Photonic Crystal – Wikipedia, La Enciclopedia Libre

The opal in this bracelet contains a natural periodic microstructure responsible for iridescent color. It is basically a natural photonic glass, despite not having a complete prohibited band.

And photonic crystal It is a structured material so that its dielectric function varies periodically in space. Although there are natural manifestations of these materials, such as opals or certain microscopic structures that give rise to colorations in the wings of some butterflies, these are relatively new proposed material and to produce light location respectively.

The photonic crystals ^{[ first ]} They are periodic optical nanostructures that are designed to affect the movement of photons in a similar way to that the periodicity of a semiconductor crystal affects the movement of electrons. Fotonic crystals appear in nature and have been studied by scientists with various interests during the last 100 years.

Introduction [ To edit ]

Fotonic crystals are composed of periodic dielectric or metal-dietary nanostructures that affect the propagation of electromagnetic waves (EM) in the same way as the periodic potential in a semiconductor affects the movement of electrons, defining allowed and prohibited energy bands. Basically, photonic crystals contain internal regions with high and low dielectric constants that are repeated regularly. The light waves that are allowed to spread are known as modes, the modes of modes form the bands. Not allowed wavelength bands are called prohibited bands. This results in different optical phenomena such as spontaneous emission inhibition, omni-directional high-reflection mirrors and wave guides with low losses, among others.
Because the physical phenomenon is based on diffraction, the periodicity of the structure of the photonic glass must be in the same length order of half of the wavelength of the EM waves, that is, the regions of dielectric constants high and low that they are repeated must have the following dimensions; From approximately 200 nm (blue) to 350 nm (red) for photonic crystals operating in the visible part of the spectrum. This makes the elaboration of photonic crystals tedious and difficult.

What is a photonic crystal [ To edit ]

When an electromagnetic wave affects the surface of a material with periodic refraction index (or is emitted from inside the material) interference between the waves reflected in each interference (separation between the media of different refraction index) occurs when the interference It is destructive, certain frequency range that cannot be transmitted in the glass appears.
In other words, as in electrical materials there are prohibited energy bands for electrons, in photonic crystals, there are prohibited ranges for photons. (Well said, it would be said that there are no states available for these energies inside the material). That is, a photonic glass is a material in which there is a periodic refractive index in space. In addition, so that this phenomenon can occur, it must be a non -absorbent material.

The periodicity of the refraction index can be in one, two or the three directions. This periodicity is generally achieved with periodic structures with materials of different refraction index.

The position and width of these photonic gaps will be given by the characteristics of the material, including the most important would be the value of the dielectric constants of the materials and the space period of their variation.
Thus, for example, periodic separations of the order of the millimeter or the micra, they will give rise to photonic emptiness in the range of microwave or infrared respectively.
The periodicity of the dielectric constant interacting on photons plays a role similar to that exercised by the crystalline periodic potential in its interaction with electrons.

After analyzing how the prohibited bands are created for electrons as well as for photons, it can be deepened more with some equations. The equation that governs electrons is the famous Schrodinger equation:

( −ℏ22m∇2+V(r)) Φ ( r ) = AND Φ ( r ) {Displaystyle left(-{Hbar ^{2} Over 2M} Nabla ^{2}+V(Mathbf {R}) PSI (Mathbf {R} )=EPSI (Mathbf R}}

On the other hand, Maxwell’s equations describe the behavior and spread of electromagnetic waves. If it is considered a linear medium, load densities and null current sources, two equations can be formulated from the electric field or the magnetic field.

∇ × AND ( r ) = – m ∂H(r)∂t{displaystyle nabla times mathbf {E} (mathbf {r} )=-mu {partial mathbf {H} (mathbf {r} ) over partial t}}

∇ × H ( r ) = e ∂E(r)∂t{displaystyle nabla times mathbf {H} (mathbf {r} )=varepsilon {partial mathbf {E} (mathbf {r} ) over partial t}}

If now from Maxwell’s equations and considering a frequency monochromatic wave

, propagating by a means whose relative allowance is a function in space as follows:

, and it is assumed that the absorption of light is negligible, the dielectric constant is real and positive and relative permeability is unitary, wave equations can be written as:

∇ × ∇ × AND ( r ) = e r( r ) (ωc)2AND ( r ) {Displaystyle Nabla Times Nabla Times Mathbf {E} (Mathbf {R} )=Varepsilon _{R}(Mathbf {R} )Left({Omega Over C}Aright)^{2}Mathbf {E} (Mathbf {R} )}

∇ × ( 1εr(r)∇×H(r)) = (ωc)2H ( r ) {Displaystyle Nabla Times Left({1 Over Varepsilon _{R} )}Nabla Times Mathbf {H} Right) {H} (Mathbf {R} )

where

It is the speed of light. Written thus it is only necessary to look at lines above to verify its similarity with the equation (1). The first two terms function as an analogous to kinetic energy, the third, in which the dielectric spatial dependence appears is similar to a periodic potential in the Schrödinger equation, and the part of the constant refractive index represents the energies of the modes of propagation.

There is an essential difference, in the appearance of linked states for photons with respect to electrons. While the appearance of linked electrons in the Schrödinger equation corresponds to negative energies, in the case of linked states of light the dielectric constant is positive. Therefore the appearance of these linked states will be much more difficult and will depend on geometry and need a complicated design of artificial materials

History of photonic crystals [ To edit ]

Although photonic crystals have been studied in one way or another since 1887, the term “photonic glass” was first used about 100 years later, after Eli Yablonovitch and Sajev John published two articles in 1987, publications that are referents in the countryside. ^{[ 2 ]} ​ ^{[ 3 ]} ​

Prior to 1987, they had been studied extensively unidimensional photonic crystals formed by periodically stacked multiple dielectric sheets (as in Bragg’s mirrors). Lord Rayleight began studying them in 1887, ^{[ 4 ]} Showing that these systems have a prohibited photonic band, a spectral range of great reflection, in a dimension. Today these structures are used in a wide variety of applications; From reflective coatings to improve the effectiveness of LEDs to mirrors of great reflection in some laser cavities (see, for example; the Laser Vcsel diode). Bykov ^{[ 5 ]} He developed a detailed theoretical study of one -dimensional optical structures, being the first to investigate the effect of a prohibited photonic band on the spontaneous emission of atoms and molecules infiltrated in a structure with photonic properties. Bykov even predicted what could happen if bi- and three-dimensional structures were used. ^{[ 6 ]} However, these ideas were not successful until after the two Publications of Yablonovitch and John in 1987. Both articles considered periodic structures, photonic crystals, high -dimensionality. The main motivation of Yablonovitch was to avoid the densities of photonic states, with the intention of controlling the spontaneous emission of materials infiltrated in photonic crystals. John’s idea was to use photonic crystals to influence the location and control of light spread.

After 1987 the number of scientific publications on photonic crystals began to grow exponentially. However, due to the difficulty of manufacturing these structures at an optical scale (see manufacturing), the previous studies were either theoretical or in the range of microwaves, where phototonic crystals can be manufactured in the much more accessible scale of scale of The centimeters. This is due to the property of the electromagnetic fields known as the invariability of scale – summarizing, the electromagnetic fields, as well as the solutions to the Maxwell equations, do not have their own scalar length and, therefore, a solution for a structure in the centimeters scale and a frequency in the range of microwaves is the same as for a structure on the scale of the nanometers and a frequency in the visible. In 1991 Yablonovitch showed the first prohibited photonic band in three dimensions in the order of microwave. ^{[ 7 ]} ​

In 1996 Thomas Krauss made the first demonstration of a two -dimensional photonic glass for wavelengths in the visible. ^{[ 8 ]} This opened the way to the manufacture of photonic crystals in semiconductors taking advantage of the methods used in the semiconductor industry. Later, those same techniques began to use planles planares, two -dimensional photonic crystals perforated in semiconductor sheets, total internal reflection confines light on the sheets and allows the effects of a photonic crystal, thus it is possible to use the photonic dispersion in the sheets. The investigation is directed to the use of photonic planares in integrated computers to improve the optical communication processing both inside and between the chips.

Bidimensional photonic crystals find their commercial use in the form of photonic glass fibers (also known as microstructured fibers). Fotonic glass fibers were developed by Philip Russell in 1998 and can be designed to obtain improved properties on conventional fiber.

