Methods for manufacturing photonic crystals. Photonic crystals will be the basis for a new generation of microelectronics Research from the company mit photonic crystals

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Photonic crystals

Photonic crystals (PCs) are structures characterized by a periodic change in dielectric constant in space. The optical properties of PCs are very different from the optical properties of continuous media. The propagation of radiation inside a photonic crystal, due to the periodicity of the medium, becomes similar to the movement of an electron inside an ordinary crystal under the influence of a periodic potential. As a result, electromagnetic waves in photonic crystals have a band spectrum and coordinate dependence similar to Bloch waves of electrons in ordinary crystals. Under certain conditions, gaps form in the band structure of PCs, similar to forbidden electronic bands in natural crystals. Depending on the specific properties (material of the elements, their size and lattice period), both completely forbidden frequency zones, for which the propagation of radiation is impossible regardless of its polarization and direction, and partially forbidden (stop zones), in which distribution is possible only in selected directions.

Photonic crystals are interesting both from a fundamental point of view and for numerous applications. Based on photonic crystals, optical filters, waveguides (in particular, in fiber-optic communication lines), and devices that allow the control of thermal radiation are created and developed; laser designs with a reduced pump threshold have been proposed based on photonic crystals.

In addition to changing the reflection, transmission and absorption spectra, metal-dielectric photonic crystals have a specific density of photonic states. The changed density of states can significantly affect the lifetime of the excited state of an atom or molecule placed inside a photonic crystal and, consequently, change the character of luminescence. For example, if the transition frequency in an indicator molecule located in a photonic crystal falls into the band gap, then luminescence at this frequency will be suppressed.

FCs are divided into three types: one-dimensional, two-dimensional and three-dimensional.

One-, two- and three-dimensional photonic crystals. Different colors correspond to materials with different dielectric constants.

FCs with alternating layers made of different materials are one-dimensional.

Electron image of a one-dimensional PC used in a laser as a Bragg multilayer mirror.

Two-dimensional PCs can have more diverse geometries. These, for example, include arrays of cylinders of infinite length (their transverse size is much smaller than the longitudinal one) or periodic systems of cylindrical holes.

Electronic images of two-dimensional forward and inverse photonic crystals with a triangular lattice.

The structures of three-dimensional PCs are very diverse. The most common in this category are artificial opals - ordered systems of spherical diffusers. There are two main types of opals: direct and inverse opals. The transition from direct opal to reverse opal is carried out by replacing all spherical elements with cavities (usually air), while the space between these cavities is filled with some material.

Below is the surface of PC, which is a straight opal with a cubic lattice based on self-organized spherical polystyrene microparticles.

The inner surface of a PC with a cubic lattice based on self-organized spherical polystyrene microparticles.

The following structure is an inverse opal synthesized as a result of a multi-step chemical process: self-assembly of polymer spherical particles, impregnation of the voids of the resulting material with a substance, and removal of the polymer matrix by chemical etching.

Surface of quartz inverse opal. The photograph was obtained using scanning electron microscopy.

Another type of three-dimensional PCs are logpiles-type structures formed by rectangular parallelepipeds crossed, usually at right angles.

Electronic photograph of a FC made of metal parallelepipeds.

Rice. 2. Schematic representation of a one-dimensional photonic crystal.

1. one-dimensional, in which the refractive index periodically changes in one spatial direction as shown in Fig. 2. In this figure, the symbol Λ indicates the period of change of the refractive index, and - the refractive indices of two materials (but in general, any number of materials can be present). Such photonic crystals consist of layers of different materials parallel to each other with different refractive indices and can exhibit their properties in one spatial direction, perpendicular to the layers.

Rice. 3. Schematic representation of a two-dimensional photonic crystal.

2. two-dimensional, in which the refractive index periodically changes in two spatial directions as shown in Fig. 3. In this figure, a photonic crystal is created by rectangular regions of refractive index , which are in a medium of refractive index. In this case, regions with a refractive index are ordered in a two-dimensional cubic lattice. Such photonic crystals can exhibit their properties in two spatial directions, and the shape of the regions with the refractive index is not limited to rectangles, as in the figure, but can be any (circles, ellipses, arbitrary, etc.). The crystal lattice in which these areas are ordered can also be different, and not just cubic, as in the above figure.

3. three-dimensional, in which the refractive index periodically changes in three spatial directions. Such photonic crystals can exhibit their properties in three spatial directions, and they can be represented as an array of volumetric regions (spheres, cubes, etc.) ordered in a three-dimensional crystal lattice.

