topological-insulator laser is significantly more efficient than today’s semiconductor laser designs. The laser consists of a two-dimensional (2D) nonmagnetic lattice of microresonators that, when pumped with light or electrical energy at the outer edge of the lattice, ferry photons easily around the perimeter before escaping as a single-mode lasing beam at one corner. Unlike other lasers that depend on flawless fabrication methods, the topological insulator laser still allows photons to flow even in the presence of lattice defects, which have little effect on the overall efficiency of the device. The laser is now being explored for use in quantum communications and silicon photonics Topological photonics has recently been proven as a robust framework for manipulating light. Active topological photonic systems, in particular, enable richer fundamental physics by employing nonlinear light-matter interactions, thereby opening a new landscape for applications such as topological lasing.
1.Photonic crystal: https://en.wikipedia.org/wiki/Photonic_crystal
A photonic crystal is a periodic optical nanostructure that affects the motion of photons in much the same way that ionic lattices affect electrons in solids. Photonic crystals occur in nature in the form of structural coloration and animal reflectors, and, in different forms, promise to be useful in a range of applications. 光子晶体是由周期性排列的不同折射率的介质制造的规则光学结构。这种材料因为具有光子带隙而能够阻断特定频率的光子，从而影响光子运动的。这种影响类似于半导体晶体对于电子行为的影响。由半导体在电子方面的应用，人们推想可以通过光子晶体制造的器件来控制光子运动，例如制造光子计算机。另外，光子晶体也在自然界中发现。由于介電係數存在空间上的周期性，进而引起空间折射率的周期变化。当介電係數的变化足够大且变化周期与光波长相当时，光波的色散关系会出现带状结构，此即光子能带结构（Photonic Band structures）。这些被终止的频率区间称为“光子频率禁带”（Photonic Band Gap，PBG），频率落在禁带中的光或电磁波是无法传播的。我们将具有“光子频率禁带”的周期性介电结构称作为光子晶体。
2.T-symmetry: https://en.wikipedia.org/wiki/T-symmetry
T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal. Since the second law of thermodynamics states that entropy increases as time flows toward the future, in general, the macroscopic universe does not show symmetry under time reversal. In other words, time is said to be non-symmetric, or asymmetric, except for special equilibrium states when the second law of thermodynamics predicts the time symmetry to hold. 时间反演对称（T-symmetry或time reversal symmetry）描述的是在时间反演{\displaystyle T:t\mapsto -t} T: t \mapsto -t运算下，物理系统所保有的对称性，又可标作T对称。 虽然在一些限定条件下存在时间反演对称性，但是由于热力学第二定律我们观测到的宇宙并不具有时间反演对称性. 发生不对称性有两种情况: 第一种是物理定律时间反演的不对称性，比如弱相互作用；第二个是宇宙初始条件所导致的不对称性。
3.Resonator: https://en.wikipedia.org/wiki/Resonator
A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator can be either electromagnetic or mechanical (including acoustic). Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones. Another example is quartz crystals used in electronic devices such as radio transmitters and quartz watches to produce oscillations of very precise frequency.
4.Optical ring resonators: https://en.wikipedia.org/wiki/Optical_ring_resonators
An optical ring resonator is a set of waveguides in which at least one is a closed loop coupled to some sort of light input and output. (These can be, but are not limited to being, waveguides.) The concepts behind optical ring resonators are the same as those behind whispering galleries except that they use light and obey the properties behind constructive interference and total internal reflection. When light of the resonant wavelength is passed through the loop from input waveguide, it builds up in intensity over multiple round-trips due to constructive interference and is output to the output bus waveguide which serves as a detector waveguide. Because only a select few wavelengths will be at resonance within the loop, the optical ring resonator functions as a filter. Additionally, as implied earlier, two or more ring waveguides can be coupled to each other to form an add/drop optical filter.[1] 光学环形谐振器由至少一个光路封闭的波导以及光线的输入与输出端(比如波导)所组成。光学环形谐振器的概念与回音廊相仿，不同处在于使用光线，并且需遵守建设性干涉与全内反射条件。当符合共振条件的光线从输入端波导进入，并经过环形波导，在环形波导里由于建设性干涉而逐渐增加光强，最后在输出端波导输出。 由于只有特定的波长的光才能在环形波导中发生共振，整个光学环形谐振器可视为是一个滤波器。此外，两个或多个环形波导可以互相耦合，产生出加/减光学滤波器。
5.Laser: https://en.wikipedia.org/wiki/Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym[1][2] for "light amplification by stimulated emission of radiation".[3][4][5] The first laser was built in 1960 by Theodore H. Maiman at Hughes Research Laboratories, based on theoretical work by Charles Hard Townes and Arthur Leonard Schawlow. 激光器是利用受激辐射原理使光在某些受激发的物质中放大或振荡发射激光（laser）的器件。 用光、电及其他办法对物质进行激励，使得其中一部分粒子激发到能量较高的状态，当这种状态的粒子数大于能量较低状态的粒子数时，由于受激辐射，物质就能对某一波长的光辐射产生放大作用，也就是这种波长的光辐射通过物质时，会发射强度放大并与入射光波位、频率和方向一致的光辐射，这种称为激光放大器。 若把激发的物质放置于共振腔内，光辐射在共振腔内沿轴线方向往复反射传播，多次通过物质，光辐射被放大许多倍，形成一束强度大、方向集中的光束“激光”，这就是激光振荡器。
5.Topological insulator: https://en.wikipedia.org/wiki/Topological_insulator
