Metamaterials with a negative refractive index. Nano-alphabet: metamaterials Dispersion of the left-handed medium

Metamaterials are special composite materials that are obtained by artificial modification of the elements introduced into them. The structure is changed at the nanoscale, which makes it possible to change the sizes, shapes and lattice periods of the atom, as well as other parameters of the material. Thanks to the artificial transformation of the structure, the modified object acquires completely new properties that materials of natural origin do not have.

Thanks to the above transformation, the magnetic, dielectric permeability, as well as other physical indicators of the selected object are modified. As a result, the transformed materials acquire unique optical, radiophysical, electrical and other properties, which open up broad prospects for the development of scientific progress. Work in this direction can lead to the emergence of completely new devices and inventions that will amaze the imagination. These are invisibility cloaks, super lenses and much more.

Kinds

Metamaterials are usually classified according to their degree of refraction:

• One-dimensional. In them, the degree of refraction constantly changes only in a single direction in space. Such materials are made of layers of elements arranged in parallel and having different degrees of refraction. They are able to demonstrate unique properties only in a single direction of space, which is perpendicular to the specified layers.
• 2D. In them, the degree of refraction constantly changes in only 2 directions of space. Such materials are in most cases made of rectangular structures having refraction m1 and located in a medium with refraction m2. At the same time, elements with refraction m1 are located in a 2-dimensional lattice with a cubic base. As a result, such materials are able to demonstrate their properties in 2 directions of space. But the two-dimensionality of materials is not limited to just a rectangle; it can be created using a circle, ellipse or other arbitrary shape.
• 3D. In them, the degree of refraction constantly changes in 3 directions of space. Such materials can be conventionally represented as an array of areas in a volumetric sense (ellipse, cube, and so on), located in a three-dimensional lattice.

Metamaterials are also divided into:

• Conductors. They move quasiparticles over significant distances, but with small losses.
• Dielectrics . The mirrors are in almost perfect condition.
• Semiconductors . These are elements that can, for example, reflect quasiparticles only of a certain wavelength.
• Superconductors . In these materials, quasiparticles can travel almost unlimited distances.

In addition, there are materials:

• Non-resonant.
• Resonant.

The difference between resonant materials and non-resonant elements is that they have a dielectric constant only at a certain resonance frequency.

Metamaterials can be created with different electrical properties. Therefore, they are divided according to their relative permeability:

• DNG, that is, double negative - the permeabilities are negative.
• DPS, that is, double positive - the permeabilities are positive.
• Hi-Z, that is, high impedance surfaces.
• SNG, that is, single negative - materials of mixed type.
• DZR, that is, double zero – the material has a permeability equal to zero.

Device

Metamaterials are substances whose properties are provided by a microscopic structure introduced by people. They are synthesized by incorporating periodic structures with various geometric shapes into a given element of natural origin, modifying the magnetic and dielectric susceptibility of the original structure.

Conventionally, such inclusions can be considered as artificial atoms that are quite large in size. During synthesis, the creator of the material has the opportunity to give it various parameters, which are based on the shape and size of the structures, period variability, and the like. Thanks to this, it is possible to obtain materials that have amazing properties.

One of the most famous such elements are photonic crystals. Their peculiarity is manifested by a periodic change in the degree of refraction in space in one, two and three directions. Thanks to these parameters, the material can have zones that may or may not receive photon energy.

As a result, if a photon with a certain energy (of the required frequency and wavelength) that does not correspond to the zone of the specified crystal is released onto the specified substance, then it is reflected in the opposite direction. If a photon with parameters that correspond to the parameters of the allowed zone hits the crystal, then it moves along it. In another way, the crystal acts as an optical filter element. That is why these crystals have incredibly rich and bright colors.

Operating principle

The main feature of artificially formed materials is the periodicity of their structure. It could be 1D, 2D or 3D structure. In fact, they can have very different structures. For example, they can be arranged as dielectric elements, between which there will be open wire rings. In this case, the rings can be deformed from round to square.

To ensure that electrical properties are maintained at any frequency, the rings are structured closed. In addition, rings in a substance are often arranged randomly. The realization of the unique parameters of a new substance occurs at resonance of its frequency, as well as the effective frequency of an electromagnetic wave from the outside.

Application

Metamaterials are and will continue to be widely used in all areas where electromagnetic radiation is used. These are medicine, science, industry, space equipment and much more. Today, a huge amount of electromagnetic materials are being created that are already being used.

