# Metamaterial **A metamaterial** is a material whose useful properties come from a pattern built into it rather than from the substances it is made of. The pattern repeats on a scale much smaller than the wavelength it is meant to control, so a passing wave cannot resolve the pieces and responds to their average: the assembly behaves as a homogeneous medium with an effective [[Refractive_index|refractive index]], stiffness or density that none of its ingredients has.[^veselago][^pendry2000] Copper rings printed on circuit board can make a slab that bends [[Microwave_engineering|microwaves]] the wrong way; lead spheres in rubber, a block effectively lighter than nothing at one frequency; a lattice of ribs, a solid that grows fatter when stretched. In the microsim below the reader controls one number, the refractive index `n_2` of the lower half-space, and slides it from +2 down to −2. A ray crosses the boundary and [[Snell's_law|Snell's law]], `n_1·sin(theta_1) = n_2·sin(theta_2)`, is solved live for the refracted direction. At the glass preset `n_2` = 1.5 a ray arriving at 30° refracts to 19.5°; at the water preset 1.33 it refracts to 22.1°; as `n_2` passes through zero the refracted ray swings across the normal to the *same* side as the incident ray, and at the "left-handed" preset −1 it leaves at −30°, the mirror image of the ordinary case (derived).[^up3-ch1] Give that medium a finite thickness and the sim draws [[Negative-index_metamaterial|Veselago's]] flat lens: a slab with no curved surface that brings a point source to a focus inside itself and to a second focus beyond it.[^veselago] On the [[Materials_science]] flagship this page serves Part X, Emerging technologies, beside [[Metal_foam|metal foam]] — both designed at the scale of a repeating cell rather than chosen from a table of substances. ## History Making a medium out of obstacles rather than molecules is older than the word for it: in the 1940s microwave engineers built "artificial dielectrics" from arrays of metal strips and spheres, which steered a beam because the array polarised like an oversized atom, and used them as light radar lenses.[^kock1948] The modern subject begins with a short 1968 paper by Victor Veselago, who asked what [[Maxwell's_equations|Maxwell's equations]] permit if the permittivity `eps` and permeability `mu` were both negative at once. Waves would still propagate, he found, but with the [[Electric_field|electric field]], magnetic field and wave vector forming a left-handed set; the phase would run backwards against the flow of energy; refraction, the Doppler shift and Cherenkov radiation would reverse; and a flat slab would act as a lens.[^veselago] No substance had negative `mu`, and the paper lay unused for thirty years. What revived it was the realisation that both signs could be engineered. In 1996 John Pendry and colleagues showed that a lattice of thin metal wires has an effective plasma frequency in the gigahertz range rather than the ultraviolet, giving negative `eps` below it; in 1999 that a split ring — a single-turn inductor closed by the capacitance of its gap — is a magnetic [[Resonance|resonator]] with negative `mu` just above resonance.[^pendry1996][^pendry1999] In 2000 David Smith's group combined the two into one composite and found a transmission band where either medium alone was opaque; in 2001 they cut a prism from it and measured the beam leaving on the negative side of the normal.[^smith2000][^shelby2001] Pendry's proposal that such a slab would beat the [[Diffraction|diffraction]] limit, and the 2006 transformation-optics papers that turned the field towards [[Metamaterial_cloaking|cloaking]], set the agenda since.[^pendry2000][^pendry2006][^leonhardt2006] ## Types Metamaterials are classified by the kind of wave or load they act on, since the cell physics differs between families even though the design logic — a resonator much smaller than the wavelength, repeated — is shared. In each family the cell drives the effective parameter of interest through a resonance, because only near resonance can it take a value, negative ones included, outside the range spanned by the constituents. ### Electromagnetic metamaterials The original and largest family acts on [[Electromagnetic_radiation|electromagnetic waves]] and is described by the effective parameters `eps` and `mu`. A medium of thin [[Copper|copper]] wires behaves like a dilute electron gas whose plasma frequency the geometry has lowered, `eps_eff(w) = 1 - w_p^2/(w^2 + i·G·w)`, so `eps` is negative for `w < w_p`.