A topological insulator is a material that behaves as an insulator in its interior but whose surface contains conducting states,[3] meaning that electrons can only move along the surface of the material. Topological insulators have non-trivial symmetry-protected topological order; however, having a conducting surface is not unique to topological insulators, since ordinary band insulators can also support conductive surface states. What is special about topological insulators is that their surface states are symmetry-protected Dirac fermions[1][2][3][4][5][6][7] by particle number conservation and time-reversal symmetry. In two-dimensional (2D) systems, this ordering is analogous to a conventional electron gas subject to a strong external magnetic field causing electronic excitation gap in the sample bulk and metallic conduction at the boundaries or surfaces 拓扑绝缘体是一种内部绝缘，界面允许电荷移动的材料。 在拓扑绝缘体的内部，电子能带结构和常规的绝缘体相似，其费米能级位于导带和价带之间。在拓扑绝缘体的表面存在一些特殊的量子态，这些量子态位于块体能带结构的带隙之中，从而允许导电。这些量子态可以用类似拓扑学中的亏格的整数表征，是拓扑序的一个特例[1]。
6.Optical modulator: https://en.wikipedia.org/wiki/Optical_modulator
An optical modulator is a device which is used to modulate a beam of light. The beam may be carried over free space, or propagated through an optical waveguide (optical fibre). Depending on the parameter of a light beam which is manipulated, modulators may be categorized into amplitude modulators, phase modulators, polarization modulators etc. Often the easiest way to obtain modulation of intensity of a light beam, is to modulate the current driving the light source, e.g. a laser diode. This sort of modulation is called direct modulation, as opposed to the external modulation performed by a light modulator. For this reason light modulators are, e.g. in fiber optic communications, called external light modulators.
7.Dispersion relation: https://en.wikipedia.org/wiki/Dispersion_relation
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the phase velocity and group velocity of waves in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig relations describe the frequency dependence of wave propagation and attenuation. 在物理科学和电气工程学中，色散关系描述波在介质中传播的色散现象的性质。色散关系将波的波长或波数与其频率建立了联系。由这组关系，波的相速度和群速度有了方便的确定介质中折射率的表达式。克拉莫-克若尼关系式可以描述波的传播、衰减的频率依赖性，这关系比与几何相关和与材料相关的色散关系更具一般性。
8.Dispersion Diagram: https://www.igi-global.com/dictionary/dispersion-diagram/56263
It is a diagram between Phase constant (ß) and Wave Number ( k ) is plotted with each propagating mode having different phase velocity, group velocity and fields vectors.
8.1 Phase constant: https://en.wikipedia.org/wiki/Propagation_constant#Phase_constant
In electromagnetic theory, the phase constant, also called phase change constant, parameter or coefficient is the imaginary component of the propagation constant for a plane wave. It represents the change in phase per unit length along the path travelled by the wave at any instant and is equal to the real part of the angular wavenumber of the wave. It is represented by the symbol β and is measured in units of radians per unit length.
From the definition of (angular) wavenumber for TEM waves in lossless media:
{\displaystyle k={\frac {2\pi }{\lambda }}=\beta }k={\frac {2\pi }{\lambda }}=\beta
8.2 Propagation constant: https://en.wikipedia.org/wiki/Propagation_constant#Phase_constant
The propagation constant of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it propagates in a given direction. The quantity being measured can be the voltage, the current in a circuit, or a field vector such as electric field strength or flux density. The propagation constant itself measures the change per unit length, but it is otherwise dimensionless. In the context of two-port networks and their cascades, propagation constant measures the change undergone by the source quantity as it propagates from one port to the next. 传播常数是表征电磁波在传播媒介中的变化特性的参数。这是一个复数，其实部表征衰减常数，虚部表征相位常数。
8.3 Wavenumber: https://en.wikipedia.org/wiki/Wavenumber
In the physical sciences, the wavenumber (also wave number or repetency[1]) is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency can be thought of as the number of waves per unit time, wavenumber is the number of waves per unit distance.
In multidimensional systems, the wavenumber is the magnitude of the wave vector. The space of wave vectors is called reciprocal space. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck's constant is the canonical momentum.
Wavenumber can be used to specify quantities other than spatial frequency. In optical spectroscopy, it is often used as a unit of temporal frequency assuming a certain speed of light. 在物理学里，波数是波动的一种性质，定义为每 2π 长度的波长数量（即每单位长度的波长数量乘以2π）。更明确地说，波数是每2π长度内，波动重复的次数（一个波动取同样相位的次数）。波数与波长成反比。
8.4 Waveguide (optics): https://en.wikipedia.org/wiki/Waveguide_(optics)
An optical waveguide is a physical structure that guides electromagnetic waves in the optical spectrum. Common types of optical waveguides include optical fiber and transparent dielectric waveguides made of plastic and glass. Optical waveguides are used as components in integrated optical circuits or as the transmission medium in local and long haul optical communication systems. Optical waveguides can be classified according to their geometry (planar, strip, or fiber waveguides), mode structure (single-mode, multi-mode), refractive index distribution (step or gradient index) and material (glass, polymer, semiconductor).