• In radiophysics and astronomy, special coatings are used that are excellently used to protect telescopes or sensors that use long-wave radiation.
• In optics, diffraction refraction also finds wide application. For example, a superlens has already been created, which allows us to solve the problem of the diffraction limit of resolution of standard optics. As a result, the first experimental sample of the lens demonstrated phenomenal performance; its resolution was 3 times higher than the existing diffraction limit.

• In microelectronics, metamaterials can produce a real revolution that can change the life of almost every person on Earth. This could lead to the emergence of orders of magnitude smaller and incredibly efficient devices and antennas for mobile phones. Thanks to new materials, it will be possible to expand the density of data storage, which means that disks and many other electronic devices will appear that will be able to have a significant amount of memory;
• Creating incredibly powerful lasers. Thanks to the use of materials with a modified structure, powerful lasers are already appearing, which, with less energy consumed, produce an order of magnitude powerful and destructive light pulse. As a result, laser weapons may appear that will make it possible to shoot down ballistic missiles located at a distance of tens of kilometers.

Industrial lasers will be able to efficiently cut not only metal materials with a thickness of several tens of millimeters, but also those that are an order of magnitude larger.

Thanks to new laser systems, new industrial 3D printers will appear that will be able to print metal products quickly and with high quality. In terms of their quality, they will be practically not inferior to products produced using typical metalworking methods. For example, it could be a gear or other complex part, the production of which under normal conditions would require a lot of time and effort.

• Creation of new anti-reflective materials. Thanks to their creation and use, it will be possible to create fighters, bombers, ships, submarines, tanks, robotic systems, mobile installations such as Yars and Sarmat, which will not be visible to enemy sensors and radars. Similar technologies can already be used in sixth and seventh generation fighters.

Already today it is possible to ensure “invisibility” for equipment in the terahertz frequency range. In the future, it will be possible to create technology that will be invisible in the entire frequency range, including “visible” to the human eye. One such solution is the invisibility cloak. At the moment, the invisibility cloak can already hide small objects, but it has some flaws.

• Ability to see through walls. The use of new artificial materials will make it possible to create devices that will allow you to see through walls. Already today, devices are being created that exhibit a strong magnetic response to radiation in the terahertz range.
• Creating a bluff wall or non-existent “copies” of military equipment. Metamaterials allow you to create the illusion of the presence of an object in a place where it does not exist. For example, similar technologies are already being used by the Russian military to create many non-existent missiles that “fly” next to the real one in order to deceive the enemy’s missile defense system.

Metamaterial

Metamaterial- a composite material, the properties of which are determined not so much by the properties of its constituent elements, but by an artificially created periodic structure.

Metamaterials are synthesized by introducing into the original natural material various periodic structures with a variety of geometric shapes, which modify the dielectric “ε” and magnetic “μ” susceptibility of the original material. To a very rough approximation, such implants can be considered as atoms of extremely large sizes artificially introduced into the source material. The developer of metamaterials, when synthesizing them, has the opportunity to select (vary) various free parameters (sizes of structures, shape, constant and variable period between them, etc.).

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 dielectric and magnetic permeabilities are simultaneously negative. An example of such a metamaterial is shown in the Figure.

Effect Basics

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

where is the wave vector, is the wave frequency, is the speed of light, is the square of the refractive index. From these equations it is obvious that the simultaneous change of signs of the dielectric and magnetic susceptibility 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 in which the dielectric and magnetic susceptibility of the medium are 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 in which , are at the same time negative, are called “left”. In such media, the electric, magnetic and wave vectors form a system of left-handed vectors.

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

Transfer of energy by right and left waves

The flow of energy carried by the wave is determined by the Poynting vector, which is equal to . A vector always forms a right-hand triple with vectors. Thus, for right-handed substances and are directed in one direction, and for left-handed ones - in different directions. Since the vector 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, an inverted Doppler effect is 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 , , then the wave energy will be negative(!). The only way to avoid this contradiction is if the medium has frequency dispersion and .

Examples of wave propagation in a left-handed medium

Superlens

This proposal by J. Pendry was criticized as untenable by Victor Veselago. Thus, the issue of creating superlenses based on left-handed media is currently being discussed, and experimental attempts to create lenses continue.

The first experimentally demonstrated negative index superlens had a resolution three times better than the diffraction limit. The experiment was carried out at microwave frequencies. The superlens was implemented in the optical range in 2005. It was a lens that did not use negative refraction, but used a thin layer of silver to amplify the evanescent waves.