Like electrical media, depending on the width of the forbidden and allowed zones, photonic crystals can be divided into conductors - capable of conducting light over long distances with low losses, dielectrics - almost ideal mirrors, semiconductors - substances capable, for example, of selectively reflecting photons of a certain wavelength and superconductors, in which, thanks to collective phenomena, photons are able to propagate over almost unlimited distances.

A distinction is also made between resonant and non-resonant photonic crystals. Resonant photonic crystals differ from non-resonant ones in that they use materials whose dielectric constant (or refractive index) as a function of frequency has a pole at some resonant frequency.

Any inhomogeneity in a photonic crystal (for example, the absence of one or more squares in Fig. 3, their larger or smaller size relative to the squares of the original photonic crystal, etc.) is called a defect in the photonic crystal. The electromagnetic field is often concentrated in such areas, which is used in microcavities and waveguides built on the basis of photonic crystals.

Methods for theoretical study of photonic crystals, numerical methods and software

Photonic crystals allow manipulation of electromagnetic waves in the optical range, and the characteristic dimensions of photonic crystals are often close to the wavelength. Therefore, the methods of ray theory are not applicable to them, but wave theory and the solution of Maxwell's equations are used. Maxwell's equations can be solved analytically and numerically, but it is numerical solution methods that are most often used to study the properties of photonic crystals due to their availability and easy adjustment to the problems being solved.

It is also appropriate to mention that two main approaches are used to consider the properties of photonic crystals - methods for the time domain (which provide a solution to the problem depending on the time variable), and methods for the frequency domain (which provide the solution to the problem as a function of frequency).

Time domain methods are convenient for dynamic problems that involve the time dependence of the electromagnetic field. They can also be used to calculate the band structures of photonic crystals, but it can be practically difficult to identify the band positions in the output of such methods. In addition, when calculating band diagrams of photonic crystals, the Fourier transform is used, the frequency resolution of which depends on the total calculation time of the method. That is, to obtain greater resolution in the band diagram, you need to spend more time performing calculations. There is also another problem - the time step of such methods must be proportional to the size of the spatial grid of the method. The requirement to increase the frequency resolution of band diagrams requires a decrease in the time step, and therefore the size of the spatial grid, an increase in the number of iterations required random access memory computer and calculation time. Such methods are implemented in well-known commercial modeling packages Comsol Multiphysics (uses the finite element method to solve Maxwell’s equations), RSOFT Fullwave (uses the finite difference method), independently developed program codes for finite element and difference methods, etc.

Methods for the frequency domain are convenient primarily because the solution of Maxwell’s equations occurs immediately for a stationary system and the frequencies of the optical modes of the system are determined directly from the solution; this makes it possible to calculate band diagrams of photonic crystals faster than using methods for the time domain. Their advantages include the number of iterations, which is practically independent of the resolution of the spatial grid of the method and the fact that the error of the method numerically decreases exponentially with the number of iterations performed. The disadvantages of the method are the need to calculate the natural frequencies of the optical modes of the system in the low-frequency region in order to calculate frequencies in the higher-frequency region, and, naturally, the impossibility of describing the dynamics of the development of optical oscillations in the system. These methods are implemented in the free MPB software package and the commercial package. Both software packages mentioned cannot calculate the band diagrams of photonic crystals in which one or more materials have complex refractive index values. To study such photonic crystals, a combination of two RSOFT packages - BandSolve and FullWAVE - is used, or the perturbation method is used

Undoubtedly, theoretical research photonic crystals are not limited only to the calculation of band diagrams, but also require knowledge about stationary processes during the propagation of electromagnetic waves through photonic crystals. An example is the problem of studying the transmission spectrum of photonic crystals. For such problems, you can use both of the approaches mentioned above based on convenience and their availability, as well as radiative transfer matrix methods, a program for calculating the transmission and reflection spectra of photonic crystals using this method, the pdetool software package which is part of the Matlab package and the Comsol Multiphysics package mentioned above.

Photonic band gap theory

As noted above, photonic crystals make it possible to obtain allowed and forbidden bands for photon energies, similar to semiconductor materials, in which there are allowed and forbidden bands for charge carrier energies. In the literature, the appearance of band gaps is explained by the fact that under certain conditions, the intensities of the electric field of standing waves of a photonic crystal with frequencies close to the frequency of the band gap are shifted to different regions of the photonic crystal. Thus, the field intensity of low-frequency waves is concentrated in areas with a high refractive index, and the field intensity of high-frequency waves is concentrated in areas with a lower refractive index. The work contains another description of the nature of band gaps in photonic crystals: “photonic crystals are usually called media in which the dielectric constant changes periodically in space with a period allowing Bragg diffraction of light.”