9. Single-mode optical fiber: https://en.wikipedia.org/wiki/Single-mode_optical_fiber
In fiber-optic communication, a single-mode optical fiber (SMF) is an optical fiber designed to carry only a single mode of light - the transverse mode. Modes are the possible solutions of the Helmholtz equation for waves, which is obtained by combining Maxwell's equations and the boundary conditions. These modes define the way the wave travels through space, i.e. how the wave is distributed in space. Waves can have the same mode but have different frequencies. This is the case in single-mode fibers, where we can have waves with different frequencies, but of the same mode, which means that they are distributed in space in the same way, and that gives us a single ray of light. Although the ray travels parallel to the length of the fiber, it is often called transverse mode since its electromagnetic oscillations occur perpendicular (transverse) to the length of the fiber. The 2009 Nobel Prize in Physics was awarded to Charles K. Kao for his theoretical work on the single-mode optical fiber.[1] The standards G.652 and G.657 define the most widely used forms of single-mode optical fiber.[2]
9.1 Transverse mode: https://en.wikipedia.org/wiki/Transverse_mode
A transverse mode of electromagnetic radiation is a particular electromagnetic field pattern of the radiation in the plane perpendicular (i.e., transverse) to the radiation's propagation direction. Transverse modes occur in radio waves and microwaves confined to a waveguide, and also in light waves in an optical fiber and in a laser's optical resonator.[1] Transverse modes occur because of boundary conditions imposed on the wave by the waveguide. For example, a radio wave in a hollow metal waveguide must have zero tangential electric field amplitude at the walls of the waveguide, so the transverse pattern of the electric field of waves is restricted to those that fit between the walls. For this reason, the modes supported by a waveguide are quantized. The allowed modes can be found by solving Maxwell's equations for the boundary conditions of a given waveguide.
10. Multi-mode optical fiber: https://en.wikipedia.org/wiki/Multi-mode_optical_fiber
Multi-mode optical fiber is a type of optical fiber mostly used for communication over short distances, such as within a building or on a campus. Multi-mode links can be used for data rates up to 100 Gbit/s. Multi-mode fiber has a fairly large core diameter that enables multiple light modes to be propagated and limits the maximum length of a transmission link because of modal dispersion.
10.1 Modal dispersion: https://en.wikipedia.org/wiki/Modal_dispersion
Modal dispersion is a distortion mechanism occurring in multimode fibers and other waveguides, in which the signal is spread in time because the propagation velocity of the optical signal is not the same for all modes. Other names for this phenomenon include multimode distortion, multimode dispersion, modal distortion, intermodal distortion, intermodal dispersion, and intermodal delay distortion.
11. Wave vector: https://en.wikipedia.org/wiki/Wave_vector
In physics, a wave vector (also spelled wavevector) is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important. Its magnitude is either the wavenumber or angular wavenumber of the wave (inversely proportional to the wavelength), and its direction is ordinarily the direction of wave propagation (but not always, see below). In the context of special relativity the wave vector can also be defined as a four-vector.
12. Chromatic dispersion: https://www.m2optics.com/blog/bid/61431/chromatic-dispersion-in-optical-fibers#:~:text=Chromatic%20dispersion%20is%20a%20phenomenon,destination%20at%20slightly%20different%20times.
Chromatic dispersion is a phenomenon that is an important factor in fiber optic communications. It is the result of the different colors, or wavelengths, in a light beam arriving at their destination at slightly different times. The result is a spreading, or dispersion, of the on-off light pulses that convey digital information. Special care must be taken to compensate for this dispersion so that the optical fiber delivers its maximum capacity.
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.[1] Media having this common property may be termed dispersive media. Sometimes the term chromatic dispersion is used for specificity. Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, in gravity waves (ocean waves), and for telecommunication signals along transmission lines (such as coaxial cable) or optical fiber. Physically, dispersion translates in a loss of kinetic energy through absorption.
In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light,[2] as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses, in which chromatic aberration is largely cancelled, uses a quantification of a glass's dispersion given by its Abbe number V, where lower Abbe numbers correspond to greater dispersion over the visible spectrum. In some applications such as telecommunications, the absolute phase of a wave is often not important but only the propagation of wave packets or "pulses"; in that case one is interested only in variations of group velocity with frequency, so-called group-velocity dispersion.
13. Absorption Coefficient: https://www.pveducation.org/pvcdrom/pn-junctions/absorption-coefficient
Different semiconductor materials have different absorption coefficients. Materials with higher absorption coefficients more readily absorb photons, which excite electrons into the conduction band. Knowing the absorption coefficients of materials aids engineers in determining which material to use in their solar cell designs. The absorption coefficient determines how far into a material light of a particular wavelength can penetrate before it is absorbed. In a material with a low absorption coefficient, light is only poorly absorbed, and if the material is thin enough, it will appear transparent to that wavelength. The absorption coefficient depends on the material and also on the wavelength of light which is being absorbed. Semiconductor materials have a sharp edge in their absorption coefficient, since light which has energy below the band gap does not have sufficient energy to excite an electron into the conduction band from the valence band. Consequently, this light is not absorbed.