The latest advances in the creation of superlenses are presented in the review. To create a superlens, alternating layers of silver and magnesium fluoride deposited on a substrate are used, onto which a nanograting is then cut. The result was a three-dimensional composite structure with a negative refractive index in the near-infrared region. In the second case, the metamaterial was created using nanowires that were electrochemically grown on a porous alumina surface.

At the beginning of 2007, the creation of a metamaterial with a negative refractive index in the visible region was announced. The material's refractive index at a wavelength of 780 nm was −0.6.

Application

Recently, reports have appeared from a number of scientific centers that another step has been taken towards creating an invisibility cloak. This cloak makes it possible to make the object it covers invisible, since it does not reflect light.

Due to the fact that metamaterials have a negative refractive index, they are ideal for camouflaging objects, since they cannot be detected by radio reconnaissance.

Story

In most cases, the history of the issue of materials with a negative refractive index begins with a mention of the work of the Soviet physicist Viktor Veselago, published in the journal "Uspekhi Fizicheskikh Nauk" for the year (http://ufn.ru/ru/articles/1967/7/d/ ). The article discussed the possibility of a material with a negative refractive index, which was called "left-handed". The author came to the conclusion that with such a material almost all known optical phenomena of wave propagation change significantly, although at that time materials with a negative refractive index were not yet known. Here, however, it should be noted that in reality, much earlier such “left-handed” media were discussed in the work of Sivukhin (Sivukhin D.V. // Optics and Spectroscopy, T.3, P.308 (1957)) and in the articles of Pafomov (Pafomov V. E. // JETP, T.36, P.1853 (1959); T.33, P.1074 (1957); T.30, P.761 (1956)). A detailed description of the history of the issue can be found in the work of V. M. Agranovich and Yu. N. Gartstein (http://ufn.ru/ru/articles/2006/10/c/).

In recent years, intensive research has been carried out on phenomena associated with a negative refractive index. The reason for the intensification of these studies was the emergence of a new class of artificially modified materials with a special structure, called metamaterials. The electromagnetic properties of metamaterials are determined by the elements of their internal structure, placed according to a given pattern at the microscopic level. Therefore, the properties of these materials can be changed so that they have a wider range of electromagnetic characteristics, including a negative refractive index.

see also

Notes

1. Engheta Nader Metamaterials: Physics and Engineering Explorations. - Wiley & Sons. - P. xv, 3–30, 37, 143–150, 215–234, 240–256. - ISBN 9780471761020
2. Smith, David R. What are Electromagnetic Metamaterials? . Novel Electromagnetic Materials. The research group of D.R. Smith (June 10, 2006). Archived from the original on February 15, 2012. Retrieved August 19, 2009.
3. collection of free-download papers by J. Pendry
4. Veselago V. G. Electrodynamics of materials with a negative refractive index // UFN. - 2003. - 7. - p. 790-794. - DOI:10.3367/UFNr.0173.200307m.0790
5. Munk, B. A. Metamaterials: Critique and Alternatives. - Hoboken, N.J.: John Wiley, 2009. - ISBN 0470377046
6. A. Grbic and G.V. Eleftheriades (2004). "Overcoming the Diffraction Limit with a Planar Left-handed Transmission-line Lens." Physical Review Letters 92 . DOI:10.1103/PhysRevLett.92.117403.
7. N. Fang et al. (2005). "Sub-Diffraction-Limited Optical Imaging with a Silver Superlens." Science 308 (5721): 534–7. DOI:10.1126/science.1108759. PMID 15845849. Lay summary.
8. (2008) “Metamaterials Bend Light to new Levels.” Chemical & Engineering News 86 (33).
9. J. Valentine et al. (2008). "Three-dimensional optical metamaterial with a negative refractive index." Nature 455 (7211): 376–9.

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.

Constructed from a metamaterial with amazing optical properties, the superlens can create images with detail smaller than the wavelength of light used.

Almost 40 years ago, Soviet scientist Viktor Veselago put forward a hypothesis about the existence of materials with a negative refractive index (UFN, 1967, vol. 92, p. 517). The light waves in them must move against the direction of propagation of the beam and generally behave in an amazing way, while lenses made from these materials must have magical properties and unsurpassed characteristics. However, all known substances have a positive refractive index: after several years of intensive searches, Veselago did not find a single material with suitable electromagnetic properties, and his hypothesis was forgotten. They remembered it only at the beginning of the 21st century. (cm.: ).

Thanks to recent advances in materials science, Veselago's idea has been revived. The electromagnetic properties of substances are determined by the characteristics of the atoms and molecules that form them, which have a rather narrow range of characteristics. Therefore, the properties of the millions of materials known to us are not so diverse. However, in the mid-1990s. scientists from the Center for Materials Technology. Marconi in England began creating metamaterials that consist of macroscopic elements and scatter electromagnetic waves in a completely different way than any known substances.

