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Metamaterials and nanotechnology Physicists have learned how to make materials with amazing properties. The phenomena of total internal reflection of light in transparent media, arising in thin films of materials created using nanotechnology, can be used to control ultrashort laser and radio pulses. And coatings of these materials applied to an object can make it “invisible.”

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Negative refractive index. Refraction of light at the boundary with a material having a negative refractive index. A. In nature, when crossing the boundary of two media, a ray incident on it obliquely always continues its movement in the original direction, just at a slightly different angle - larger or smaller, depending on the ratio of refractive indices. B. When crossing a boundary with a metamaterial that has a negative refractive index, the beam seems to be “reflected” from the perpendicular at the intersection point - that is, it continues to move into the metamaterial, but if it fell from the top left, it will go further down not to the right, but back to the left .

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Snell's Law: If the refractive index is negative, then the ray is refracted in the other direction

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“Unnatural?” There are no materials with a negative refractive index in nature, so pictures illustrating the operation of such media look “unnatural.”

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It is necessary that the metamaterial elements have a size of 10-100 nm (much smaller than the wavelength).

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Optical microscope Physicists from Manchester and Singapore have designed an optical microscope with record-breaking resolution that can resolve 50-nanometer image details. The new “nanoscope” works on the same principle, but does not use metamaterials, which are replaced by simple transparent spheres with a diameter of several micrometers, made, for example, of silicon dioxide. The experiments carried out convincingly prove that the placement of such spheres on the surface of the samples significantly improves the quality of the images. Diagram and micrograph of the “fishing net”,

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Scientists have created a new "invisibility cloak." A new design of an invisibility cloak has been proposed: it consists of glass cylinders and is able to “hide” a metal rod with a diameter of 15 microns. However, it will be possible to hide behind such glass only from the infrared eye: invisibility in a wider range of wavelengths has not yet been achieved.

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The Invisible Cap Until now, the invisibility hat has been the preserve of fairy tales and science fiction writers. However, recently everything has changed, and the search for the “cap of invisibility” has become a favorite pastime of some physicists - a new promising direction in science. A duo of publications in Science and Nature describe bulk nanomaterials in which light rays are bent in the “wrong” direction without being absorbed to the point where nothing is left behind. Until now, strong absorption has been one of the main problems.

So cathedrals of supervital crystals
Conscientious spider light,
Unraveling the ribs, them again
Collects into a single bundle.
O. Mandelstam

Children's problem “Which is heavier, a kilogram of cotton wool or a kilogram of iron filings?” will only confuse a slow-witted first-grader. It is much more interesting to speculate on the topic: “What properties will the material that we get if we carefully mix finely ground cotton wool and iron filings have?” It’s intuitively clear: to answer this question, you need to remember the properties of iron and cotton wool, after which you can confidently say that the resulting material will most likely, for example, react to the presence of a magnet and water. However, are the properties of a multiphase material always determined solely by the properties of the components that form it? I would like to answer this question positively, because it is difficult to imagine, say, a mixture of dielectrics (for example, sawdust and foam balls) that conducts electric current.

“This only happens in fairy tales!” - the first-grader will try to rehabilitate himself, remembering the numerous sorcerers and sorceresses from children's fairy tales, who, by mixing all kinds of fly agarics, frog legs and bat wings, received magic powders, the magical properties of which, strictly speaking, are not characteristic of fly agarics and frog legs. However, surprisingly, modern science knows examples of how the combination of quite ordinary materials makes it possible to create objects whose properties are not only not inherent in the components used, but, in principle, cannot be found in nature and, as it might seem at first glance , are prohibited by the laws of physics. “This is a miracle!” the first grader will say. “No, these are metamaterials!” - a modern scientist will object. And both will be right in their own way, because from the point of view of classical science, metamaterials are capable of creating real miracles. However, the process of creating a metamaterial is also similar to magic, because It is not enough to simply mix the components of a metamaterial; they must be properly structured.

Metamaterials are composite materials whose properties are determined not so much by the individual physical properties of their components as by their microstructure. The term “metamaterials” is especially often applied to those composites that exhibit properties that are not characteristic of objects found in nature.

One of the most hotly debated types of metamaterials recently are objects with a negative refractive index. It is well known from the school physics course that the refractive index of the medium ( n) is a quantity showing how many times the phase velocity of electromagnetic radiation in the medium ( V) less than the speed of light in vacuum ( c): n=c/V. The refractive index of vacuum is equal to 1 (which, in fact, follows from the definition), whereas for most optical media it is greater. For example, ordinary silicate glass has a refractive index of 1.5, which means that light propagates in it at a speed 1.5 times less than in a vacuum. It is important to note that depending on the wavelength of electromagnetic radiation, the value n may vary.