If radiation with a band gap frequency was generated inside such a photonic crystal, then it cannot propagate in it, but if such radiation is sent from outside, then it is simply reflected from the photonic crystal. One-dimensional photonic crystals make it possible to obtain band gaps and filtering properties for radiation propagating in one direction, perpendicular to the layers of materials shown in Fig. 2. Two-dimensional photonic crystals can have band gaps for radiation propagating in one, two directions, or in all directions of a given photonic crystal, which lie in the plane of Fig. 3. Three-dimensional photonic crystals can have band gaps in one, several or all directions. Forbidden zones exist for all directions in a photonic crystal with a large difference in the refractive indices of the materials that make up the photonic crystal, certain shapes of regions with different refractive indices and a certain crystal symmetry.

The number of band gaps, their position and width in the spectrum depends both on the geometric parameters of the photonic crystal (the size of regions with different refractive indices, their shape, the crystal lattice in which they are ordered) and on the refractive indices. Therefore, forbidden zones can be tunable, for example, due to the use of nonlinear materials with a pronounced Kerr effect, due to changes in the sizes of areas with different refractive indexes, or due to changes in refractive indices under the influence of external fields.

Rice. 5. Band diagram for photon energies (TE polarization).

Rice. 6. Band diagram for photon energies (TM polarization).

Let us consider the band diagrams of the photonic crystal shown in Fig. 4. This two-dimensional photonic crystal consists of two materials alternating in the plane - gallium arsenide GaAs (base material, refractive index n=3.53, black areas in the figure) and air (with which the cylindrical holes are filled, indicated in white, n=1 ). The holes have a diameter and are ordered in a hexagonal crystal lattice with a period (the distance between the centers of adjacent cylinders). In the photonic crystal under consideration, the ratio of the hole radius to the period is equal to . Let's consider the band diagrams for TE (the electric field vector is directed parallel to the axes of the cylinders) and TM (the magnetic field vector is directed parallel to the axes of the cylinders) shown in Fig. 5 and 6, which were calculated for a given photonic crystal using free program MPB. The X axis shows the wave vectors in the photonic crystal, and the Y axis shows the normalized frequency ( - wavelength in vacuum) corresponding to the energy states. The blue and red solid curves in these figures represent the energy states in a given photonic crystal for TE and TM polarized waves, respectively. The blue and pink areas show the photon band gaps in a given photonic crystal. The black dashed lines are the so-called light lines (or light cone) of a given photonic crystal. One of the main applications of these photonic crystals is optical waveguides, and the light line defines the region within which the waveguide modes of the low-loss waveguides built using such photonic crystals are located. In other words, the light line defines the area of interest to us energy states of this photonic crystal. The first thing worth paying attention to is that this photonic crystal has two band gaps for TE-polarized waves and three wide band gaps for TM-polarized waves. Secondly, the forbidden zones for TE and TM-polarized waves, lying in the region of small values of the normalized frequency, overlap, which means that a given photonic crystal has a complete forbidden zone in the region of overlap of the forbidden zones of TE and TM waves, not only in all directions, but also for waves of any polarization (TE or TM).

Rice. 7. Reflection spectrum of the photonic crystal under consideration (TE polarization).

Rice. 8. Reflection spectrum of the photonic crystal under consideration (TM polarization).

From the given dependencies we can determine the geometric parameters of a photonic crystal, the first band gap of which, with the value of the normalized frequency, falls on the wavelength nm. The period of the photonic crystal is nm, the radius of the holes is nm. Rice. 7 and 8 show the reflectance spectra of a photonic crystal with the parameters defined above for TE and TM waves, respectively. The spectra were calculated using the Translight program, it was assumed that this photonic crystal consists of 8 pairs of layers of holes and the radiation propagates in the Γ-K direction. From the above dependencies we can see the most well-known property of photonic crystals - electromagnetic waves with natural frequencies corresponding to the band gaps of the photonic crystal (Fig. 5 and 6) are characterized by a reflection coefficient close to unity and are subject to almost complete reflection from a given photonic crystal. Electromagnetic waves with frequencies outside the band gaps of a given photonic crystal are characterized by lower reflection coefficients from the photonic crystal and pass through it completely or partially.

Fabrication of photonic crystals

There are currently many methods for making photonic crystals, and new methods continue to emerge. Some methods are more suitable for the formation of one-dimensional photonic crystals, others are convenient for two-dimensional ones, others are more often applicable to three-dimensional photonic crystals, others are used in the production of photonic crystals on other optical devices, etc. Let's consider the most famous of these methods.

