagation properties in such chiral metamaterials demonstrate that negative refraction can be realized in metamaterials with a strong chirality and positive and .
This is because the refractive index has distinct values for left and right circularly polarized waves, given by
It can be seen that a negative index will occur for one polarization if > . In this case, it is not necessary that either or both and be negative for backward wave propagation. A negative refractive index due to chirality was first observed simultaneously and independently by Plum et al. and Zhang et al. in 2009.
Control of sound waves is mostly accomplished through the bulk modulus β, mass density ρ 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 ).
A ceramic nanotruss metamaterial can be flattened and revert to its original state.
While metamaterials derive their extraordinary properties from engineered micro- or nano-scale architectures that manipulate wave behaviour, metastructures operate at the macro-scale, leveraging geometric design and modular assembly to achieve multifunctional mechanical performance across larger systems. Fully bio-based composite and modular metastructure cells based on trussed geometry encompassing bamboo rods and plant-based polymer joints demonstrate scalable mechanical performance, supporting up to 700 kg in compression with a mass of only 30 g.
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. 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.
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.
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.
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.
Three conceptions- negative-index medium, non-reflecting crystal and superlens are foundations of the metamaterial theory. Other techniques for analyzing triply-periodic electromagnetic media may be found in Computing photonic band structure
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History
Electromagnetic metamaterials
Negative refractive index
Single negative
Hyperbolic
/ref> all-optical ultra-fast switching for integrated photonics, Pianelli, Alessandro, et al. "Si-CMOS compatible epsilon-near-zero metamaterial for two-color ultrafast all-optical switching." Communications Physics 7.1 (2024): 164. imaging, super high resolution and single photon source,Pianelli, Alessandro, et al. "Active control of dielectric singularities in indium-tin-oxides hyperbolic metamaterials." Scientific Reports 12.1 (2022): 16961. steering of optical signals, enhanced plasmon resonance effects.
Bandgap
Double positive medium
Bi-isotropic and bianisotropic
Chiral
FSS based
Mechanical metamaterials (Elastic metamaterials)
Other types
Acoustic
Structural
Thermal
Nonlinear
Liquid
Hall metamaterials
Meta-biomaterials
Frequency bands
Terahertz
Photonic
Tunable
Plasmonic
Applications
Antennas
Absorber
Superlens
Cloaking devices
Radar cross-section (RCS-)reducing metamaterials
Seismic protection
Sound filtering
Guided mode manipulations
Theoretical models
Institutional networks
MURI
Metamorphose
See also
External links
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