14. Interferometry: https://en.wikipedia.org/wiki/Interferometry
Interferometry is a technique in which waves are superimposed to cause the phenomenon of interference, which is used to extract information.[1] Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, spectroscopy (and its applications to chemistry), quantum mechanics, nuclear and particle physics, plasma physics, remote sensing, biomolecular interactions, surface profiling, microfluidics, mechanical stress/strain measurement, velocimetry, optometry, and making holograms. Interferometry makes use of the principle of superposition to combine waves in a way that will cause the result of their combination to have some meaningful property that is diagnostic of the original state of the waves. This works because when two waves with the same frequency combine, the resulting intensity pattern is determined by the phase difference between the two waves—waves that are in phase will undergo constructive interference while waves that are out of phase will undergo destructive interference. Waves which are not completely in phase nor completely out of phase will have an intermediate intensity pattern, which can be used to determine their relative phase difference. Most interferometers use light or some other form of electromagnetic wave. 依据叠加原理，波汇合的结果具有能够反映波原始状态的性质。干涉测量术正是基于这一点。当两束频率相同的光叠加时，它们产生的条纹取决于它们的相位差：相位相同时会产生增强条纹，相反则会产生减弱条纹。两种情况之间则会产生中间强度的条纹。这些条纹可以用来分析这两束波的相对相位关系。绝大多数的干涉仪利用的是可见光等电磁波。
15. Mach–Zehnder interferometer: https://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer
https://www.youtube.com/watch?v=os4rDtjrP4c https://www.sciencedirect.com/topics/engineering/mach-zehnder-interferometer The Mach–Zehnder check interferometer is a highly configurable instrument. In contrast to the well-known Michelson interferometer, each of the well-separated light paths is traversed only once. If the source has a low coherence length then great care must be taken to equalize the two optical paths. White light in particular requires the optical paths to be simultaneously equalized over all wavelengths, or no fringes will be visible. As seen in Fig. 1, a compensating cell made of the same type of glass as the test cell (so as to have equal optical dispersion) would be placed in the path of the reference beam to match the test cell. Note also the precise orientation of the beam splitters. The reflecting surfaces of the beam splitters would be oriented so that the test and reference beams pass through an equal amount of glass. In this orientation, the test and reference beams each experience two front-surface reflections, resulting in the same number of phase inversions. The result is that light travels through an equal optical path length in both the test and reference beams leading to constructive interference. 曾干涉仪的内部设置可以很容易更改。与迈克耳孙干涉仪明显不同，两道被分裂的光束只会分别行经一次马曾干涉仪的两条严格分隔的路径。 由于白光的相干长度很有限，数量级为微米，必须非常仔细的将白光的所有波长的光程都调整为一样，才能通过马曾干涉仪将白光制成黑白相间的干涉条纹，否则无法观察到干涉条纹。如首段火焰图所示，一个同样玻璃材质的“补偿盒”被置入参考光束的路径来匹配“检验盒”，这样，两个盒子的光学色散可以调整为一样。注意到两个分束器的精确取向，两个分束器的反射表面应该有完全相反取向（一个面向左上方，一个面向右下方），这样，检验光束与参考光束会透射过同样厚度的玻璃。由于检验光束与参考光束都经历到两个“空气－镜面的界面反射”，造成同样的相移，因此，在最右方屏幕会形成相长干涉图样，显示为白色火焰；而在最上方屏幕会另外形成相消干涉图样，显示为黑色火焰。
16. Diffraction grating: https://en.wikipedia.org/wiki/Diffraction_grating
In optics, a diffraction grating is an optical component with a periodic structure that splits and diffracts light into several beams travelling in different directions. The emerging coloration is a form of structural coloration.[1][2] The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as the dispersive element. Because of this, gratings are commonly used in monochromators and spectrometers. 衍射光栅（diffractio rating） 是光栅的一种。它通过有规律的结构，使入射光的振幅或相位（或两者同时）受到周期性空间调制。衍射光栅在光学上的最重要应用是作为分光器件，常被用于单色仪和光谱仪上。 实际应用的衍射光栅通常是在表面上有沟槽或刻痕的平板。这样的光栅可以是透射光栅或反射光栅。可以调制入射光的相位而不是振幅的衍射光栅现在也能生产。
17. grating coupler: https://www.sciencedirect.com/topics/materials-science/coupler
Grating couplers have been extensively used in silicon photonics to provide efficient coupling to silicon waveguides, also offering better alignment tolerances than facet coupling
18. directional coupler: https://www.everythingrf.com/community/what-is-a-directional-coupler#:~:text=A%20directional%20coupler%20is%20a,signal%20power%20for%20measurement%20purposes.&text=The%20coupling%20is%20one%20of,dB%20to%20over%2030%20dB.
A directional coupler is a 4-port device that is used to sample a small amount of input signal power for measurement purposes. As seen in the diagram below, Port 1 is the input port, port 2 is the output port, port 3 is the coupled port and port 4 is the isolated/terminated port. Power dividers (also power splitters and, when used in reverse, power combiners) and directional couplers are passive devices used mostly in the field of radio technology. They couple a defined amount of the electromagnetic power in a transmission line to a port enabling the signal to be used in another circuit. An essential feature of directional couplers is that they only couple power flowing in one direction. Power entering the output port is coupled to the isolated port but not to the coupled port. A directional coupler designed to split power equally between two ports is called a hybrid coupler.
