Metamaterial

Explorations of artificial materials for manipulating

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.[14]

In 2000,

In 2000,

From the standpoint of governing equations, contemporary researchers can classify the realm of metamaterials into three primary branches:[27] 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).^[28] 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, please refer to Section I.B, "Evolution of metamaterial physics," in Ref.^[27]

Electromagnetic metamaterials

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v t e

An electromagnetic metamaterial affects

Electromagnetic metamaterials can be divided into different classes, as follows:[3]^[19][4][31]

Negative refractive index

Negative-index metamaterials (NIM) are characterized by a negative index of refraction. Other terms for NIMs include "left-handed media", "media with a negative refractive index", and "backward-wave media".^[3] NIMs where the negative index of refraction arises from simultaneously negative permittivity and negative permeability are also known as double negative metamaterials or double negative materials (DNG).^[19]

Assuming a material well-approximated by a real permittivity and permeability, the relationship between permittivity ${\displaystyle \varepsilon _{r}}$, permeability ${\displaystyle \mu _{r}}$ and refractive index n is given by ${\textstyle n=\pm {\sqrt {\varepsilon _{\mathrm {r} }\mu _{\mathrm {r} }}}}$. All known non-metamaterial transparent materials (glass, water, ...) possess positive ${\displaystyle \varepsilon _{r}}$ and ${\displaystyle \mu _{r}}$. By convention the positive square root is used for n. However, some engineered metamaterials have ${\displaystyle \varepsilon _{r}}$ and ${\displaystyle \mu _{r}<0}$. Because the product ${\displaystyle \varepsilon _{r}\mu _{r}}$ is positive, n is real. Under such circumstances, it is necessary to take the negative square root for n. When both ${\displaystyle \varepsilon _{r}}$ and ${\displaystyle \mu _{r}}$ are positive (negative), waves travel in the forward (backward) direction. Electromagnetic waves cannot propagate in materials with ${\displaystyle \varepsilon _{r}}$ and ${\displaystyle \mu _{r}}$ of opposite sign as the refractive index becomes imaginary. Such materials are opaque for electromagnetic radiation and examples include plasmonic materials such as metals (gold, silver, ...).

The foregoing considerations are simplistic for actual materials, which must have complex-valued ${\displaystyle \varepsilon _{r}}$ and ${\displaystyle \mu _{r}}$. The real parts of both ${\displaystyle \varepsilon _{r}}$ and ${\displaystyle \mu _{r}}$ do not have to be negative for a passive material to display negative refraction.^[32][33] Indeed, a negative refractive index for circularly polarized waves can also arise from chirality.^[34][35] Metamaterials with negative n have numerous interesting properties:^[4][36]

• Snell's law (n₁sinθ₁ = n₂sinθ₂) still describes refraction, but as n₂ is negative, incident and refracted rays are on the same side of the surface normal at an interface of positive and negative index materials.
• Cherenkov radiation points the other way.^{[further explanation needed]}
• The time-averaged
  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 ${\displaystyle kc=\omega {\sqrt {\mu \varepsilon }}}$.

Negative index of refraction derives mathematically from the vector triplet E, H and k.^[4]

For

To date, only metamaterials exhibit a negative index of refraction.^[3][36][37]

Single negative

Single negative (SNG) metamaterials have either negative relative permittivity (εr) or negative relative permeability (µr), but not both.^[19] 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.

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.[36]

Hyperbolic

Hyperbolic metamaterials (HMMs) behave as a metal for certain polarization or direction of light propagation and behave as a dielectric for the other due to the negative and positive permittivity tensor components, giving extreme anisotropy. The material's dispersion relation in wavevector space forms a hyperboloid and therefore it is called a hyperbolic metamaterial. The extreme anisotropy of HMMs leads to directional propagation of light within and on the surface.^[38] HMMs have showed various potential applications, such as sensing, reflection modulator,^[39] imaging, steering of optical signals, enhanced plasmon resonance effects.^[40]

Bandgap

Electromagnetic

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.[44]