Most often, the refractive index of a material is remembered when considering the effect of light refraction at the interface between two optical media. This phenomenon is described by Snell's law:

n 1 sinα = n 2 sinβ,

where α is the angle of incidence of light coming from a medium with refractive index n 1, and β is the angle of refraction of light in a medium with refractive index n 2.

For all media that can be found in nature, the rays of incident and refracted light are on opposite sides of the normal restored to the interface between the media at the point of refraction (Fig. 1a). However, if we formally substitute n 2 into Snell’s law<0, реализуется ситуация, которая еще до недавнего времени казалась физикам абсурдной: лучи падающего и преломленного света находятся по одну сторону от нормали (Рис.1б).

The theoretical possibility of the existence of unique materials with a negative refractive index was pointed out by the Soviet physicist V. Veselago almost 40 years ago. The fact is that the refractive index is related to two other fundamental characteristics of matter, dielectric constant ε and magnetic permeability μ, by a simple relationship: n 2 = ε·μ. Despite the fact that this equation is satisfied by both positive and negative values ​​of n, scientists for a long time refused to believe in the physical meaning of the latter - until Veselago showed that n< 0 в том случае, если одновременно ε < 0 и μ < 0.

Natural materials with a negative dielectric constant are well known - any metal at frequencies above the plasma frequency (at which the metal becomes transparent). In this case ε< 0 достигается за счет того, что свободные электроны в металле экранируют внешнее электромагнитное поле. Гораздо сложнее создать материал с μ < 0, в природе такие материалы не существуют. Именно по этой причине работы Веселаго долгое время не привлекали должного внимания научной общественности. Прошло 30 лет, прежде чем английский ученый Д.Пендри (John Pendry) в 1999 г. показал, что отрицательная магнитная проницаемость может быть получена для проводящего кольца с зазором. Если поместить такое кольцо в переменное магнитное поле, в кольце возникнет электрический ток, а на месте зазора возникнет дуговой разряд. Поскольку металлическому кольцу можно приписать индуктивность L, а зазору соответствует эффективная емкость С, систему можно рассматривать как простейший колебательный контур с резонансной частотой ω 0 ~ 1/(LC) -1/2 . При этом система создает собственное магнитное поле, которое будет положительным при частотах переменного магнитного поля ω < ω 0 и отрицательным при ω > ω 0 .

Thus, systems with a negative response to both the electrical and magnetic components of electromagnetic radiation are possible. American researchers under the leadership of David Smith were the first to combine both systems in one material in 2000. The created metamaterial consisted of metal rods responsible for ε< 0, и медных кольцевых резонаторов, благодаря которым удалось добиться μ < 0. Несомненно, структуру, изображенную на Рис.2, сложно назвать материалом в традиционном смысле этого слова, поскольку она состоит из отдельных макроскопических объектов. Между тем, данная структура «оптимизирована» для микроволнового излучения, длина волны которого значительного больше отдельных структурных элементов метаматериала. Поэтому с точки зрения микроволн последний также однороден, как например, оптическое стекло для видимого света. Последовательно уменьшая размеры структурных элементов можно создавать метаматериалы с отрицательным показателем преломления для терагерцового и инфракрасного диапазонов спектра. Ученые ожидают, что благодаря достижениям современных нанотехнологий в самое ближайшее время будут созданы метаматериалы и для видимого диапазона спектра.

From a physics point of view, metamaterials with a negative refractive index are the antipodes of conventional materials. In the case of a negative refractive index, the phase velocity of electromagnetic radiation is reversed; the Doppler shift occurs in the opposite direction; Cherenkov radiation from a moving charged particle occurs not forward, but backward; converging lenses become divergent and vice versa... And all this is only a small part of those amazing phenomena that are possible for metamaterials with a negative refractive index. The practical use of such materials is, first of all, associated with the possibility of creating terahertz optics based on them, which, in turn, will lead to the development of meteorology and oceanography, the emergence of radars with new properties and all-weather navigation tools, devices for remote diagnostics of the quality of parts and safety systems that allow you to detect weapons under clothing, as well as unique medical devices.

Literature

D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, S. Schultz, Composite Medium with Simultaneously Negative Permeability and Permittivity, Physical Review Letters 84 (2000) 4184.

MOSCOW,26 Sep - RIA Novosti, Olga Kolentsova. Sometimes the achievements of modern technology can be mistaken for magic. Only instead of magic, exact science works. One of the areas of research, the results of which could well serve as an illustration of the properties of “fairytale attributes,” is the development and creation of metamaterials.

From a purely physical point of view, metamaterials are artificially formed and specially constructed structures that have electromagnetic or optical properties unattainable in nature. The latter are determined not even by the characteristics of their constituent substances, namely the structure. After all, houses that are similar in appearance can be built from the same materials, but one will have a different soundproofed, and in another you will even hear the breathing of your neighbor from the apartment opposite. What's the secret? Only in the ability of the builder to manage the funds provided.