In 2000, David Smith and colleagues at the University of California, San Diego fabricated a metamaterial with a negative refractive index. The behavior of light in it turned out to be so strange that theorists had to rewrite books on the electromagnetic properties of substances. Experimentalists are already developing technologies that take advantage of the amazing properties of metamaterials, creating superlenses that can produce images with details smaller than the wavelength of light used. With their help, it would be possible to make microcircuits with nanoscopic elements and record huge amounts of information on optical disks.

Negative refraction

To understand how negative refraction occurs, let us consider the mechanism of interaction of electromagnetic radiation with matter. An electromagnetic wave (such as a beam of light) passing through it causes the electrons of atoms or molecules to move. This consumes part of the wave energy, which affects its properties and the nature of propagation. To obtain the required electromagnetic characteristics, researchers select the chemical composition of the material.

But as the example of metamaterials shows, chemistry is not the only way to obtain interesting properties of matter. The electromagnetic response of a material can be "engineered" by creating tiny macroscopic structures. The fact is that usually the length of an electromagnetic wave is several orders of magnitude greater than the size of atoms or molecules. The wave “sees” not an individual molecule or atom, but the collective reaction of millions of particles. This is also true for metamaterials, the elements of which are also significantly smaller than the wavelength.

The field of electromagnetic waves, as their name suggests, has both an electrical and a magnetic component. Electrons in a material move back and forth under the influence of an electric field and in a circle under the influence of a magnetic field. The degree of interaction is determined by two characteristics of the substance: dielectric constant ε and magnetic permeability μ . The first shows the degree of reaction of electrons to an electric field, the second - the degree of reaction to a magnetic field. The vast majority of materials ε And μ Above zero.

The optical properties of a substance are characterized by its refractive index n, which is associated with ε And μ simple relation: n = ± √(ε∙μ). All known materials must have a "+" sign in front of the square root and therefore have a positive refractive index. However, in 1968 Veselago showed that substances with negative ε And μ refractive index n must be less than zero. Negative ε or μ are obtained when electrons in a material move in the opposite direction to the forces created by electric and magnetic fields. Although this behavior seems paradoxical, getting electrons to move against the forces of electric and magnetic fields is not that difficult.

If you push the pendulum with your hand, it will obediently move in the direction of the push and begin to oscillate with the so-called resonant frequency. By pushing the pendulum in time with the swing, you can increase the amplitude of the oscillations. If you push it with a higher frequency, then the shocks will no longer coincide with the oscillations in phase, and at some point the hand will be hit by a pendulum moving towards it. Similarly, electrons in a material with a negative refractive index go out of phase and begin to resist the “pushes” of the electromagnetic field.

Metamaterials

The key to this kind of negative reaction is resonance, that is, the tendency to vibrate at a specific frequency. It is created artificially in a metamaterial using tiny resonant circuits that simulate the response of a substance to a magnetic or electric field. For example, in a broken ring resonator (RRR), a magnetic flux passing through a metal ring induces circular currents in it, similar to the currents that cause the magnetism of some materials. And in a lattice of straight metal rods, the electric field creates currents directed along them.

Free electrons in such circuits oscillate with a resonant frequency, depending on the shape and size of the conductor. If a field with a frequency below the resonant frequency is applied, a normal positive response will be observed. However, as the frequency increases, the response becomes negative, just as in the case of a pendulum moving towards you if you push it with a frequency above the resonant one. Thus, conductors in a certain frequency range can respond to an electric field as a medium with a negative ε , and rings with cuts can imitate material with a negative μ . These conductors and rings with cuts are the elementary blocks needed to create a wide range of metamaterials, including those that Veselago was looking for.

The first experimental confirmation of the possibility of creating a material with a negative refractive index was obtained in 2000 at the University of California at San Diego ( UCSD). Because the fundamental building blocks of the metamaterial must be much smaller than the wavelength, the researchers worked with centimeter-wavelength radiation and used elements a few millimeters in size.

Californian scientists have designed a metamaterial consisting of alternating conductors and RKR, assembled in the form of a prism. The conductors provided negative ε , and rings with cuts - negative μ . The result should have been a negative refractive index. For comparison, a prism of exactly the same shape was made from Teflon, which n= 1.4. The researchers directed a beam of microwave radiation at the edge of the prism and measured the intensity of the waves emerging from it at different angles. As expected, the beam was positively refracted by the Teflon prism and negatively refracted by the metamaterial prism. Veselago's assumption became a reality: a material with a negative refractive index was finally obtained. Or not?