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.^[45] Each unit of the prescribed periodic structure acts like one atom, albeit of a much larger size.^[3][45]

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.^[3][4]

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.^[3][4]

Double positive medium

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.^[3][19]

Bi-isotropic and bianisotropic

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

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.^[4]

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 ${\displaystyle \mathbf {D} =\varepsilon \mathbf {E} +\xi \mathbf {H} ,}$ ${\displaystyle \mathbf {B} =\zeta \mathbf {E} +\mu \mathbf {H} ,}$ where ${\displaystyle \varepsilon }$ and ${\displaystyle \mu }$ are the permittivity and the permeability tensors, respectively, whereas ${\displaystyle \xi }$ and ${\displaystyle \zeta }$ are the two magneto-electric tensors. If the medium is reciprocal, permittivity and permeability are symmetric tensors, and ${\displaystyle \xi =-\zeta ^{T}=-i\kappa ^{T}}$, where ${\displaystyle \kappa }$ is the chiral tensor describing chiral electromagnetic and reciprocal magneto-electric response. The chiral tensor can be expressed as ${\displaystyle \kappa ={\tfrac {1}{3}}\operatorname {tr} (\kappa )I+N+J}$, where ${\displaystyle \operatorname {tr} (\kappa )}$ is the trace of ${\displaystyle \kappa }$, 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 (${\displaystyle \operatorname {tr} (\kappa )\neq 0,N\neq 0,J=0}$), (ii) pseudochiral media (${\displaystyle \operatorname {tr} (\kappa )=0,N\neq 0,J=0}$), (iii) omega media (${\displaystyle \operatorname {tr} (\kappa )=0,N=0,J\neq 0}$).

Chiral

Handedness of metamaterials 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.

Generally a chiral and/or bianisotropic electromagnetic response is a consequence of 3D geometrical chirality:

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 ${\displaystyle \kappa }$ 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 ${\displaystyle \varepsilon _{r}}$ and ${\displaystyle \mu _{r}}$.

${\displaystyle n}$

${\displaystyle n=\pm {\sqrt {\varepsilon _{r}\mu _{r}}}\pm \kappa }$

It can be seen that a negative index will occur for one polarization if ${\displaystyle \kappa }$ > ${\displaystyle {\sqrt {\varepsilon _{r}\mu _{r}}}}$. In this case, it is not necessary that either or both ${\displaystyle \varepsilon _{r}}$ and ${\displaystyle \mu _{r}}$ be negative for backward wave propagation.^[4] A negative refractive index due to chirality was first observed simultaneously and independently by Plum et al.^[34] and Zhang et al.^[35] in 2009.

FSS based

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.^[58]

Other types

Elastic

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

Main article:

Acoustic metamaterials

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v t e

Acoustic metamaterials control, direct and manipulate

infrasonic or ultrasonic waves in gases, liquids and solids. As with electromagnetic waves, sonic waves can exhibit negative refraction.^[16]

Control of sound waves is mostly accomplished through the

resonant system and the mechanical (sonic) resonance may be excited by appropriate sonic frequencies (for example audible pulses

).

Structural

Structural metamaterials provide properties such as crushability and light weight. Using

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.^[60][61]

A ceramic nanotruss metamaterial can be flattened and revert to its original state.[62]

Thermal

Typically materials found in nature, when homogeneous, are thermally isotropic. That is to say, heat passes through them at roughly the same rate in all directions. However, thermal metamaterials are anisotropic usually due to their highly organized internal structure. Composite materials with highly aligned internal particles or structures, such as fibers, and carbon nanotubes (CNT), are examples of this.

Nonlinear

Main article:

Nonlinear metamaterials

Metamaterials may be fabricated that include some form of

phase matching

conditions that must be satisfied in any nonlinear optical structure.

Liquid

Metafluids offer programmable properties such as viscosity, compressibility, and optical. One approach employed 50-500 micron diameter air-filled

cornstarch, it can act as either a Newtonian or a non-Newtonian fluid. Under pressure, it becomes non-Newtonian – meaning its viscosity changes in response to shear force.^[66]

Hall metamaterials

Main article: Hall effect

In 2009, Marc Briane and Graeme Milton^[67] 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.^[68] 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.^[69]

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.^[70] 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.