19. Multi mode interferometer: https://en.wikipedia.org/wiki/Multi_mode_interferometer
A multi-mode interferometer (MMI), also known as a multimode interference coupler, is a micro-scale structure in which light waves can travel, such that the optical power is split or combined in a predictable way. In an MMI, light is confined and guided, and thus the MMI is essentially a broad optical waveguide.[1] For example, an ideal 1x2 MMI would be a 50-50 splitter,[2] such that light enters along one path and exits along two paths, with half the power in each exit path. These entrance and exit paths are narrow waveguides, and the MMI itself is in the shape of a broad rectangular box. An ideal 50-50 splitter is nearly impossible in practice, due to the complex behavior of light. Optical loss will always occur as light travels through an MMI, which means that the total output power of a real MMI is less than the total input power. Additionally, the light propagates through the rectangular box in multiple modes, while also experiencing reflection and interference. This leads to mathematical models and equations that are too complex to solve by hand, and thus MMIs are typically designed through computer simulations. MMI, 全称是multi-mode inferometer, 即多模干涉器（有些文献里也称为multi-mode interference coupler, 即多模干涉耦合器)。顾名思义，MMI的工作原理是基于多模干涉，在特定位置处形成自成像，周期性地复现输入光场。
20. The Grating Equation: https://www.plymouthgrating.com/guidance/technical-notes/fundamentals/the-grating-equation/
https://mp.weixin.qq.com/s?__biz=MzU2NTA2NTQwNA==&mid=2247483887&idx=1&sn=cd8fc83af9a2db4fec849ad72ada312d&chksm=fc40223ccb37ab2a8c01a583cdf956b9a54dcc253c55f4adb9770fcf8b193c94716c8d72e17a&scene=21#wechat_redirect 所谓光栅，就是通过一定的微加工手段，使得材料的折射率满足一定的分布，从而实现对光操控的一类光器件。
22. Arrayed waveguide grating: https://en.wikipedia.org/wiki/Arrayed_waveguide_grating
https://zhuanlan.zhihu.com/p/98484444 Arrayed waveguide gratings (AWG) are commonly used as optical (de)multiplexers in wavelength division multiplexed (WDM) systems. These devices are capable of multiplexing many wavelengths into a single optical fiber, thereby increasing the transmission capacity of optical networks considerably.
The devices are based on a fundamental principle of optics that light waves of different wavelengths do not interfere linearly with each other. This means that, if each channel in an optical communication network makes use of light of a slightly different wavelength, then the light from many of these channels can be carried by a single optical fiber with negligible crosstalk between the channels. The AWGs are used to multiplex channels of several wavelengths onto a single optical fiber at the transmission end and are also used as demultiplexers to retrieve individual channels of different wavelengths at the receiving end of an optical communication network. AWG (Arrayed Waveguide Grating)是密集波分复用系统（DWDM）中的首选技术。一组具有相等长度差的阵列波导形成的光栅，使用具有分波的能力。其原理为：含有多个波长的复用信号光经中心输入信道波导输出后，在输入平板波导内发生衍射，到达输入凹面光栅上进行功率分配，并耦合进入阵列波导区。因阵列波导端面位于光栅圆的圆周上，所以衍射光以相同的相位到达阵列波导端面上。经阵列波导传输后，因相邻的阵列波导保持有相同的长度差ΔL，因而在输出凹面光栅上相邻阵列波导的某一波长的输出光具有相同的相位差，对于不同波长的光此相位差不同，于是不同波长的光在输出平板波导中发生衍射并聚焦到不同的输出信道波导位置，经输出信道波导输出后完成了波长分配即解复用功能。这一过程的逆过程，即如果信号光反向输入，则完成复用功能，原理相同。
23. Echelle grating: https://en.wikipedia.org/wiki/Echelle_grating
An echelle grating (from French échelle, meaning "ladder") is a type of diffraction grating characterised by a relatively low groove density, but a groove shape which is optimized for use at high incidence angles and therefore in high diffraction orders. Higher diffraction orders allow for increased dispersion (spacing) of spectral features at the detector, enabling increased differentiation of these features. Echelle gratings are, like other types of diffraction gratings, used in spectrometers and similar instruments. They are most useful in cross-dispersed high resolution spectrographs, such as HARPS, PRL Advanced Radial Velocity Abu Sky Search (PARAS), and numerous other astronomical instruments. 阶梯光栅（Echelle grating，来自法语échelle，阶梯）是一种刻线密度较低，但刻线的形状是针对高入射角，即高衍射阶数的衍射光栅。高衍射阶数可以使光谱发生进一步色散，从而为探测器提供更详细的特征。
定向耦合器是微波系统中应用广泛的一种微波器件，它的本质是将微波信号按一定的比例进行功率分配。
An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric oscillators and some interferometers. Light confined in the cavity reflects multiple times, producing standing waves for certain resonance frequencies. The standing wave patterns produced are called modes; longitudinal modes differ only in frequency while transverse modes differ for different frequencies and have different intensity patterns across the cross-section of the beam. Light confined in a resonator will reflect multiple times from the mirrors, and due to the effects of interference, only certain patterns and frequencies of radiation will be sustained by the resonator, with the others being suppressed by destructive interference. In general, radiation patterns which are reproduced on every round-trip of the light through the resonator are the most stable, and these are the eigenmodes, known as the modes, of the resonator. Resonator modes can be divided into two types: longitudinal modes, which differ in frequency from each other; and transverse modes, which may differ in both frequency and the intensity pattern of the light. The basic, or fundamental transverse mode of a resonator is a Gaussian beam.
26. F-P谐振腔: https://baike.baidu.com/item/F-P%E8%B0%90%E6%8C%AF%E8%85%94#:~:text=F%2DP%E8%B0%90%E6%8C%AF%E8%85%94%EF%BC%8C%E5%85%A8%E5%90%8D,%E4%BA%8E%E5%8D%8A%E5%AF%BC%E4%BD%93%E6%BF%80%E5%85%89%E5%99%A8%EF%BC%88LD%EF%BC%89%20%E3%80%82
https://www.zhihu.com/question/21796925 横模是强度空间分布，纵模是频域分布（波长）
27. Optical band gap: https://www.researchgate.net/post/What_is_Optical_and_Photonic_band_gap#:~:text=The%20Photonic%20band%20gap%20corresponds,individual%20elements%20of%20the%20object.
