In recent years, the international application of photonic crystals has been further deepened in the following aspects:
1. Combined with nanotechnology, it is used to manufacture micron-scale lasers and silicon-based lasers;
2. Combined with quantum dots, the interaction between atoms and photons affects the properties of materials, thus reducing the speed of light and absorption.
3. Photonic crystal fiber applications
With the development of society, the once famous semiconductor devices can no longer meet the needs of information technology development, so we must find new materials with higher information transmission rate and higher efficiency. It is generally believed that photonic technology will continue to write the glory of electronic technology, and photonic crystals will become new materials that can be relied on in the future.
4. Realization of Dirac Cone in Photonic Crystals The theoretical study of Photonic Crystals began in the late 1980s. Although Yablonovich and John put forward the concept of photonic crystal in 1987, it was not until 1989 that Yablonovich and Gmitter proved the existence of three-dimensional photonic band structure for the first time, and physicists began to devote themselves to theoretical research in this field. Because photonic crystals have a structure similar to electronic crystals, people usually use structural electromagnetic theory to analyze the characteristics of photonic crystals, and the results are consistent with the experiments. The main methods are: planewaveexpansionmethod (PWM), transfermatrixmethod (TMN), Finite Difference Time Domain Method (FDTD) and Scattering Matrix Method (SMM).
Plane wave expansion method is a common method. The basic idea is that the electromagnetic field is expanded in the form of plane wave, and Maxwell equations can be transformed into eigenequations, and the eigenfrequencies of propagating photons can be obtained by solving the eigenvalues of the equations. The disadvantage of this method is that when the photonic crystal structure is complex or the defective system is processed, it may be impossible or difficult to calculate accurately due to the limitation of computing power. Moreover, if the dielectric constant is not constant but varies with frequency, there is no definite eigenequation and it cannot be solved at all.
The transfer matrix method is to expand the lattice position of magnetic field in real space, and transform Maxwell equations into the form of transfer matrix, which also becomes the eigenvalue of solving problems. The transmission matrix represents the relationship between the field strength of one layer (plane) and the field strength of another layer (plane) adjacent to it. It assumes that there are the same states and the same frequencies on the same layer (plane) in the constructed space, so the field can be extrapolated from one position to the whole crystal space by Maxwell equations. This method is especially effective for our metal system whose dielectric constant varies with frequency, and it is also convenient to calculate the transmission spectrum because of its small transmission matrix, few matrix elements and small amount of calculation. However, it is troublesome and inefficient to solve the electromagnetic field distribution by this method, which is not very helpful 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. In this paper, a unit primitive journey is divided into many grid units, and the finite difference agenda of each node in the network is listed. Using Zeus condition of Brillouin zone boundary, Maxwell's equations are also transformed into characteristic equations in matrix form, which are quasi-diagonal, with only a few non-zero matrix elements, and the amount of calculation is minimal. However, because the finite difference time domain method does not consider the specific shape of the lattice, it is difficult to accurately solve photonic crystals with special-shaped lattices.
The scattering matrix method assumes that photonic crystals are composed of isotropic media filled with non-overlapping optical scattering centers with different starting points and sizes. Fourier-Bessel expansion is applied to the scattering fields of all scattering centers, Helmholtz equation is solved, and the field distribution transmitted in photonic crystals is calculated. The application of this method is feasible for solving the field distribution and transmission spectrum, but it is actually not feasible in some cases because it requires a long operation time.
In the 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 chosen reasonably according to the actual situation. These analytical methods are very important in the study of photonic crystals. Because the preparation of photonic crystals is very difficult, these methods are usually used to analyze some characteristics of photonic crystals first, and then these conclusions are verified by experiments. Predictions are always hard to come true. However, the future of photonic crystal circuits and devices seems certain. Within five years, there will be many basic applications of photonic crystals on the market. In these applications, there will be efficient photonic crystal laser emitters and high brightness light emitting diodes.
When every household is connected to the optical fiber network, the signal decoding equipment similar to the current set-top box will use photonic crystal circuits and devices instead of bulky optical fibers and silicon rings.
In five to ten years, we should make the first photonic crystal diode and transistor; In ten to fifteen years, we can make the first photonic crystal logic circuit and make it occupy the main position; In the next twenty-five years, it should be possible to manufacture photonic computers driven by photonic crystals. Surprisingly, synthetic opal can even find a living environment in the jewelry and art market; Photonic crystal films can be attached to credit cards as anti-counterfeiting marks.
If our prediction is just a completely impossible distortion of the future, we hope that most people will forget that we once said so. However, the future of photonic crystals still looks bright.