Methods using spontaneous formation of photonic crystals

In the spontaneous formation of photonic crystals, colloidal particles are used (most often monodisperse silicone or polystyrene particles are used, but other materials are gradually becoming available for use as technological methods for their production are developed), which are located in a liquid and, as the liquid evaporates, settle in a certain volume. As they deposit on each other, they form a three-dimensional photonic crystal, and are ordered predominantly into face-centered or hexagonal crystal lattices. This method is quite slow and can take weeks to form a photonic crystal.

Another method for spontaneously forming photonic crystals, called the honeycomb method, involves filtering a liquid containing particles through small pores. This method, presented in the works, makes it possible to form a photonic crystal at a speed determined by the speed of liquid flow through the pores, but when such a crystal dries, defects are formed in the crystal.

It was already noted above that in most cases a large refractive index contrast in a photonic crystal is required to obtain photonic band gaps in all directions. The above-mentioned methods of spontaneous formation of a photonic crystal were most often used to deposit spherical colloidal particles of silicone, the refractive index of which is small, and therefore the refractive index contrast is also small. To increase this contrast, additional technological steps are used in which the space between the particles is first filled with a material with a high refractive index, and then the particles are etched. The step-by-step method for forming inverse opal is described in the laboratory work instructions.

Etching methods

Holographic methods

Holographic methods for creating photonic crystals are based on the application of the principles of holography to form a periodic change in the refractive index in spatial directions. This uses the interference of two or more coherent waves, which creates a periodic distribution of electric field intensity. The interference of two waves allows you to create one-dimensional photonic crystals, three or more beams - two-dimensional and three-dimensional photonic crystals.

Other methods for creating photonic crystals

Single-photon photolithography and two-photon photolithography create three-dimensional photonic crystals with a resolution of 200 nm and take advantage of the properties of some materials, such as polymers, that are sensitive to one- and two-photon radiation and can change their properties when exposed to this radiation. Electron beam lithography is an expensive but highly accurate method for fabricating two-dimensional photonic crystals. In this method, a photoresist that changes its properties under the action of an electron beam is irradiated by the beam at specific locations to form a spatial mask. After irradiation, part of the photoresist is washed off, and the remaining part is used as a mask for etching in the subsequent technological cycle. The maximum resolution of this method is 10nm. Ion beam lithography is similar in principle, but instead of an electron beam, an ion beam is used. The advantages of ion beam lithography over electron beam lithography are that the photoresist is more sensitive to ion beams than to electron beams and there is no “proximity effect” that limits the smallest possible area size in beam lithography electrons

Application

The distributed Bragg reflector is an already widely used and well-known example of a one-dimensional photonic crystal.

The future of modern electronics is associated with photonic crystals. At the moment, there is an intensive study of the properties of photonic crystals, the development theoretical methods their research, development and research of various devices with photonic crystals, practical implementation of theoretically predicted effects in photonic crystals, and it is assumed that:

Research groups around the world

Research on photonic crystals is carried out in many laboratories of institutes and companies involved in electronics. For example:

Moscow State Technical University named after N. E. Bauman
Moscow State University named after M.V. Lomonosov
Institute of Radio Engineering and Electronics RAS
Dnipropetrovsk National University named after Oles Gonchar
Sumy State University

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I cannot pretend to judge colors impartially. I rejoice in the sparkling hues and truly regret the sparse browns. (Sir Winston Churchill).

Origin of photonic crystals

Looking at the wings of a butterfly or the mother-of-pearl coating of shells (Figure 1), you are amazed at how Nature - even over many hundreds of thousands or millions of years - was able to create such amazing biostructures. However, not only in the bioworld there are similar structures with iridescent colors, which are an example of the almost limitless creative possibilities of Nature. For example, the semi-precious stone opal has fascinated people since ancient times with its brilliance (Figure 2).

Today, every ninth grader knows that not only the processes of absorption and reflection of light lead to what we call the color of the world, but also the processes of diffraction and interference. Diffraction gratings, which we can find in nature, are structures with periodically changing dielectric constant, and their period is comparable to the wavelength of light (Figure 3). These can be 1D lattices, as in the mother-of-pearl coating of mollusk shells such as abalone, 2D lattices, like the antennae of the sea mouse, polychaete worm, and 3D lattices, which give the iridescent blue color to butterflies from Peru, as well as opal.

In this case, Nature, as undoubtedly the most experienced materials chemist, pushes us to the following solution: three-dimensional optical diffraction gratings can be synthesized by creating dielectric gratings that are geometrically complementary to each other, i.e. one is inverse to the other. And since Jean-Marie Lehn uttered the famous phrase: “If something exists, then it can be synthesized,” we simply have to put this conclusion into practice.