Optical band gap is the same as material band gap. In materials the electrons are distributed inside bands of energy separated by energy gaps. If the last occupied band is only half occupied (metal) then the electrons of this band can absorb any photon with energy between 0 and a few eVs. If the last band is fully occupied (insulators and semiconductors) then the electrons can only be promoted on the next band at higher energy and that can only be done by photons having an energy at least equal to that of the band gap that separates the last occupied electron band from the next. The Photonic band gap corresponds to the reflection of light by a periodic object which period is equal to half the wavelength of the light that falls onto it. It is the result of an interference of the various wavelets that are reflected by the periodic individual elements of the object. No light is absorbed in the process. The wavelengths not matching the periodicity of the object just do pass through the object. https://www.sciencedirect.com/topics/materials-science/photonic-band-gap Photonic band-gap (PBGs) materials or photonic crystals (PhCs) are materials with a periodic dielectric profile, which can prevent light of certain frequencies or wavelengths from propagating in one, two or any number of polarisation directions within the materials. This range of frequencies is similar to an electronic band-gap; thus, it is often called a photonic band-gap. As shown in Fig. 7.1, the PBG materials can be one (1D), two (2D) or three-dimensional (3D). The Bragg grating structure is the best known one-dimensional PBG. Like an electronic band-gap, the PBG is caused by a lattice or a crystal structure. The lattice scale of PBG is in the order of the wavelength of light (0.1–2 mm), rather than in the order of atoms.
A photonic band gap (PBG) crystal is a structure that could manipulate beams of light in the same way semiconductors control electric currents. • A semiconductor cannot support electrons of energy lying in the electronic band gap. Similarly, a photonic crystal cannot support photons lying in the photonic band gap. By preventing or allowing light to propagate through a crystal, light processing can be done.
Photonic crystals usually consist of dielectric materials, that is, materials that serve as electrical insulators or in which an electromagnetic field can be propagated with low loss. • Holes (of the order of the relevant wavelength) are drilled into the dielectric in a lattice-like structure and repeated identically and at regular intervals. • If built precisely enough, the resulting holey crystal will have what is known as a photonic band gap, a range of frequencies within which a specific wavelength of light is blocked.
In semiconductors, electrons get scattered by the row of atoms in the lattice separated by a few nanometers and consequently an electronic band gap is formed. The resulting band structure can be modified by doping. • In a photonic crystal, perforations are analogous to atoms in the semiconductor. Light entering the perforated material will reflect and refract off interfaces between glass and air. The complex pattern of overlapping beams will lead to cancellation of a band of wavelengths in all directions leading to prevention of propagation of this band into the crystal. The resulting photonic band structure can be modified by filling in some holes or creating defects in the otherwise perfectly periodic system.
28. Non-Hermitian quantum mechanics: https://en.wikipedia.org/wiki/Non-Hermitian_quantum_mechanics#:~:text=Non%2DHermitian%20quantum%20mechanics%20is,symmetry%20have%20all%20real%20eigenvalues.
Non-Hermitian quantum mechanics[1][2] is the study of quantum-mechanical Hamiltonians that are not Hermitian. Notably, they appear in the study of dissipative systems. Also, non-Hermitian Hamiltonians with unbroken parity-time (PT) symmetry have all real eigenvalues.[3]
29. Photodetector: https://en.wikipedia.org/wiki/Photodetector
Photodetectors, also called photosensors, are sensors of light or other electromagnetic radiation.[1] There is a wide variety of photodetectors which may be classified by mechanism of detection, such as photoelectric or photochemical effects, or by various performance metrics, such as spectral response. Semiconductor-based photodetectors typically have a p–n junction that converts light photons into current. The absorbed photons make electron–hole pairs in the depletion region. Photodiodes and phototransistors are a few examples of photodetectors. Solar cells convert some of the light energy absorbed into electrical energy.
30.Quantum efficiency: https://en.wikipedia.org/wiki/Quantum_efficiency
The term quantum efficiency (QE) may apply to incident photon to converted electron (IPCE) ratio[1] of a photosensitive device, or it may refer to the TMR effect of a Magnetic Tunnel Junction.
This article deals with the term as a measurement of a device's electrical sensitivity to light. In a charge-coupled device (CCD) or other photodetector, it is the ratio between the number of charge carriers collected at either terminal and the number of photons hitting the device's photoreactive surface. As a ratio, QE is dimensionless, but it is closely related to the responsivity, which is expressed in amps per watt. Since the energy of a photon is inversely proportional to its wavelength, QE is often measured over a range of different wavelengths to characterize a device's efficiency at each photon energy level. For typical semiconductor photodetectors, QE drops to zero for photons whose energy is below the band gap. A photographic film typically has a QE of much less than 10%,[2] while CCDs can have a QE of well over 90% at some wavelengths.
A magneto-optic effect is any one of a number of phenomena in which an electromagnetic wave propagates through a medium that has been altered by the presence of a quasistatic magnetic field. In such a medium, which is also called gyrotropic or gyromagnetic, left- and right-rotating elliptical polarizations can propagate at different speeds, leading to a number of important phenomena. When light is transmitted through a layer of magneto-optic material, the result is called the Faraday effect: the plane of polarization can be rotated, forming a Faraday rotator. The results of reflection from a magneto-optic material are known as the magneto-optic Kerr effect (not to be confused with the nonlinear Kerr effect).