[^pendry1996] A split-ring resonator is an LC circuit, and its permeability follows a Lorentz form, `mu_eff(w) = 1 - F·w^2/(w^2 - w_0^2 + i·G·w)`, which dips below zero just above the ring's resonance `w_0`.[^pendry1999] Interleaving the two lattices gives a band where both are negative and the index is real and negative.[^smith2000] Later designs — paired strips, "fishnet" layers and flat metasurfaces one element thick — reached the same effects at [[Nanotechnology|nanometre]] scales, at the cost of much higher loss. ### Mechanical metamaterials A mechanical metamaterial gets its stiffness, strength or [[Poisson's_ratio|Poisson's ratio]] from the geometry of a repeating cell, not from the bulk solid it is printed in. The best-known example is the auxetic structure, whose re-entrant ribs rotate rather than stretch when pulled, so the material expands sideways as it is extended and its Poisson's ratio is negative — the opposite of almost every ordinary solid.[^lakes1987] Other cells target a ratio of stiffness to density, a collapse plateau that absorbs a fixed energy per unit volume, or an instability that snaps between two shapes. The boundary with [[Composite_material|composites]] and cellular solids such as [[Honeycomb_structure|honeycomb]] is one of intent: a foam happens to have a cell, a mechanical metamaterial is designed around one, and [[3D_printing|additive manufacturing]] made arbitrary cells cheap. ### Acoustic Acoustic metamaterials act on pressure waves in fluids and elastic waves in solids; their effective parameters are the mass density and the bulk modulus. In 2000 a group in Hong Kong embedded silicone-coated lead spheres in epoxy and measured a stop band two orders of magnitude below the frequency at which the lattice spacing would have given Bragg reflection: each coated sphere is a mass on a spring, and just above resonance it moves out of phase with the driving [[Sound|sound]] field, so the effective density is negative and the wave cannot propagate.[^liu2000] Since audible sound in air has wavelengths of order a metre, a locally resonant panel a few centimetres thick can stop a frequency that would otherwise need a far heavier wall — the basis of metamaterial [[Noise_control|noise control]] and low-frequency [[Damping|damping]] panels. ### Other types The same trick applies wherever a field obeys a wave or diffusion equation. Thermal metamaterials route heat around an object by layering materials of contrasting conductivity, exploiting the similarity between steady conduction and electrostatics; the effect re-routes flux rather than insulating. Elastic metamaterials for seismic frequencies, structures that steer water waves, and lattices with a full [[Band_gap|band gap]] — the [[Photonic_crystal|photonic crystals]] — are grouped here too, though the last works by Bragg scattering at a cell comparable to the wavelength.[^liu2000] ## Frequency bands An electromagnetic metamaterial is a scale model of itself: a split ring's resonance follows from its inductance and capacitance, hence from its size, so halving the cell roughly doubles the operating frequency. That scaling makes the subject an engineering discipline rather than a search through the periodic table — and also limits it, as metal stops behaving like a perfect conductor. ### Terahertz Between about 0.1 and 10 THz lies a band in which few natural materials respond strongly and sources and detectors are historically weak — the "terahertz gap". Planar metal resonators patterned by ordinary lithography have cells of tens of micrometres, putting their resonance squarely in this band; terahertz metamaterials serve as filters, modulators and phase plates for imaging and [[Spectroscopy|spectroscopy]]. ### Photonic Scaling to visible and near-infrared wavelengths demands features of tens of nanometres, made by electron-beam lithography or self-assembly. Negative index has been shown in the near infrared in stacked "fishnet" layers of [[Silver|silver]] and dielectric, but ohmic loss, negligible at microwave frequencies, becomes dominant; the figure of merit, the ratio of real to imaginary index, falls sharply with frequency.