Photonic semiconductors and photonic band gap

So, in a simple formulation, a photonic crystal is a material whose structure is characterized by a periodic change in the refractive index in spatial directions, which leads to the formation of a photonic band gap. Typically, to understand the meaning of the terms “photonic crystal” and “photonic band gap,” such a material is considered as an optical analogy to semiconductors. Solving Maxwell's equations for the propagation of light in a dielectric lattice shows that, due to Bragg diffraction, the frequency distribution of photons ω(k) depending on the wave vector k (2π/λ) will have discontinuity regions. This statement is graphically presented in Figure 4, which shows the analogy between the propagation of an electron in a 1D crystal lattice and a photon in a 1D photonic lattice. The continuous density of states of both a free electron and a photon in a vacuum undergoes a break inside, respectively, the crystal and photon lattices in the so-called “stop zones” at the value of the wave vector k (i.e., momentum), which corresponds to a standing wave. This is the condition for Bragg diffraction of an electron and a photon.

The photonic bandgap is a range of frequencies ω(k) in the reciprocal space of wave vectors k, where the propagation of light of a certain frequency (or wavelength) is prohibited in the photonic crystal in all directions, while the light incident on the photonic crystal is completely reflected from it. If light “appears” inside a photonic crystal, then it will be “frozen” into it. The zone itself may be incomplete, the so-called stop zone. Figure 5 shows 1D, 2D and 3D photonic crystals in real space and the photon density of states in reciprocal space.

The photonic band gap of a three-dimensional photonic crystal is somewhat analogous to the electronic band gap in a silicon crystal. Therefore, the photonic band gap “controls” the flow of light in a silicon photonic crystal in a similar way to how charge carrier transport occurs in a silicon crystal. In these two cases, the formation of the bandgap is caused by standing waves of photons or electrons, respectively.

Make your own photonic crystal

Oddly enough, Maxwell's equations for photonic crystals are not sensitive to scaling, unlike the Schrödinger equation in the case of electronic crystals. This arises due to the fact that the wavelength of an electron in a “normal” crystal is more or less fixed at a level of several angstroms, while the dimensional scale of the wavelength of light in photonic crystals can vary from ultraviolet to microwave radiation, solely due to changes in the dimensionality of the photonic components grates. This leads to truly inexhaustible possibilities for fine-tuning the properties of a photonic crystal.

Currently, there are many methods for producing photonic crystals. Some of them are more suitable for the formation of one-dimensional photonic crystals, others are convenient for two-dimensional ones, others are more often applicable to three-dimensional photonic crystals, others are used in the production of photonic crystals on other optical devices, etc. However, not everything is limited only to varying the dimensions of structural elements. Photonic crystals can also be created due to optical nonlinearity, metal-nonmetal transition, liquid crystalline state, ferroelectric birefringence, swelling and contraction of polymer gels, and so on, as long as the refractive index changes.

Where are there no defects?!

There are practically no materials in the world that are free from defects, and this is good. It is defects in solid-phase materials in b O To a greater extent than the crystal structure itself, they influence the various properties of materials and, ultimately, their functional characteristics, as well as possible areas of application. A similar statement is true in the case of photonic crystals. From the theoretical consideration it follows that the introduction of defects (point, extended - dislocations - or bending) at the microlevel into an ideal photonic lattice makes it possible to create certain states inside the photonic band gap on which light can be localized, and the propagation of light can be limited or, on the contrary, enhanced along and around a very small waveguide (Figure 6). If we draw an analogy with semiconductors, then these states resemble impurity levels in semiconductors. Photonic crystals with such “controlled defectivity” can be used to create all-optical devices and circuits for the new generation of optical telecommunications technologies.

Light information technology

Figure 7 shows one of the futuristic images of the all-light chip of the future, which, undoubtedly, has been exciting the imagination of chemists, physicists and materials scientists for a whole decade. The all-optical chip consists of integrated micro-sized photonic crystals with 1D, 2D and 3D periodicity, which can act as switches, filters, low-threshold lasers, etc., while light is transmitted between them through waveguides solely due to structural defects. And although the topic of photonic crystals exists in the “road maps” for the development of photonic technologies, research and practical applications of these materials still remain at the forefront. early stages of its development. This is the topic of future discoveries that could lead to the creation of all-light ultrafast computers, as well as quantum computers. However, in order for the dreams of science fiction writers and many scientists who have devoted their lives to the study of such interesting and practically significant materials as photonic crystals to come true, it is necessary to answer a number of questions. For example, such as: what needs to be changed in the materials themselves to solve the problem associated with making such integrated chips from micro-sized photonic crystals smaller for widespread practical use? Is it possible, using microdesign (“top-down”), or self-assembly (“bottom-up”), or some fusion of these two methods (for example, directed self-assembly), to realize on an industrial scale the production of chips from micro-sized photonic crystals? Is the science of computers based on microphotonic crystal light chips a reality or is it still a futurist fantasy?