32.Franz–Keldysh effect: https://en.wikipedia.org/wiki/Franz%E2%80%93Keldysh_effect
The Franz–Keldysh effect is a change in optical absorption by a semiconductor when an electric field is applied. The effect is named after the German physicist Walter Franz and Russian physicist Leonid Keldysh (nephew of Mstislav Keldysh). Karl W. Böer observed first the shift of the optical absorption edge with electric fields [1] during the discovery of high-field domains[2] and named this the Franz-effect.[3] A few months later, when the English translation of the Keldysh paper became available, he corrected this to the Franz–Keldysh effect.[4] As originally conceived, the Franz–Keldysh effect is the result of wavefunctions "leaking" into the band gap. When an electric field is applied, the electron and hole wavefunctions become Airy functions rather than plane waves. The Airy function includes a "tail" which extends into the classically forbidden band gap. According to Fermi's golden rule, the more overlap there is between the wavefunctions of a free electron and a hole, the stronger the optical absorption will be. The Airy tails slightly overlap even if the electron and hole are at slightly different potentials (slightly different physical locations along the field). The absorption spectrum now includes a tail at energies below the band gap and some oscillations above it. This explanation does, however, omit the effects of excitons, which may dominate optical properties near the band gap.
33.Quantum-confined Stark effect: https://en.wikipedia.org/wiki/Quantum-confined_Stark_effect
The quantum-confined Stark effect (QCSE) describes the effect of an external electric field upon the light absorption spectrum or emission spectrum of a quantum well (QW). In the absence of an external electric field, electrons and holes within the quantum well may only occupy states within a discrete set of energy subbands. Only a discrete set of frequencies of light may be absorbed or emitted by the system. When an external electric field is applied, the electron states shift to lower energies, while the hole states shift to higher energies. This reduces the permitted light absorption or emission frequencies. Additionally, the external electric field shifts electrons and holes to opposite sides of the well, decreasing the overlap integral, which in turn reduces the recombination efficiency (i.e. fluorescence quantum yield) of the system. [1] The spatial separation between the electrons and holes is limited by the presence of the potential barriers around the quantum well, meaning that excitons are able to exist in the system even under the influence of an electric field. The quantum-confined Stark effect is used in QCSE optical modulators, which allow optical communications signals to be switched on and off rapidly.
34.Electro–optic effect: https://en.wikipedia.org/wiki/Electro%E2%80%93optic_effect
An electro–optic effect is a change in the optical properties of a material in response to an electric field that varies slowly compared with the frequency of light. The term encompasses a number of distinct phenomena, which can be subdivided into
a) change of the absorption Electroabsorption: general change of the absorption constants Franz–Keldysh effect: change in the absorption shown in some bulk semiconductors Quantum-confined Stark effect: change in the absorption in some semiconductor quantum wells Electrochromic effect: creation of an absorption band at some wavelengths, which gives rise to a change in colour b) change of the refractive index and permittivity Pockels effect (or linear electro-optic effect): change in the refractive index linearly proportional to the electric field. Only certain crystalline solids show the Pockels effect, as it requires lack of inversion symmetry Kerr effect (or quadratic electro-optic effect, QEO effect): change in the refractive index proportional to the square of the electric field. All materials display the Kerr effect, with varying magnitudes, but it is generally much weaker than the Pockels effect electro-gyration: change in the optical activity. Electron-refractive effect or EIPM In December 2015, two further electro-optic effects of type (b) were theoretically predicted to exist [1] but have not, as yet, been experimentally observed.
Changes in absorption can have a strong effect on refractive index for wavelengths near the absorption edge, due to the Kramers–Kronig relation.
Using a less strict definition of the electro-optic effect allowing also electric fields oscillating at optical frequencies, one could also include nonlinear absorption (absorption depends on the light intensity) to category a) and the optical Kerr effect (refractive index depends on the light intensity) to category b). Combined with the photoeffect and photoconductivity, the electro-optic effect gives rise to the photorefractive effect.
35.Pockels effect: https://en.wikipedia.org/wiki/Pockels_effect
The Pockels effect (after Friedrich Carl Alwin Pockels who studied the effect in 1893), or Pockels electro-optic effect, changes or produces birefringence in an optical medium induced by an electric field. In the Pockels effect, also known as the linear electro-optic effect, the birefringence is proportional to the electric field. In the Kerr effect, the refractive index change (birefringence) is proportional to the square of the field. The Pockels effect occurs only in crystals that lack inversion symmetry, such as lithium niobate, and in other noncentrosymmetric media such as electric-field poled polymers or glasses.