[^pendry2000] ### Tunable A metamaterial fixed at fabrication is a filter; one whose resonance can be moved is a device. Tunability comes from putting something switchable into each cell's capacitive gap — a liquid crystal, a semiconductor whose carrier density follows a bias, a phase-change compound, a micromechanical element. A few volts across a micrometre gap changes the capacitance and slides the band. ### Plasmonic At optical frequencies the electrons of a metal surface support collective oscillations, and a nanoscale particle's resonance is set by that plasma rather than a circuit. Plasmonic metamaterials use the field confinement near such a particle to concentrate light far below the wavelength; [[Gold|gold]] and silver are the usual metals, their losses lowest in the visible and near infrared. ## Applications Almost all deployed uses are at radio and microwave frequencies, where cells are millimetres across, metal is nearly lossless and printed-circuit manufacture suffices. Optical applications remain mostly demonstrations, limited by loss and by the difficulty of stacking nanometre cells into a thick structure. ### Antennas A metamaterial ground plane can be made to reflect with zero phase shift instead of the half-wave shift of a metal sheet, letting an antenna element sit directly on it rather than a quarter-wavelength above; other loadings make a small element radiate efficiently. The gain is compactness, the cost bandwidth, since the effect rests on a resonance. ### Absorber Tuning `eps` and `mu` together gives a layer the same impedance as free space, so nothing reflects, while its loss is made large enough to dissipate everything that enters. Such a structure absorbed nearly all the incident power in a layer a small fraction of a wavelength thick, far thinner than a conventional absorber for the same frequency.[^landy2008] Similar designs shape [[Thermal_radiation|thermal radiation]] by giving a surface a narrow-band [[Emissivity|emissivity]] instead of the broad [[Black-body_radiation|blackbody]] spectrum. ### Superlens An ordinary lens loses fine detail because the field components that carry it — the evanescent waves — decay before reaching the image, limiting resolution to roughly half a wavelength. Pendry showed in 2000 that a slab of `n` = −1 does two things: it refocuses the propagating waves, as Veselago had found, and it *amplifies* the evanescent ones, so in an ideal lossless slab every component arrives with its original amplitude and phase and resolution has no limit.[^pendry2000][^veselago] The sim's flat-lens preset draws the propagating half: rays from a point source cross inside the slab and again beyond it, source-to-image distance exactly twice the thickness, with no curvature anywhere. ILLUSTRATIVE: the sim traces geometric rays only, not the evanescent components the sub-wavelength claim rests on; absorption destroys the amplification in real materials, so measured near-field superlenses beat the diffraction limit by a factor of a few.[^pendry2000] ### Cloaking devices Transformation optics treats a coordinate change as a prescription for a material. Maxwell's equations keep their form under a change of coordinates if `eps` and `mu` transform with the metric, so any smooth deformation of space that pushes light around a hole can be realised by a shell with the corresponding anisotropic, position-dependent parameters — values a metamaterial can supply and a substance cannot.[^pendry2006][^leonhardt2006] A copper cylinder wrapped in concentric split-ring layers was shown in 2006 to cast a strongly reduced shadow at one microwave frequency.[^schurig2006] Broadband cloaking in the visible meets a hard limit: the phase speeds required exceed the [[Speed_of_light|speed of light]] in vacuum, possible only over a narrow band. ### Radar cross-section (RCS-)reducing metamaterials Reducing what a target returns to a [[Radar|radar]] is absorption plus redirection. Absorbers thin enough to coat a surface remove returned power in a chosen band, and checkerboard surfaces of two cells 180° out of phase scatter the beam off-specular instead of back at the transmitter. ### Seismic protection The idea transfers to the ground if cells are made metres across, since seismic surface waves have wavelengths of tens to hundreds of metres. Field experiments have used grids of boreholes and soil inclusions to deflect surface waves in the few-hertz band that damages buildings — a complement to conventional [[Earthquake_engineering|earthquake engineering]], not a replacement.