Desired or actual?

Experiments in UCSD along with the remarkable new predictions that physicists were making about the properties of materials with a negative refractive index, sparked a wave of interest among other researchers. When Veselago expressed his hypothesis, metamaterials did not yet exist, and experts did not carefully study the phenomenon of negative refraction. Now they began to pay much more attention to her. Skeptics have asked whether materials with a negative refractive index violate fundamental laws of physics. If this turned out to be the case, the entire research program would be called into question.

The most heated debate was caused by the question of wave speed in complex material. Light travels in a vacuum at maximum speed c= 300 thousand km/s. The speed of light in the material is less: v =c/n. But what happens if n negative? A simple interpretation of the formula for the speed of light shows that light travels in the opposite direction.

A more complete answer takes into account that the wave has two speeds: phase and group. To understand their meaning, imagine a pulse of light moving through a medium. It will look something like this: The amplitude of the wave increases to a maximum at the center of the pulse, and then decreases again. Phase velocity is the speed of the individual bursts, and group velocity is the speed at which the pulse envelope is moving. They don't have to be the same.

Veselago discovered that in a material with a negative refractive index, the group and phase velocities move in opposite directions: individual maxima and minima move backward, while the entire momentum moves forward. It is interesting to consider how a continuous beam of light from a source (for example, a spotlight) immersed in a material with a negative refractive index will behave. If we could observe individual oscillations of a light wave, we would see them appear on an object illuminated by the beam, move backwards, and ultimately disappear into the spotlight. However, the energy of the light beam moves forward, moving away from the light source. It is in this direction that the beam actually propagates, despite the surprising backward motion of its individual oscillations.

In practice, it is difficult to observe individual oscillations of a light wave, and the shape of the pulse can be very complex, so physicists often use a clever trick to show the difference between phase and group velocities. When two waves with slightly different wavelengths move in the same direction, they interfere, creating a pattern of beats whose peaks move with group velocity.

Applying this technique to the experiment UCSD refraction in 2002, Prashant M. Valanju and his colleagues at the University of Texas at Austin observed something interesting. Refracting at the interface between media with a negative and positive refractive index, two waves with different wavelengths were deflected at slightly different angles. The beat pattern turned out not as it should have been for rays with negative refraction, but as it should have been with positive refraction. By comparing the pattern of beats with group velocity, the Texas researchers concluded that any physically feasible wave should experience positive refraction. Although a material with a negative refractive index could exist, negative refraction cannot be achieved.

How then can we explain the results of experiments in UCSD? Valanjou and many other researchers attributed the observed negative refraction to other phenomena. Perhaps the sample absorbed so much energy that the waves only emerged from the narrow side of the prism, simulating negative refraction? After all, metamaterial UCSD really strongly absorbs radiation, and the measurements were carried out near the prism. Therefore, the absorption hypothesis looks quite plausible.

The findings were of great concern: they could invalidate not only the experiments UCSD, but also the whole range of phenomena predicted by Veselago. However, after some thought, we realized that we cannot rely on the beat pattern as an indicator of group velocity: for two waves moving in different directions, the interference pattern has nothing to do with the group velocity.

As the critics' arguments began to crumble, further experimental evidence for negative refraction emerged. Minas Tanielian Group ( Minas Tanielian) from the company Boeing Phantom Works in Seattle repeated the experiment UCSD with a prism made of metamaterial with very low absorption. In addition, the sensor was located much further from the prism so that absorption in the metamaterial could not be confused with negative refraction of the beam. The superior quality of the new data puts an end to doubts about the existence of negative refraction.

To be continued

As the smoke of the battle cleared, we began to realize that the remarkable story Veselago told was not the last word on negative-index materials. The Soviet scientist used the method of geometrically constructing light rays, taking into account reflection and refraction at the boundaries of various materials. This powerful technique helps us understand, for example, why objects in a swimming pool appear closer to the surface than they actually are, and why a pencil half-immersed in liquid appears bent. The thing is that the refractive index of water ( n= 1.3) is greater than that of air, and light rays are refracted at the boundary between air and water. The refractive index is approximately equal to the ratio of real depth to apparent depth.