At the moment, materials scientists have already created many structures whose properties are not found in nature, although they do not go beyond the boundaries of physical laws. For example, one of the created metamaterials can control sound waves so brilliantly that they hold a small ball in the air. It consists of two gratings assembled using bricks filled with thermoplastic rods, which are laid in a “snake” pattern. The sound wave is focused like light in a lens, and the researchers believe that this device will allow them to develop the control of sound to the ability to change its direction, as they now change the path of a light beam using optics.

© Illustration by RIA Novosti. A. Polyanina

© Illustration by RIA Novosti. A. Polyanina

Another metamaterial can rearrange itself. The object is assembled from it without the help of hands, because the change in shape can be programmed! The structure of such a “smart” material consists of cubes, each wall of which is made up of two outer layers of polyethylene terephthalate and one inner layer of double-sided adhesive tape. This design allows you to change the shape, volume and even rigidity of an object.

But the most amazing properties are those of optical metamaterials, which can change the visual perception of reality. They “work” in the wavelength range that the human eye can see. It is from such materials that scientists have created a fabric from which an invisibility cloak can be made.

True, so far only a micro-object can be made invisible in the optical range.

The possibility of creating a material with a negative refractive angle was predicted back in 1967 by Soviet physicist Viktor Veselago, but only now are the first examples of real structures with such properties appearing. Due to the negative refractive angle, rays of light bend around an object, making it invisible. Thus, the observer notices only what is happening behind the back of the person wearing the “wonderful” cloak.

© Photo: Xiang Zhang group, Berkeley Lab/UC Berkeley

© Photo: Xiang Zhang group, Berkeley Lab/UC Berkeley

The latest achievement in the creation of optical metamaterials belongs to Russian scientists from NUST MISIS. Moreover, the most common “ingredients” were used - air, glass and water. The scientists' work was published in one of the highest-rated journals in the world, Scientific Reports. publishing house Nature. “, each such sample can cost thousands of euros,” emphasized Alexey Basharin, a researcher at the NUST MISIS Laboratory of Superconducting Metamaterials, Candidate of Technical Sciences. — In addition, the probability of error when forming such a system is very high even with the use of the most high-precision tools. However, if you create a larger-scale material that contains not optical (400-700 nm), but radio waves (7-8 cm long), the physics of the process This scaling will not change, but the technology for creating them will become simpler."

By studying the properties of the created structures, the authors of the work showed that this type of substance has several practical applications. First of all, these are sensors of complex molecules, since the latter, when entering the field of the metamaterial, begin to glow. In this way, even single molecules can be determined, which could potentially have a significant impact on the development of, for example, forensic science. In addition, such a metamaterial can be used as a light filter, isolating light of a certain length from the incident radiation. It is also applicable as the basis for creating ultra-reliable magnetic memory, because the structure of the metamaterial cells prevents them from reversing magnetization to each other and thereby losing information.

Speed ​​of light ratio With in vacuum to phase velocity v light in the environment:

called absolute refractive index this environment.

ε - relative dielectric constant,

μ - relative magnetic permeability.

For any medium other than vacuum, the value n depends on the frequency of light and the state of the medium (its temperature, density, etc.). For rarefied environments (for example, gases under normal conditions).

Most often, the refractive index of a material is remembered when considering the effect of light refraction at the interface between two optical media.

This phenomenon is described Snell's law:

where α is the angle of incidence of light coming from a medium with a refractive index n 1, and β is the angle of refraction of light in a medium with a refractive index n 2.

For all media that can be found in nature, the rays of incident and refracted light are on opposite sides of the normal restored to the interface between the media at the point of refraction. However, if we formally substitute into Snell’s law n 2<0 , the following situation is realized: the rays of incident and refracted light are on one side of the normal.

The theoretical possibility of the existence of unique materials with a negative refractive index was pointed out by the Soviet physicist V. Veselago almost 40 years ago. The fact is that the refractive index is related to two other fundamental characteristics of matter, dielectric constant ε and magnetic permeability μ , by a simple relation: n 2 = ε·μ. Despite the fact that this equation is satisfied by both positive and negative values ​​of n, scientists for a long time refused to believe in the physical meaning of the latter - until Veselago showed that n< 0 in the event that at the same time ε < 0 And μ < 0 .

Natural materials with a negative dielectric constant are well known - any metal at frequencies above the plasma frequency (at which the metal becomes transparent). In this case ε < 0 is achieved due to the fact that free electrons in the metal shield the external electromagnetic field. It is much more difficult to create material with μ < 0 , such materials do not exist in nature.