The study of three -dimensional photonic crystals has evolved more slowly than its two -dimensional counterpart. This is due to the greatest difficulty in its manufacture since it has not inherited or there is any available technique from the semiconductor industry for the manufacture of three -dimensional photonic crystals. It has tried, in any case, adapt some techniques and some great advance has been demonstrated, ^{[ 9 ]} For example, in the manufacture of “woodcot” structure (in English; “woodpile”) built based on depositing successive layers of materials. Another line of research is to manufacture three-dimensional photonic structures by self-assembly, basically, it is basically Try to allow dielectric nanospheras to be suspended in a solvent are arranged in periodic trimensional structures that have a prohibited photonic band (see colloidal photonic crystals).

Manufacturing [ To edit ]

The greatest challenge to obtain high -dimensioning photonic crystals is the manufacture of these structures with sufficient precision to prevent losses due to the dispersion that attenuate the properties of the glass and that allow their manufacture in series. A promising method of manufacturing two -dimensional photonic crystals are photonic glass fibers or microstructured fibers. Using engraving techniques developed for optical fibers, these two requirements meet and the photonic glass fibers are available for commercialization. Another promising method to develop two -dimensional photonic crystals are the planks planares. These structures consist of sheets of a material (for example, silicon) that can be lithographed using borrowed techniques of the semiconductor industry. These designs have the potential to combine phototonic applications with electronic in the same integrated circuit.

For three -dimensional photonic crystals, several techniques have been used including photolithography and engraving techniques similar to those used in the manufacture of integrated circuits. Some of these techniques are already available, for example; “Nanoscibe’s Direct Laser Writing System”. Trying to avoid nanotechnology methods and its complex machinery, other alternatives to grow colloidal photonic crystals through self-assembly have been sought.

Calculation of La Fotonic Band Structure [ To edit ]

The prohibited photonic band is basically a jump between the air line and the dielectric line in the structure of energy bands due to the refractive dispersion. When designing a photonic glass it is necessary to predict the position and size of the forbidden band, this is done by a simulation calculation using one of the following methods.

1. Flat Wave Expansion Method or Scalar Approach
2. Finit Differences Method in the Time Domain ^{[ ten ]} ​
3. Spectral Order-N Method ^{[ 11 ]} ​ ^{[ twelfth ]} ​
4. Método de Corring-time-Rotoker (KKR)

Basically these methods calculate the frequencies (normal modes) of the photonic crystals for each value of the propagation direction given by the wave or vice versa vector, the values ​​of the wave vector K for each frequency, in the reciprocal space. The different lines in the band structure correspond to the different values ​​of N, the index of the bands. For an introduction to the structure of photonic bands, Joannopoulos’s book is recommended; Photonic Crystals: Molding The Flow of Light, ^{[ 13 ]} In English.

Structure of unidimensional photonic crystal bands, BRAGG’s expense, calculated using the scalar approach method.

The flat wave expansion method, or climbing approach, can be used to calculate the band structure by raising the Maxwell equations as a problem of own values, and thus solving its own frequencies for each direction of propagation of the wave vector. The dispersion diagram is directly resolved. The strength values ​​of the electric field can be calculated over the whole problem using the vectors of the same problem. The photo shown to the right corresponds to the band structure of a Bragg mirror, or a monodimensional photonic glass, consisting of a dielectric sheets with a dielectric constant of 13 interspersed with air sheets, and a relationship between periodicity between layers and its thickness (d/a) of 0.5. The solution is obtained by applying flat waves in 101 on the first area of ​​Billouin.

Applications [ To edit ]

Fotonic crystals are attractive materials with optical properties that allow controlling and manipulating light flow. Monodimensional photonic crystals are widely used as thin optical sheets with applications ranging from lens and mirrors coatings with low and high reflection to paintings that change color and inks. The greatest photonic crystals are of great interest for both theoretical and practical research and two -dimensional begin to find commercial uses. The first marketed products that included periodic photonic crystals in two dimensions are the microstructured fibers, which thanks to their microscopic structure confine the light with radically better results than for conventional optical fibers and find their application in non -linear optics devices and how unusual guides of light. Its three -dimensional analogues are far from being marketed but offer additional characteristics that can lead to a new concept of technologies (for example; optical computers) once certain technological facets are controlled such as their manufacture and the main problems such as disorder In structures.

See also [ To edit ]

References [ To edit ]

external links [ To edit ]