Meta-biomaterials

Meta-biomaterials have been purposefully crafted to engage with biological systems, amalgamating principles from both metamaterial science and biological areas. Engineered at the nanoscale, these materials adeptly manipulate electromagnetic, acoustic, or thermal properties to facilitate biological processes. Through meticulous adjustment of their structure and composition, meta-biomaterials hold promise in augmenting various biomedical technologies such as medical imaging,^[71] drug delivery,^[72] and tissue engineering.^[73] This underscores the importance of comprehending biological systems through the interdisciplinary lens of materials science.

Frequency bands

Terahertz

Main article: Terahertz metamaterial

Terahertz metamaterials interact at

far-infrared

light).

Photonic

Main article:

Photonic metamaterials

Photonic metamaterial interact with optical frequencies (

photonic band gap structures.^[74][75]

Tunable

Main article:

Tunable metamaterials

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

Main article:

Plasmonic metamaterials

Plasmonic metamaterials exploit

surface plasmon polaritons. Bulk plasma oscillations make possible the effect of negative mass (density).^[77][78]

Applications

Metamaterials are under consideration for many applications.[79] 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.^[80]

Antennas

Main article:

Metamaterial antennas

Metamaterial antennas are a class of antennas that use metamaterials to improve performance.^{[13][19][81][82]} Demonstrations showed that metamaterials could enhance an antenna's radiated power.^[13][83] Materials that can attain negative permeability allow for properties such as small antenna size, high directivity and tunable frequency.^[13][19]

Absorber

Main article: Metamaterial absorber

A metamaterial absorber manipulates the loss components of metamaterials' permittivity and magnetic permeability, to absorb large amounts of

solar photovoltaic applications.^[87] 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 used in these applications.

Superlens

Main article: Superlens

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.^[88][89]

Cloaking devices

Main article: Metamaterial cloaking

Metamaterials are a potential basis for a practical

proof of principle was demonstrated on October 19, 2006. No practical cloaks are publicly known to exist.^{[90][91][92][93][94][95]}

Radar cross-section (RCS-)reducing metamaterials

Metamaterials have applications in

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^{[96][97][98][99]} or generalized Snell's law.^[100][101]

This has led to aerodynamically favorable shapes for the targets with the reduced RCS.

Seismic protection

Main article:

Seismic metamaterials

Seismic metamaterials counteract the adverse effects of seismic waves on man-made structures.[10]^[102][103]

Sound filtering

Metamaterials textured with nanoscale wrinkles could control sound or light signals, such as changing a material's color or improving

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.^[104][105]

Guided mode manipulations

Metamaterials can be integrated with

electromagnetic waves (meta-waveguide).^[106] Subwavelength structures like metamaterials can be integrated with for instance silicon waveguides to develop and polarization beam splitters^[107] and optical couplers,^[108] adding new degrees of freedom of controlling light propagation at nanoscale for integrated photonic devices.^[109] Other applications such as integrated mode converters,^[110] polarization (de)multiplexers,^[111] structured light generation,^[112] and on-chip bio-sensors^[113] can be developed.^[106]

Theoretical models

All materials are made of

ferroelectric atom, while the ring acts as an inductor L, while the open section acts as a capacitor C. 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

plasma frequency. Other component distinctions call for the use of one of these models, depending on its polarity or purpose.^[3]

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.^[114][115]

Three conceptions- negative-index medium, non-reflecting crystal and superlens are foundations of the metamaterial theory. Other first principles techniques for analyzing triply-periodic electromagnetic media may be found in Computing photonic band structure

Institutional networks

MURI

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

Defense Advanced Research Project Agency.^[116]

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.[117]

Metamorphose

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.^[118][119]

See also

• Metasurface
• 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
• Magnonics
• Metamaterials (journal)
• Metamaterials Handbook
• Metamaterials: Physics and Engineering Explorations

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External links

• Media related to Metamaterials at Wikimedia Commons