Veselago used ray tracing to predict that the beam was made of a material with a negative refractive index n= −1 should act as a lens with unique properties. Most of us are familiar with lenses made from positive refractive materials - in cameras, magnifiers, microscopes and telescopes. They have a focal length, and where the image is formed depends on a combination of the focal length and the distance between the object and the lens. Images typically differ in size from the object, and lenses work best for objects that lie on an axis through the lens. The Veselago lens works completely differently from conventional ones: its operation is much simpler, it only affects objects located next to it, and transfers the entire optical field from one side of the lens to the other.

Veselago's lens is so unusual that John Pendry ( John B. Pendry) I had to wonder: how perfectly can it work? And in particular, what could be the maximum resolution of the Veselago lens? Optical elements with a positive refractive index are limited by the diffraction limit—they can resolve features that are equal to or larger than the wavelength of light reflected from the object. Diffraction places an ultimate limit on all imaging systems, like the smallest object that can be seen with a microscope, or the smallest distance between two stars that a telescope can resolve. Diffraction also determines the smallest detail that can be created in the optical lithography process in the production of microchips (chips). Likewise, diffraction limits the amount of information that can be stored or read on an optical digital video disc (DVD). A way to bypass the diffraction limit could revolutionize technology, allowing optical lithography to penetrate the nanoscale range and possibly increase the amount of data stored on optical disks by hundreds of times.

To determine whether negative refractive optics could actually outperform conventional (“positive”) optics, we need to go further than just looking at the path of rays. The former approach neglects diffraction and thus cannot be used to predict the resolution of negatively refractive lenses. To include diffraction, we had to use a more precise description of the electromagnetic field.

Superlens

To describe it more precisely, electromagnetic waves from any source—emitting atoms, radio antennas, or a beam of light—after passing through a small hole create two different types of fields: far field and near field. The far field, as its name indicates, is observed far from an object and is captured by a lens, forming an image of the object. Unfortunately, this image contains only a rough picture of the object, in which diffraction limits resolution to wavelength. The near field contains all the fine details of an object, but its intensity quickly decreases with distance. Positive refractive lenses offer no chance of intercepting the extremely weak near field and transmitting its data into the image. However, this is not true for negative refractive lenses.

Having studied in detail how the source's near and far fields interact with the Veselago lens, Pendry in 2000, to everyone's surprise, came to the conclusion that the lens, in principle, could focus both near and far fields. If this stunning prediction were to be true, it would mean that the Veselago lens, unlike all other known optics, is not subject to the diffraction limit. Therefore, a flat structure with negative refraction was called a superlens.

In subsequent analysis, we and others found that the resolution of the superlens is limited by the quality of its negative refractive material. For best performance, it is necessary not only that the refractive index n was equal to −1, but also that ε and μ were both equal to −1. A lens for which these conditions are not met has sharply degraded resolution. The simultaneous fulfillment of these conditions is a very serious requirement. But in 2004 Anthony Grbic ( Anthony Grbic) and George Eleftheriades ( George V. Eleftheriades) from the University of Toronto have experimentally shown that a metamaterial constructed to have ε =−1, and μ =−1 in the radio frequency range can indeed resolve objects on a scale smaller than the diffraction limit. Their result proved that a superlens can be built, but can it be created for even shorter optical wavelengths?

The difficulty of scaling metamaterials to optical wavelengths has two sides. First, the metallic conductive elements that form the metamaterial chips, such as conductors and split rings, need to be scaled down to the nanometer scale so that they are smaller than the wavelength of visible light (400-700 nm). Secondly, short wavelengths correspond to higher frequencies, and metals at such frequencies have poorer conductivity, thus suppressing the resonances on which the properties of metamaterials are based. In 2005 Kostas Soukolis ( Costas Soukoulis) from the University of Iowa and Martin Wegener ( Martin Wegener) from the University of Karlsruhe in Germany have experimentally demonstrated that it is possible to make slit rings that operate at wavelengths as low as 1.5 microns. Despite the fact that at such short wavelengths the resonance on the magnetic component of the field becomes very weak, interesting metamaterials can still be formed with such elements.

But we cannot yet make a material that, at visible light wavelengths, results in μ =−1. Fortunately, a compromise is possible. When the distance between the object and the image is much smaller than the wavelength, only the condition ε =−1 needs to be satisfied, and the value of μ can be neglected. Just last year Richard Blakey's band ( Richard Blaikie) from the University of Canterbury in New Zealand and Xiang Jang's group ( Xiang Zhang) from the University of California, Berkeley, following these guidelines, independently demonstrated superresolution in an optical system. At optical wavelengths, the metal's intrinsic resonances can result in a negative dielectric constant (ε). Therefore, a very thin layer of metal at a wavelength where ε = −1 can act as a superlens. Both Blakey and Jung used a layer of silver about 40 nm thick to image beams of 365 nm light emitted by shaped holes smaller than the wavelength of the light. Although the silver film was far from an ideal lens, the silver superlens significantly improved image resolution, proving the basic principle of the superlens to be correct.

