A metamaterial (from the Greek word , meaning 'beyond' or 'after', and the Latin word , meaning 'matter' or 'material') is an engineered material whose properties arise not from the chemical composition of its base substances, but from their deliberately designed internal structure. These properties are often rare or absent in naturally occurring materials. Metamaterials are typically fashioned from multiple materials, such as metals and plastics, and arranged in repeating patterns at scales that are smaller than the wavelengths of the phenomena they influence. Their shape, geometry, size, orientation, and arrangement give them their properties of manipulating electromagnetic, acoustic, or seismic waves: by blocking, absorbing, enhancing, or bending waves, to achieve benefits that go beyond what is possible with conventional materials. Those that exhibit a negative index of refraction for particular wavelengths have been the focus of a substantial amount of research.V.M. Shalaev, W. Cai, U.K. Chettiar, H.-K. Yuan, A.K. Sarychev, V.P. Drachev, and A.V. Kildishev, Negative Index of Refraction in Optical Metamaterials, Optics Letters, v. 30, pp. 3356–3358 (2005); arxiv.org/abs/physics/0504091 (April 13, 2005)S. Xiao, V.P. Drachev, A.V. Kildishev, X. Ni, U.K. Chettiar, H.-K. Yuan, and V.M. Shalaev, Loss-free and active optical negative-index metamaterials, Nature, v. 466, pp. 735–738 (2010)
Potential applications of metamaterials are diverse and include sports equipment, optical filters, medical devices, remote aerospace applications, sensor detection and infrastructure monitoring, smart solar power management, lasers, crowd control, radomes, high-frequency battlefield communication and lenses for high-gain antennas, improving ultrasonic sensors, and even shielding structures from earthquakes. Metamaterials offer the potential to create super-lenses. A form of 'invisibility' was demonstrated using gradient-index materials. Acoustic and seismic metamaterials are also research areas.
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. Recent developments also suggest potential applications of metamaterials in optical computing, with metamaterial-based systems theoretically being able to perform certain tasks more efficiently than conventional computing.
History
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.
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 dielectrics 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 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, 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. Negative index of refraction in the optical range was first demonstrated by Vladimir Shalaev et al. By 2007, experiments that involved negative refractive index had been conducted by many groups. At microwave frequencies, the first, imperfect invisibility cloak 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.
Types Electromagnetic metamaterials
Mechanical metamaterials
Acoustic
Acoustic metamaterials, sometimes referred to as sonic or phononic crystals, are architected materials designed to manipulate sound waves or phonons in gases, liquids, and solids. By tailoring effective parameters such as bulk modulus (β), density (ρ), and in some cases chirality, they can be engineered to transmit, trap, or attenuate waves at selected frequencies, functioning as acoustic resonators when local resonances dominate. Within the broader field of mechanical metamaterials, acoustic metamaterials represent the dynamic branch where wave control is the primary goal.
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.
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 pulses).
Willis materials exhibit additional nonlocal material parameters for elastic-wave manipulation—analogous to the bianisotropic moduli in electromagnetic media—that couple stress with particle velocity and linear momentum with strain, known as Willis couplings. They are named after J. R. Willis, who predicted them using a dynamic homogenization method. Much of the recent interest in Willis couplings has been driven by their local form (the Milton–Briane–Willis equations). By extending Willis's homogenization method, Pernas-Salomón and Shmuel were the first to show that piezoelectric composites exhibit an effective coupling between linear momentum and the electric field, which they termed electro-momentum coupling. Electro-momentum coupling provides a mechanism for wave manipulation similar to Willis coupling, with the added benefit of electrical tunability.
Other types
Structural Structural metamaterials are a type of mechanical metamaterial that provide properties such as crushability and lightweight characteristics. 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.
A ceramic nanotruss metamaterial can be flattened and revert to its original state.
While metamaterials derive their properties from engineered micro- or nano-scale architectures that manipulate wave behaviour, metastructures operate at the macro-scale, using 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 30 g.
Thermal Typically, materials found in nature, when homogeneous, are thermally isotropic, meaning heat diffuses at roughly the same rate in all directions. Thermal metamaterials, as a subclass of mechanical metamaterials, achieve anisotropic and tailored thermal responses through architected internal structures. The term arose around 2008, when Fan, Gao, and Huang demonstrated shaped graded materials with apparent negative thermal conductivity, and introduced the concept of a thermal cloak through transformation thermotics. By carefully designing their geometry at nano, micro, meso, or macro scales, these materials exhibit effective thermal conductivities not accessible in natural materials. Their classification as mechanical metamaterials stems from the fact that their unusual thermal behavior arises from engineered structure rather than chemical composition. Examples include composites with highly aligned fibers, particle arrays, or carbon nanotubes, where directional organization enables controlled heat flow.
Nonlinear