What is a Photonic Crystal?

Photonic crystal refers to an artificial periodic dielectric structure with Photonic Band-Gap (abbreviated as PBG) characteristics, and is sometimes called a PBG photonic crystal structure. The so-called photonic band gap means that a certain frequency range of waves cannot propagate in this periodic structure, that is, this structure itself has a "forbidden band".

As we all know, a lot of research started with the assumption that similar phenomena exist in different fields of nature. Because everything in the universe follows the same rules, even if the appearance is ever-changing, the internal rules are highly consistent. This is the magic of the universe, and it is also a secret that is difficult for human beings to understand. The same is true for the creation of photonic crystals, which were developed by scientists on the assumption that photons can also have a law similar to the propagation of electrons in ordinary crystals.

From the crystal structure diagram, we can see that the atoms in the crystal are arranged periodically and orderly. It is the existence of this periodic potential field that causes the moving electrons to be Bragg-scattered by the periodic potential field to form an energy band structure. There may be a band gap between the bands.

Photonic crystal applications

So far, a variety of new photonic devices based on photonic crystals have been proposed successively, including thresholdless lasers, lossless mirrors and curved optical paths, high quality factor optical microcavities, low drive energy nonlinear switches and Amplifiers, super prisms with extremely high wavelength resolution and small volume, photonic crystal fibers with dispersion compensation, and light-emitting diodes that improve efficiency. The advent of photonic crystals

Photonic crystals

The "all-photonization" of information processing technology and the miniaturization and integration of photon technology become possible. It may lead to a revolution in information technology in the future, and its impact may be comparable to that of semiconductor technology.

The recent application of photonic crystals in the world has been further deepened, as follows:

(1) Combined with nanotechnology for manufacturing micron-level lasers and silicon-based lasers;

(2) In combination with quantum dots, the interaction between atoms and photons affects the properties of materials, thereby reducing the speed of light and reducing absorption;

(3) Photonic crystal fiber application: With the development of society, prominent semiconductor devices can no longer meet the needs of the development of information technology, and new materials with higher information transmission rates and higher efficiency must be found. It is generally believed that photonic technology will continue to write the glory of electronic technology, and photonic crystals will become new materials on which the future depends;

(5) Implementation of Dirac cone in photonic crystal.

Photonic crystal preparation

The preparation of photonic crystals is difficult because the lattice dimensions of the photonic crystals and the wavelength of light have the same order of magnitude. For example, for optical communication bands (wavelengths of 1.55 m), the photonic crystals' lattice is required to be about 0.5 m. In recent years, in the process of continuous exploration and experimentation, many feasible artificial preparation methods have appeared, such as: dielectric rod stacking, precision mechanical drilling, colloidal particle self-organization growth, colloidal solution self-organization growth, and semiconductor technology. With these methods, by manually controlling the ratio of the dielectric constant between the dielectric materials in the photonic crystal and the microperiodical structure of the photonic crystal, photonic crystals with various band gaps can be prepared.

Photonic Crystal Theory

The theoretical research of photonic crystals began in the late 1980s. Although Yablonovitch and John proposed the concept of photonic crystals in 1987, it was not until 1989 that Yablonovitch and Gmitter experimentally confirmed the existence of a three-dimensional photon band structure, and the physical community began to invest heavily in theoretical research in this area. Because photonic crystals have a structure similar to electronic crystals, people usually use the method of analyzing electronic crystals to analyze the characteristics of photonic crystals and obtain the results consistent with the experiments. The main methods are: plane wave expansion

Photonic crystals

Method (planewaveexpansionmethod abbreviation: PWM), transfer matrix method (abbreviation: TMM), finite difference time domain method (finishedifferencetimedomain abbreviation: FDTD), and scattering matrix method (scatteringmatrixmethod abbreviation: SMM).

The plane wave expansion method is a more commonly used method. Its basic idea is: by expanding the electromagnetic field in the form of plane waves, the Maxwell equations can be grouped into an eigen equation, and the eigenvalue of the propagated photon can be obtained by solving the eigenvalue of the equation. frequency. The disadvantage of this method is that when the photonic crystal structure is complex or the system is defective, it may not be calculated or it is difficult to calculate accurately due to the limitation of the computing power. And if the dielectric constant is not constant but changes with frequency, there is no definite form of the eigenequation, which cannot be solved at all in this case.

The transmission matrix method is to expand the magnetic field at the grid position in real space, and transform the Maxwell equations into a transmission matrix form, which also becomes an eigenvalue problem. The transfer matrix represents the relationship between the field strength of one layer (area) grid point and the field strength of another layer (area) grid next to it. It assumes that the same state of the same grid layer (area) exists in the formed space. At the same frequency, the Maxwell equations can be used to extrapolate the field from one location to the entire crystal space. This method is particularly effective for our metal systems whose dielectric constant changes with frequency, and because the transmission matrix is small, the matrix elements are small, the amount of calculation is small, and it is very convenient to calculate the transmission spectrum. However, it is troublesome to solve the electromagnetic field distribution by this method, and the efficiency is not very high, so it does not help much to understand the physical characteristics of photonic crystals.

The finite-difference time-domain method is one of the classical methods for numerical calculation of electromagnetic fields. Here, a unit run is divided into many small grids, and the finite difference agenda of each node on the network is listed. Using the Zhous condition at the boundary of the Brillouin zone, the Maxwell equations are also grouped into a matrix.

Photonic crystals

This matrix is quasi-diagonal, with only a small number of non-zero matrix elements, and the calculation is minimal. However, because the finite difference time domain method does not consider the specific shape of the crystal lattice, it is difficult to accurately solve it when encountering a photonic crystal with a special shape lattice.

The scattering matrix method assumes that the photonic crystal is composed of an isotropic medium, which is filled with various overlapping and non-overlapping optical scattering centers. By applying the Fourier-Bessel expansion to the scattering fields of all scattering centers, the Helmholtz equation is solved to calculate the field distribution transmitted in the photonic crystal. Applying this method is feasible for solving the field distribution and transmission spectrum, but because this method requires a long calculation time, it is actually not feasible in some cases.

In actual theoretical analysis, there are many other methods, such as: finite element method, N-order method, and so on. These methods have their own advantages and disadvantages, and should be selected reasonably according to the actual situation when applying. These analysis methods are very important in the research of photonic crystals. Because the preparation of photonic crystals is very difficult, it is usually first to apply these methods to analyze some characteristics of photonic crystals, and then verify these conclusions by experiments.

Future development of photonic crystals

Prophecies are always difficult to fulfill. However, the future of photonic crystal circuits and devices looks certain. Within five years, many basic applications of photonic crystals will appear on the market. In these applications, there will be high-efficiency photonic crystal laser emitters and high-brightness light-emitting diodes.

And when each home is connected to a fiber optic network, signal-decoding devices similar to today's "view-top boxes" will use photonic crystal circuits and devices instead of bulky fiber and silicon circuits.

Within five to ten years, we should make the first photonic crystal "diode" and "transistor"; in

Photonic crystals

In ten to fifteen years, we will be able to make the first photonic crystal logic circuit and dominate it; in the next twenty-five years, a photonic computer driven by a photonic crystal should be possible. Surprisingly, synthetic opals can even find a living environment in the jewelry and art market; and photonic crystal films can be pasted on credit cards as anti-counterfeiting signs.

If our predictions are simply a distortion of the future that is completely impossible, we hope that most people will forget what we said before. However, the future of photonic crystals looks bright.