A look into the future

The superlens demonstration is just the latest of many predictions about the properties of negatively refractive materials to come, a sign of the rapid progress taking place in this expanding field. The possibility of negative refraction forced physicists to reconsider almost the entire field of electromagnetism. And when this range of ideas is fully understood, basic optical phenomena such as refraction and the diffraction limit of resolution will have to be reconsidered to take into account the new unexpected twists associated with negatively refractive materials.

The magic of metamaterials and the magic of negative refraction still needs to be “converted” into applied technology. Such a step will require improving the design of metamaterials and producing them at a reasonable cost. There are now many research groups in this area, vigorously developing ways to solve the problem.

Theory and practice of Victor Veselago

The fate of Viktor Georgievich Veselago, Doctor of Physical and Mathematical Sciences, IOFAN employee and professor at the Moscow Institute of Physics and Technology, played an interesting joke on him. Having devoted his entire life to practice and experiment, he received international recognition for his theoretical prediction of one of the most interesting phenomena of electrodynamics.

Fateful accident

Viktor Georgievich Veselago was born on June 13, 1929 in Ukraine and, according to him, until a certain point he was not interested in physics. And then one of those fateful accidents occurred that change not only the direction of a person’s life, but also, ultimately, the vector of the development of science. In the seventh grade, the boy fell ill and, in order to pass the time, began to read all the books in a row. Among them was “What is radio?” Kina, after reading which the schoolboy became seriously interested in radio engineering. At the end of the tenth grade, when the question of choosing a university arose, one of my friends mentioned that a new physics and technology department was opening at Moscow University, where, in addition to other specialties, there was also radiophysics.

Applicants to the Moscow State University Technical Faculty had to endure a “marathon” of nine exams. At the very first of them - written mathematics - Veselago received a “two”... Today he explains this “embarrassment” by the fact that he was simply confused, finding himself in a huge audience, where he literally felt like a grain of sand. The next day, when he came to pick up his documents, Deputy Dean Boris Osipovich Solonouts (who was simply called BOS behind his back) advised him to come to the next exam. Since there was nothing to lose, the young man did just that. I passed all the other eight exams with straight A's and was accepted. Later, many years later, it turned out that there were quite a lot of such “losers”, and the dean’s office decided not to screen out applicants based on the results of the first exam.

Then there were four years of study, which Viktor Georgievich now calls the happiest time of his life. Students were given lectures by such luminaries as Pyotr Leonidovich Kapitsa, Lev Davidovich Landau... Viktor Veselago spent his summer internship at a radio astronomy station in Crimea, where he met its director, FIAN employee Professor Semyon Emmanuilovich Khaikin. It turned out that it was he who wrote the very book “What is Radio?”, signing the pseudonym Keen.

In 1951, the Faculty of Physics and Technology of Moscow State University was closed - it “grew” into the Moscow Institute of Physics and Technology, and students of the former Physics and Technology Faculty were distributed to other faculties. Viktor Georgievich ended up at the Faculty of Physics of Moscow State University and formally graduated from it, but considers himself a graduate of the Physics and Technology Institute. Veselago defended his thesis with Alexander Mikhailovich Prokhorov at the Physics Institute. P.N. Lebedev, where he later continued to work under his leadership. First - at FIAN, and from 1982 to this day - at the Institute of General Physics that spun off from it (IOFAN, which now bears the name of A.M. Prokhorov).

Construction of "Solenoid"

To obtain super-strong magnetic fields, in the 1960s, the Lebedev Physical Institute was building an installation called “Solenoid”. GIPRONII was involved in the design, but Viktor Georgievich developed the main elements of the project himself. He still believes that one of his most important achievements, besides scientific ones, was the ramp that allowed carts with heavy equipment to be brought to the ground floor. For the creation of an installation for producing strong magnetic fields, Veselago, together with a number of employees of the Lebedev Physical Institute and other scientific organizations, received a State Prize in 1974.

Left and right

In the 1960s, Viktor Georgievich became interested in materials that are both semiconductors and ferromagnets. In 1967, in the journal Uspekhi Fizicheskikh Nauk (UFN), he published an article entitled “Electrodynamics of substances with simultaneously negative values ​​of ε and μ,” where the term “substances with a negative refractive index n” was first introduced and their possible properties were described.