[^brule2014] ### Sound filtering The locally resonant panels above are the nearest to practical use: a light membrane loaded with small masses gives transmission loss at low frequencies far beyond what its weight predicts from the ordinary mass law — and it is the low frequencies that pass through walls. Similar structures act on [[Ultrasound|ultrasound]] and on machine [[Vibration|vibration]].[^liu2000] ### Guided mode manipulations A metasurface can impose a phase shift that varies along an interface, and refraction then gains a term: `n_2·sin(theta_2) - n_1·sin(theta_1) = (lambda_0/(2·pi))·(dPhi/dx)`, the generalised Snell's law.[^yu2011] A constant gradient steers a beam without a prism, a radial one focuses without curvature, a spiral one adds orbital angular momentum, and the same trick converts one guided mode into another in integrated photonics. ## Theoretical models The subject rests on homogenisation: the claim that a periodic assembly of scatterers can be replaced, for waves much longer than the period, by a uniform medium with effective parameters. The condition is that the cell size be small against the wavelength in the medium — in practice below about `lambda`/4, comfortably so below `lambda`/10 — and it fails near the band edge, where the assembly behaves as a [[Photonic_crystal|photonic crystal]] scattering by Bragg's law rather than as an effective medium.[^pendry1999][^smith2000] Given `eps` and `mu`, the index follows from `n^2 = eps·mu`, and the branch is the crux: when both are negative the product is positive and `n` is real, but requiring energy to flow away from the source forces the negative root, `n = -sqrt(eps·mu)`.[^veselago] Phase and energy then travel in opposite directions, which is what sends the sim's refracted ray to the wrong side of the normal. That negative root is what the reader manipulates. The control is `n_2` itself, swept from +2 to −2, with [[Snell's_law|Snell's law]] `n_1·sin(theta_1) = n_2·sin(theta_2)` solved at each step and the incident, reflected and refracted rays redrawn; incidence angle and presets are secondary. Three things change as the slider crosses zero: the refracted ray sweeps towards the interface and then past it; the critical angle for [[Total_internal_reflection|total internal reflection]], present whenever `|n_2| < n_1`, survives the sign change because only the magnitude enters it; and a parallel-sided slab stops displacing the beam and starts to focus it. Treating `n` as one real number is the idealisation: a real metamaterial is dispersive and lossy, `eps` and `mu` are complex, and the negative band is narrow, so `n_2` is a value at one frequency, not a property of a substance.[^pendry2000] ## Institutional networks Metamaterials research has been organised through large multi-investigator programmes more than most of [[Materials_science|materials science]], because one result typically needs theory, microfabrication and measurement in three different laboratories. The two programmes below are that pattern on either side of the Atlantic; Wikitube has not yet pinned a primary source for their scope and dates. ### MURI MURI is the United States Department of Defense's Multidisciplinary University Research Initiative, administered through the Army, Navy and Air Force research offices, which funds teams spanning several universities and disciplines over years rather than single-investigator projects. Several awards in the 2000s supported metamaterials and transformation-optics work.[citation needed] ### Metamorphose METAMORPHOSE was a European Network of Excellence on metamaterials funded under the European Union's framework programmes, pooling research groups across Europe and continuing afterwards as a virtual institute that runs conferences, schools and a shared body of design data.[citation needed] ## See also - [[Negative-index_metamaterial]] — the sub-class with `n` < 0, the sim's left-handed preset - [[Metamaterial_cloaking]] - [[Snell's_law]] - [[Refractive_index]] - [[Photonic_crystal]] - [[Refraction]] - [[Nanomaterials]] - [[Composite_material]] - [[Metal_foam]] — the neighbouring cellular solid on the flagship's Emerging technologies part ## References [^veselago]: Veselago, V. G. (1968). "The electrodynamics of substances with simultaneously negative values of ε and μ." *Soviet Physics Uspekhi* 10 (4): 509–514. https://doi.org/10.1070/PU1968v010n04ABEH003699 — negative `n`, the left-handed triad, reversed refraction, and the flat slab that focuses. [^pendry2000]: Pendry, J. B. (2000). "Negative Refraction Makes a Perfect Lens." *Physical Review Letters* 85 (18): 3966–3969. https://doi.org/10.1103/PhysRevLett.85.3966 — recovery of the evanescent components and the loss limit on real superlenses. [^up3-ch1]: OpenStax (Sanny, J.; Ling, S. J.). *University Physics Volume 3* (2016), Ch. 1 The Nature of Light, pp. 15–58 (page to pin): the law of refraction, the definition of the refractive index and the tabulated indices of water (1.33) and crown glass (about 1.5) used as the sim's presets. https://openstax.org/books/university-physics-volume-3 [^kock1948]: Kock, W. E. (1948). "Metallic Delay Lenses." *Bell System Technical Journal* 27 (1): 58–82 (DOI to pin) — the 1940s artificial-dielectric tradition of building a refracting medium from metal obstacles. [^pendry1996]: Pendry, J. B.; Holden, A. J.; Stewart, W. J.; Youngs, I. (1996). "Extremely Low Frequency Plasmons in Metallic Mesostructures." *Physical Review Letters* 76 (25): 4773–4776 (DOI to pin) — the thin-wire medium and its lowered plasma frequency. [^pendry1999]: Pendry, J. B.; Holden, A. J.; Robbins, D. J.; Stewart, W. J. (1999). "Magnetism from Conductors and Enhanced Nonlinear Phenomena." *IEEE Transactions on Microwave Theory and Techniques* 47 (11): 2075–2084 (DOI to pin) — the split-ring resonator, the Lorentz form of `mu_eff`, and the homogenisation condition on cell size. [^smith2000]: Smith, D. R.; Padilla, W. J.; Vier, D. C.; Nemat-Nasser, S. C.; Schultz, S. (2000). "Composite Medium with Simultaneously Negative Permeability and Permittivity." *Physical Review Letters* 84 (18): 4184–4187 (DOI to pin). [^shelby2001]: Shelby, R. A.; Smith, D. R.; Schultz, S. (2001). "Experimental Verification of a Negative Index of Refraction." *Science* 292 (5514): 77–79 (DOI to pin) — the wedge experiment that measured the beam on the negative side of the normal. [^pendry2006]: Pendry, J. B.; Schurig, D.; Smith, D. R. (2006). "Controlling Electromagnetic Fields." *Science* 312 (5781): 1780–1782 (DOI to pin) — transformation optics. [^leonhardt2006]: Leonhardt, U. (2006). "Optical Conformal Mapping." *Science* 312 (5781): 1777–1780 (DOI to pin). [^schurig2006]: Schurig, D.; Mock, J. J.; Justice, B. J.; Cummer, S. A.; Pendry, J. B.; Starr, A. F.; Smith, D. R. (2006). "Metamaterial Electromagnetic Cloak at Microwave Frequencies." *Science* 314 (5801): 977–980 (DOI to pin) — the split-ring shell around a copper cylinder, measured at a single microwave frequency. [^lakes1987]: Lakes, R. (1987). "Foam Structures with a Negative Poisson's Ratio." *Science* 235 (4792): 1038–1040 (DOI to pin). [^liu2000]: Liu, Z.; Zhang, X.; Mao, Y.; Zhu, Y. Y.; Yang, Z.; Chan, C. T.; Sheng, P. (2000). "Locally Resonant Sonic Materials." *Science* 289 (5485): 1734–1736 (DOI to pin) — coated lead spheres in epoxy, and a stop band two orders of magnitude below the Bragg condition. [^landy2008]: Landy, N. I.; Sajuyigbe, S.; Mock, J. J.; Smith, D. R.; Padilla, W. J. (2008). "Perfect Metamaterial Absorber." *Physical Review Letters* 100 (20): 207402 (DOI to pin). [^brule2014]: Brûlé, S.; Javelaud, E. H.; Enoch, S.; Guenneau, S. (2014). "Experiments on Seismic Metamaterials: Molding Surface Waves." *Physical Review Letters* 112 (13): 133901 (DOI to pin) — a borehole grid acting on surface waves in soil. [^yu2011]: Yu, N.; Genevet, P.; Kats, M. A.; Aieta, F.; Tetienne, J.-P.; Capasso, F.; Gaburro, Z. (2011). "Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction." *Science* 334 (6054): 333–337 (DOI to pin) — the phase-gradient term added to Snell's law. ## External links - [*University Physics Volume 3*](https://openstax.org/books/university-physics-volume-3) — OpenStax, CC BY; Chapter 1 carries the refraction background the sim assumes (Portal Book 079) - Further sites, including the research groups' own pages, are listed in the Wikipedia pair's *External links*; none is reproduced here until its URL has been checked. <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Metamaterial.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Metamaterial* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Metamaterial.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Metamaterial.html" data-title="Metamaterial"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Metamaterial) : [Wikitube](https://en.wikitube.io/wiki/Metamaterial) · pinned revision [1374308696](https://en.wikipedia.org/w/index.php?oldid=1374308696) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Materials_science]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Materials_science row M64 · sim pending (matter/Metamaterial).*