In the last decade, the development of microelectronics has slowed down, since the speed limits of standard semiconductor devices have almost been reached. An increasing number of studies are devoted to the development of alternative areas to semiconductor electronics - these are spintronics, microelectronics with superconducting elements, photonics and some others.

The new principle of transmitting and processing information using light rather than electrical signals can accelerate the onset of a new stage in the information age.

From simple crystals to photonic ones

The basis of electronic devices of the future may be photonic crystals - these are synthetic ordered materials in which the dielectric constant changes periodically within the structure. In the crystal lattice of a traditional semiconductor, the regularity and periodicity of the arrangement of atoms leads to the formation of the so-called band energy structure- with permitted and prohibited zones. An electron whose energy falls within the allowed band can move around the crystal, but an electron with energy in the bandgap becomes “locked.”

By analogy with an ordinary crystal, the idea of a photonic crystal arose. In it, the periodicity of the dielectric constant causes the appearance of photonic zones, in particular, the forbidden zone, within which the propagation of light with a certain wavelength is suppressed. That is, being transparent to a wide spectrum of electromagnetic radiation, photonic crystals do not transmit light with a selected wavelength (equal to twice the period of the structure along the length of the optical path).

Photonic crystals can have different dimensions. One-dimensional (1D) crystals are a multilayer structure of alternating layers with different refractive indices. Two-dimensional photonic crystals (2D) can be represented as a periodic structure of rods with different dielectric constants. The first synthetic prototypes of photonic crystals were three-dimensional and created in the early 1990s by researchers research center Bell Labs(USA). To obtain a periodic lattice in a dielectric material, American scientists drilled cylindrical holes in such a way as to obtain a three-dimensional network of voids. In order for the material to become a photonic crystal, its dielectric constant was modulated with a period of 1 centimeter in all three dimensions.

Natural analogues of photonic crystals are the mother-of-pearl coatings of shells (1D), the antennae of a sea mouse, a polychaete worm (2D), the wings of an African swallowtail butterfly and semi-precious stones, such as opal (3D).

But even today, even using the most modern and expensive methods of electron lithography and anisotropic ion etching, it is difficult to produce defect-free three-dimensional photonic crystals with a thickness of more than 10 structural cells.

Photonic crystals should find wide application in photonic integrated technologies, which in the future will replace electrical integrated circuits in computers. When transmitting information using photons instead of electrons, power consumption will be sharply reduced, clock frequencies and information transfer speed will increase.

Titanium Oxide Photonic Crystal

Titanium oxide TiO 2 has a set of unique characteristics, such as a high refractive index, chemical stability and low toxicity, which makes it the most promising material for creating one-dimensional photonic crystals. If we consider photonic crystals for solar cells, titanium oxide wins here due to its semiconductor properties. Previously, an increase in the efficiency of solar cells was demonstrated when using a semiconductor layer with a periodic photonic crystal structure, including titanium oxide photonic crystals.

But so far, the use of photonic crystals based on titanium dioxide is limited by the lack of reproducible and inexpensive technology for their creation.

Employees of the Faculty of Chemistry and the Faculty of Materials Sciences of Moscow State University - Nina Sapoletova, Sergei Kushnir and Kirill Napolsky - have improved the synthesis of one-dimensional photonic crystals based on porous titanium oxide films.

“Anodization (electrochemical oxidation) of valve metals, including aluminum and titanium, is effective method obtaining porous oxide films with nanometer-sized channels,” explained the head of the electrochemical nanostructuring group, Candidate of Chemical Sciences Kirill Napolsky.

Anodization is usually carried out in a two-electrode electrochemical cell. Two metal plates, the cathode and the anode, are lowered into the electrolyte solution, and an electrical voltage is applied. Hydrogen is released at the cathode, and electrochemical oxidation of the metal occurs at the anode. If the voltage applied to the cell is periodically changed, a porous film with a porosity of a given thickness is formed on the anode.

The effective refractive index will be modulated if the pore diameter changes periodically within the structure. Previously developed titanium anodizing techniques did not make it possible to obtain materials with a high degree of periodic structure. Chemists from Moscow State University have developed a new method for anodizing metal with voltage modulation depending on the anodizing charge, which makes it possible to create porous anodic metal oxides with high precision. Chemists demonstrated the capabilities of the new technique using the example of one-dimensional photonic crystals made of anodic titanium oxide.

As a result of changing the anodizing voltage according to a sinusoidal law in the range of 40–60 Volts, scientists obtained anodic titanium oxide nanotubes with a constant outer diameter and periodically changing inner diameter (see figure).