As the scientist explained, semiconductor properties are described through the value epsilon (ε) - dielectric constant, and magnetic properties through the value mu (μ) - magnetic permeability. These quantities are usually positive, although substances are known where ε is negative and μ is positive, or vice versa. Veselago wondered: what will happen if both quantities are negative? From a mathematical point of view this is possible, but from a physical point of view? Viktor Georgievich showed that such a state does not contradict the laws of nature, but the electrodynamics of such materials are noticeably different from those where and at the same time is greater than zero. First of all, the fact that in them the phase and group velocities of electromagnetic vibrations are directed in different directions (in a normal environment - in one direction).

Veselago called materials with a negative refractive index “left-handed,” and those with a positive refractive index, respectively, “right-handed,” based on the relative position of the three vectors characterizing the propagation of electromagnetic oscillations. Refraction at the boundary of two such media occurs specularly with respect to the z axis.

Having theoretically substantiated his ideas, Viktor Georgievich tried to implement them in practice, in particular, in magnetic semiconductors. However, it was not possible to obtain the required material. It was only in 2000 that a group of scientists from the University of California at San Diego in the USA, using a composite medium, proved that negative refraction is possible. Victor Veselago's research not only laid the foundation for a new scientific direction (see: D. Pandry, D. Smith. In Search of a Superlens), but also made it possible to clarify some physical formulas describing the electrodynamics of substances. The fact is that a number of formulas given in textbooks are applicable only in the so-called non-magnetic approximation, that is, when the magnetic permeability is equal to unity, namely, for the special case of non-magnetic materials. But for substances whose magnetic permeability is different from unity or negative, other, more general expressions are needed. Veselago also considers pointing out this circumstance an important result of his work.

Step into the Future

After the prophetic article, the researcher, true to the principle of changing topics every 5-6 years, became interested in new areas: magnetic fluids, photomagnetism, superconductivity.

In general, according to his recollections, during his time at FIAN-IOFAN he went through the standard path of a “Soviet scientist” - from a graduate student to a doctor of sciences, head of the department of strong magnetic fields, which by the end of the 1980s included about 70 people working in 5-7 different directions. In fact, the department was a small institute within an institute, which during this time produced more than 30 candidates of science.

Now Viktor Georgievich heads the laboratory of magnetic materials of the department of strong magnetic fields of the IOFAN named after. A. M. Prokhorova. For a series of works “Fundamentals of electrodynamics of media with a negative refractive index” in 2004 he was awarded the Academician V.A. Foka.

Viktor Georgievich has been teaching at the Moscow Institute of Physics and Technology for more than 40 years. Now he is a professor at the Department of Applied Physics, Faculty of Physics and Energy Problems, teaches the course he created “Fundamentals of Oscillation Physics,” and also conducts seminars and laboratory classes at the Department of General Physics.

V. G. Veselago belongs to a rare type of scientist, who is characterized by a breadth of scientific interests. He is an excellent theorist and at the same time an experimental physicist, engineer, designer of installations with strong magnetic fields. He is also talented as a professor, having made a great contribution to the teaching of general physics at MIPT and mentoring many students. It is these features of the scientist that make Viktor Georgievich’s personality so attractive.

Invasion of the World Wide Web

In the last 15 years, the physicist has again changed, or rather expanded, his range of interests, becoming the initiator of two network projects.

In 1993, the Infomag service was organized, distributing tables of contents of scientific and technical journals and foreign scientific electronic bulletins among scientists. It all started with the fact that IOFAN was one of the first to be connected to the Internet. Having acquired his first email address, Veselago became interested in physics teleconferences and began receiving the newsletter Physics News Update, which he forwarded to his colleagues. He then organized the distribution of contents and other scientific journals. The first publications that provided information to the Infomag service were the Journal of Experimental and Theoretical Physics (JETP), Letters to JETP, and Instruments and Experimental Techniques. Now the list includes more than 150 items.

The success of Infomag contributed to the creation of the second “brainchild” of Veselago - Russia’s first multi-subject electronic scientific journal “Researched in Russia”, which began its existence in 1998. It is published only in electronic form, and it publishes about 250 articles per year, both from the fields of natural sciences and humanities.

According to Viktor Georgievich, the need for electronic scientific publications in Russia is very great, not only as independent units, but also within the framework of online versions of printed publications. Several hundred academic scientific and technical journals are published in Russia, but the vast majority of them are not available in electronic form, and therefore domestic specialists do not have prompt access to the results of the work of their colleagues, which interferes with a fruitful and prompt dialogue between scientists.