Metamaterial
A metamaterial 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.
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 show promise for 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.
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 having 50 nm lines and spaces, and then coupled it with a standard oil immersion microscope objective 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 against its phase velocity. Pendry hypothesized that metallic wires aligned along the direction of a wave could provide negative permittivity. Natural materials display negative permittivity; the challenge was achieving negative permeability. In 1999, Pendry demonstrated that a split ring 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 negative refractive index 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, other wave equations, and diffusion equations. 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.
Electromagnetic metamaterials
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.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. 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 radiation, the features are on the order of millimeters. Microwave frequency metamaterials are usually constructed as arrays of electrically conductive elements that have suitable inductive and capacitive characteristics. Many microwave metamaterials use split-ring resonators.
Photonic metamaterials are structured on the nanometer scale and manipulate light at optical frequencies. 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 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 spectrum. The middle of the visible spectrum has a wavelength of approximately 560 nm. 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 can exhibit subwavelength characteristics and are known variously as artificial magnetic conductors or High Impedance Surfaces. FSS display inductive and capacitive characteristics that are directly related to their subwavelength structure.
Electromagnetic metamaterials can be divided into different classes, as follows:
Negative refractive index
Negative-index metamaterials 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". 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.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 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. When both and are positive, waves travel in the forward direction. Electromagnetic waves cannot propagate in materials with and of opposite sign as the refractive index becomes imaginary. Such materials are opaque for electromagnetic radiation and examples include plasmonic materials such as metals.
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. Indeed, a negative refractive index for circularly polarized waves can also arise from chirality. Metamaterials with negative n have numerous interesting properties:
- Snell's law 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.
- The time-averaged Poynting vector is antiparallel to phase velocity. However, for waves to propagate, a –μ must be paired with a –ε in order to satisfy the wave number dependence on the material parameters.
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.
To date, only metamaterials exhibit a negative index of refraction.