“Previously used anodizing techniques did not make it possible to obtain materials with a high degree of periodic structure. We have developed a new technique, the key component of which is in situ(directly during synthesis) measurement of the anodization charge, which makes it possible to highly accurately control the thickness of layers with different porosities in the formed oxide film,” explained one of the authors of the work, candidate of chemical sciences Sergei Kushnir.

The developed technique will simplify the creation of new materials with a modulated structure based on anodic metal oxides. “If we consider the use of photonic crystals made of anodic titanium oxide in solar cells as a practical use of the technique, then a systematic study of the influence of the structural parameters of such photonic crystals on the efficiency of light conversion in solar cells has yet to be carried out,” Sergey Kushnir clarified.

Ilya Polishchuk, Doctor of Physical and Mathematical Sciences, Professor at MIPT, Leading Researcher at the National Research Center "Kurchatov Institute"

The use of microelectronics in information processing and communication systems has radically changed the world. There is no doubt that the consequences of the boom in research work in the field of physics of photonic crystals and devices based on them will be comparable in importance to the creation of integrated microelectronics more than half a century ago. Materials of a new type will make it possible to create optical microcircuits in the “image and likeness” of elements of semiconductor electronics, and fundamentally new methods of transmitting, storing and processing information, developed today on photonic crystals, in turn, will find application in the semiconductor electronics of the future. It is not surprising that this area of research is one of the hottest in the world's largest research centers, high-tech companies and military-industrial complexes. Russia, of course, is no exception. Moreover, photonic crystals are the subject of effective international cooperation. As an example, let us refer to more than ten years of cooperation between the Russian Kintech Lab LLC and the famous American company General Electric.

History of photonic crystals

Historically, the theory of photon scattering on three-dimensional lattices began to develop intensively from the wavelength region ~0.01-1 nm, lying in the X-ray range, where the nodes of a photonic crystal are the atoms themselves. In 1986, Eli Yablonovich from the University of California at Los Angeles proposed the idea of creating a three-dimensional dielectric structure, similar to ordinary crystals, in which electromagnetic waves of a certain spectrum band could not propagate. Such structures are called photonic bandgap structures or photonic crystals. Five years later, such a photonic crystal was made by drilling millimeter-sized holes in a material with a high refractive index. Such an artificial crystal, which later received the name Yablonovite, did not transmit millimeter-wave radiation and actually implemented a photonic structure with a band gap (by the way, phased antenna arrays can also be classified in the same class of physical objects).

Photonic structures, in which the propagation of electromagnetic (in particular, optical) waves in a certain frequency band in one, two or three directions, can be used to create optical integrated devices for controlling these waves. Currently, the ideology of photonic structures underlies the creation of non-threshold semiconductor lasers, lasers based on rare earth ions, high-Q resonators, optical waveguides, spectral filters and polarizers. Research on photonic crystals is now being carried out in more than two dozen countries, including Russia, and the number of publications in this area, as well as the number of symposia and scientific conferences and schools, is growing exponentially.

To understand the processes occurring in a photonic crystal, it can be compared with a semiconductor crystal, and the propagation of photons with the movement of charge carriers - electrons and holes. For example, in ideal silicon, the atoms are arranged in a diamond-like crystal structure, and, according to the band theory of solids, charged carriers, propagating throughout the crystal, interact with the periodic field potential of atomic nuclei. This is the reason for the formation of allowed and forbidden bands - quantum mechanics prohibits the existence of electrons with energies corresponding to the energy range called the bandgap. Similar to conventional crystals, photonic crystals contain a highly symmetrical unit cell structure. Moreover, if the structure of an ordinary crystal is determined by the positions of atoms in the crystal lattice, then the structure of a photonic crystal is determined by periodic spatial modulation of the dielectric constant of the medium (the modulation scale is comparable to the wavelength of the interacting radiation).

Photonic conductors, insulators, semiconductors and superconductors

Continuing the analogy, photonic crystals can be divided into conductors, insulators, semiconductors and superconductors.

Photonic conductors have wide resolved bands. These are transparent bodies in which light travels a long distance without being absorbed. Another class of photonic crystals, photonic insulators, have wide band gaps. This condition is satisfied, for example, by wide-range multilayer dielectric mirrors. Unlike conventional opaque media, in which light quickly decays into heat, photonic insulators do not absorb light. As for photonic semiconductors, they have narrower band gaps than insulators.