It took 30 years before the English scientist John Pendry showed in 1999 that negative magnetic permeability could be obtained for a conductive ring with a gap. If you place such a ring in an alternating magnetic field, an electric current will arise in the ring, and an arc discharge will appear at the gap. Since inductance can be attributed to a metal ring L, and the gap corresponds to the effective capacitance WITH, the system can be considered as a simple oscillatory circuit with a resonant frequency ω 0 ~ 1/(LC) -1/2. In this case, the system creates its own magnetic field, which will be positive at frequencies of the alternating magnetic field ω < ω 0 and negative at ω > ω 0 .

Thus, systems with a negative response to both the electrical and magnetic components of electromagnetic radiation are possible. American researchers under the leadership of David Smith were the first to combine both systems in one material in 2000. The created metamaterial consisted of metal rods responsible for ε < 0 , and copper ring resonators, thanks to which it was possible to achieve μ < 0 .

Undoubtedly, such a structure can hardly be called a material in the traditional sense of the word, since it consists of individual macroscopic objects. Meanwhile, this structure is “optimized” for microwave radiation, the wavelength of which is significantly longer than the individual structural elements of the metamaterial. Therefore, from the point of view of microwaves, the latter is also homogeneous, like, for example, optical glass for visible light. By successively reducing the size of structural elements, it is possible to create metamaterials with a negative refractive index for the terahertz (from 300 GHz to 3 THz) and infrared (from 1.5 THz to 400 THz) spectral ranges. Scientists expect that, thanks to the achievements of modern nanotechnology, metamaterials for the visible range of the spectrum will be created in the very near future.

The practical use of such materials is, first of all, associated with the possibility of creating terahertz optics based on them, which, in turn, will lead to the development of meteorology and oceanography, the emergence of radars with new properties and all-weather navigation tools, devices for remote diagnostics of the quality of parts and safety systems that allow you to detect weapons under clothing, as well as unique medical devices.

Properties

Passage of light through a metamaterial with a “left-handed” refractive index.

One of the possible properties of metamaterials is a negative (or left-handed) refractive index, which appears when the permittivity and magnetic permeability are simultaneously negative.

Effect Basics

The equation for the propagation of electromagnetic waves in an isotropic medium has the form:

Where k (\displaystyle k)- wave vector, ω (\displaystyle \omega )- wave frequency, c (\displaystyle c)- speed of light, n 2 = ϵ μ (\displaystyle n^(2)=\epsilon \mu )- square of the refractive index. From these equations it is obvious that the simultaneous change of signs of the dielectric and magnetic μ (\displaystyle \mu ) the permeability of the medium will not affect these relationships in any way.

“Right” and “Left” isotropic media

Equation (1) is derived based on Maxwell's theory. For media with dielectric ϵ (\displaystyle \epsilon ) and magnetic μ (\displaystyle \mu ) the susceptibility of the medium is simultaneously positive, three vectors of the electromagnetic field - electric and magnetic and wave form a so-called system. right vectors:

Such environments are accordingly called “right-wing”.

Environments that ϵ (\displaystyle \epsilon ), μ (\displaystyle \mu )- at the same time negative, called “left”. In such media, electric E → (\displaystyle (\vec (E))), magnetic H → (\displaystyle (\vec (H))) and wave vector k → (\displaystyle (\vec (k))) form a system of left vectors.

In English-language literature, the described materials may be called right- and left-handed materials, or abbreviated as RHM (right) and LHM (left), respectively.

Transfer of energy by right and left waves

The flux of energy carried by the wave is determined by the Poynting vector, which is equal to S → = (c / 4 π) [ E → H → ] (\displaystyle (\vec (S))=(c/4\pi)\left[(\vec (E))(\vec (H)) \right]). Vector S → (\displaystyle (\vec (S))) always forms with vectors E → (\displaystyle (\vec (E))), H → (\displaystyle (\vec (H))) right three. Thus, for right-handed substances S → (\displaystyle (\vec (S))) And k → (\displaystyle (\vec (k))) directed in one direction, and for the left - in different directions. Since vector k → (\displaystyle (\vec (k))) coincides in direction with the phase velocity, it is clear that the left-handed substances are substances with the so-called negative phase velocity. In other words, in left-handed substances the phase velocity is opposite to the energy flow. In such substances, for example, a reversed Doppler effect and backward waves are observed.

Left medium dispersion

The existence of a negative indicator of a medium is possible if it has frequency dispersion. If at the same time ϵ < 0 {\displaystyle \epsilon <0} , μ < 0 {\displaystyle \mu <0} , then the wave energy W = ϵ E 2 + μ H 2 (\displaystyle W=\epsilon E^(2)+\mu H^(2)) will be negative(!). The only way to avoid this contradiction is if the medium has frequency dispersion ∂ ϵ / ∂ ω (\displaystyle \partial \epsilon /\partial \omega ) And ∂ μ / ∂ ω (\displaystyle \partial \mu /\partial \omega ).

Examples of wave propagation in a left-handed medium