Photonic crystal waveguides are used to make photonic textiles (pictured). Such textiles have just appeared, and even the area of its application is not yet fully understood. It can be used to make, for example, interactive clothing, or a soft display

Photo: emt-photoniccrystal.blogspot.com

Despite the fact that the idea of photonic bands and photonic crystals has only become established in optics over the past few years, the properties of structures with layered changes in the refractive index have long been known to physicists. One of the first practically important applications of such structures was the production of coatings with unique optical characteristics, used to create highly efficient spectral filters and reduce unwanted reflection from optical elements (such optics are called coated optics) and dielectric mirrors with a reflectivity close to 100%. Other well-known examples of 1D photonic structures include semiconductor lasers with distributed feedback, as well as optical waveguides with periodic longitudinal modulation of physical parameters (profile or refractive index).

As for ordinary crystals, nature gives them to us very generously. Photonic crystals are very rare in nature. Therefore, if we want to exploit the unique properties of photonic crystals, we are forced to develop different methods for growing them.

How to grow a photonic crystal

The creation of a three-dimensional photonic crystal in the visible wavelength range has remained over the past ten years one of the top priorities in materials science, for which most researchers have focused on two fundamentally different approaches. One of them uses the seed template method - the template method. This method creates the prerequisites for the self-organization of synthesized nanosystems. The second method is nanolithography.

Among the first group of methods, the most widespread are those that use monodisperse colloidal spheres as templates for creating solids with a periodic system of pores. These methods make it possible to obtain photonic crystals based on metals, non-metals, oxides, semiconductors, polymers, etc. At the first stage, colloidal spheres of similar sizes are uniformly “packed” in the form of three-dimensional (sometimes two-dimensional) frameworks, which subsequently act as templates, an analogue of natural opal. At the second stage, the voids in the template structure are impregnated with liquid, which subsequently turns into a solid frame under various physicochemical influences. Other methods of filling template voids with matter are either electrochemical methods, or the CVD method (Chemical Vapor Deposition - deposition from the gas phase).

At the last stage, the template (colloidal spheres) is removed using dissolution or thermal decomposition processes, depending on its nature. The resulting structures are often called reverse replicas of the original colloidal crystals, or "reverse opals."

For practical use, defect-free areas in a photonic crystal should not exceed 1000 μm2. Therefore, the problem of ordering quartz and polymer spherical particles is one of the most important when creating photonic crystals.

In the second group of methods, single-photon photolithography and two-photon photolithography allow the creation of three-dimensional photonic crystals with a resolution of 200 nm and exploit the property of some materials, such as polymers, that are sensitive to one- and two-photon irradiation and can change their properties when exposed to this radiation. Electron beam lithography is an expensive but fast method for fabricating two-dimensional photonic crystals. In this method, a photoresist, which changes its properties when exposed to an electron beam, is irradiated by the beam at specific locations to form a spatial mask. After irradiation, part of the photoresist is washed off, and the remaining part is used as a mask for etching in the subsequent technological cycle. The maximum resolution of this method is 10nm. Ion beam lithography is similar in principle, but instead of an electron beam, an ion beam is used. The advantages of ion beam lithography over electron beam lithography are that the photoresist is more sensitive to ion beams than to electron beams and there is no "proximity effect" that limits the minimum possible area size in electron beam lithography.

Let us also mention some other methods of growing photonic crystals. These include methods of spontaneous formation of photonic crystals, etching methods, and holographic methods.

Photonic future

Making predictions is as dangerous as it is tempting. However, forecasts for the future of photonic crystal devices are very optimistic. The scope of use of photonic crystals is practically inexhaustible. Currently, devices or materials using the unique features of photonic crystals have already appeared on the world market (or will appear in the near future). These are lasers with photonic crystals (low-threshold and no-threshold lasers); waveguides based on photonic crystals (they are more compact and have lower losses compared to conventional fibers); materials with a negative refractive index, making it possible to focus light into a point smaller than the wavelength; the dream of physicists is superprisms; optical storage and logic devices; displays based on photonic crystals. Photonic crystals will also perform color manipulation. A bendable large-format display on photonic crystals with a high spectral range has already been developed - from infrared radiation to ultraviolet, in which each pixel is a photonic crystal - an array of silicon microspheres located in space in a strictly defined way. Photonic superconductors are being created. Such superconductors can be used to create optical temperature sensors, which, in turn, will operate at high frequencies and be combined with photonic insulators and semiconductors.

The man is still planning technological use photonic crystals, and the sea mouse (Aphrodite aculeata) has been using them in practice for a long time. The fur of this worm has such a pronounced iridescent phenomenon that it is capable of selectively reflecting light with an efficiency close to 100% in the entire visible region of the spectrum - from red to green and blue. Such a specialized “on-board” optical computer helps this worm survive at depths of up to 500 m. It is safe to say that human intelligence will go much further in using the unique properties of photonic crystals.