36.Kerr effect: https://en.wikipedia.org/wiki/Kerr_effect
The Kerr effect, also called the quadratic electro-optic (QEO) effect, is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index change is directly proportional to the square of the electric field instead of varying linearly with it. All materials show a Kerr effect, but certain liquids display it more strongly than others. The Kerr effect was discovered in 1875 by John Kerr, a Scottish physicist. 克尔效应（Kerreffect），也称“二次电光效应”，是物质因响应外电场的作用而改变其折射率的一种效应。克尔效应与泡克耳斯效应不同，前者感应出的折射率改变与外电场平方成正比，后者则与外电场成线性关系；前者可以在液体或非晶物质出现，后者只出现于没有对称中心的晶体物质。克尔效应或多或少会出现在每一种物质，但在某些液体会比较显著。这效应最先由苏格兰科学家约翰·克尔（John Kerr）在1878年发现。
37.Free carrier absorption: https://en.wikipedia.org/wiki/Free_carrier_absorption
Free carrier absorption occurs when a material absorbs a photon, and a carrier (electron or hole) is excited from an already-excited state to another, unoccupied state in the same band (but possibly a different subband). This intraband absorption is different from interband absorption because the excited carrier is already in an excited band, such as an electron in the conduction band or a hole in the valence band, where it is free to move. In interband absorption, the carrier starts in a fixed, nonconducting band and is excited to a conducting one. It is well known that the optical transition of electrons and holes in the solid state is a useful clue to understand the physical properties of the material. However, the dynamics of the carriers are affected by other carriers and not only by the periodic lattice potential. Moreover, the thermal fluctuation of each electron should be taken into account. Therefore a statistical approach is needed. To predict the optical transition with appropriate precision, one chooses an approximation, called the assumption of quasi-thermal distributions, of the electrons in the conduction band and of the holes in the valence band. The plasma dispersion effect is related to the density of free carriers in a semiconductor, which changes both the real and imaginary parts of the refractive index.
http://aikelabs.com/news/42.htm https://www.spiedigitallibrary.org/ebooks/PM/Integrated-Silicon-based-Optical-Modulators--100-Gb-s-and/3/Introduction-to-Integrated-Optical-Modulators/10.1117/3.2519862.ch3?SSO=1 Integrated optical modulators consist of active and passive planar optical waveguides designed and fabricated on semiconductor-based integrated photonics platforms. This chapter provides a general overview of integrated optical modulators. In the first part, optical modulators are classified into three types with respect to optical-waveguide layout. The optical waveguides are treated schematically as building blocks. Their structures and theoretical characteristics are described in detail in Chapter 4. This chapter focuses on the MZ optical modulator because of its versatility in the high-quality generation of optical data in intensity modulation and phase modulation in principle. Integrated MZ optical modulators on a silicon-photonics platform are highlighted in the last part of this chapter as the theme of this book.
39.Hot-carrier injection:https://en.wikipedia.org/wiki/Hot-carrier_injection
Hot carrier injection (HCI) is a phenomenon in solid-state electronic devices where an electron or a “hole” gains sufficient kinetic energy to overcome a potential barrier necessary to break an interface state. The term "hot" refers to the effective temperature used to model carrier density, not to the overall temperature of the device. Since the charge carriers can become trapped in the gate dielectric of a MOS transistor, the switching characteristics of the transistor can be permanently changed. Hot-carrier injection is one of the mechanisms that adversely affects the reliability of semiconductors of solid-state devices.
40.Double heterostructure:https://en.wikipedia.org/wiki/Double_heterostructure
https://www.zhihu.com/question/303764781 A double heterostructure is formed when two semiconductor materials are grown into a "sandwich". One material (such as AlGaAs) is used for the outer layers (or cladding), and another of smaller band gap (such as GaAs) is used for the inner layer. In this example, there are two AlGaAs-GaAs junctions (or boundaries), one at each side of the inner layer. There must be two boundaries for the device to be a double heterostructure. If there was only one side of cladding material, the device would be a simple heterostructure. The double heterostructure is a very useful structure in optoelectronic devices and has interesting electronic properties. If one of the cladding layers is p-doped, the other cladding layer n-doped and the smaller energy gap semiconductor material undoped, a p-i-n structure is formed. When a current is applied to the ends of the pin structure, electrons and holes are injected into the heterostructure. The smaller energy gap material forms energy discontinuities at the boundaries, confining the electrons and holes to the smaller energy gap semiconductor. The electrons and holes recombine in the intrinsic semiconductor emitting photons. If the width of the intrinsic region is reduced to the order of the de Broglie wavelength, the energies in the intrinsic region no longer become continuous but become discrete. (Actually, they are not continuous but the energy levels are very close together so we think of them as being continuous.) In this situation the double heterostructure becomes a quantum well.
41.Lasing threshold: https://en.wikipedia.org/wiki/Lasing_threshold
https://zhuanlan.zhihu.com/p/338970148 The lasing threshold is the lowest excitation level at which a laser's output is dominated by stimulated emission rather than by spontaneous emission. Below the threshold, the laser's output power rises slowly with increasing excitation. Above threshold, the slope of power vs. excitation is orders of magnitude greater. The linewidth of the laser's emission also becomes orders of magnitude smaller above the threshold than it is below. Above the threshold, the laser is said to be lasing. The term "lasing" is a back formation from "laser," which is an acronym, not an agent noun.
https://www.fiberlabs.com/glossary/stimulated-emission/#:~:text=Spontaneous%20emission%20takes%20place%20without,electron%20interacts%20with%20another%20photon. Stimulated and spontaneous emission When an optical gain medium is pumped optically or electronically, an electron is pumped (excited) from a lower energy level to an upper energy level. The excited medium is eventually relaxed to some lower energy level by radiating energy – as upper energy levels are generally less stable than lower energy levels – and sometimes the energy radiation takes a form of photon. This is how spontaneous emission and stimulated emission take place, and is schematically illustrated in Figure 1. Properties of photons generated by spontaneous and stimulated emission are quite different. Spontaneous emission takes place without interaction with other photons, and the direction and phase are random. Stimulated emission takes place when the excited electron interacts with another photon. Both the direction and phase are “copied” from the other photon when stimulated emission takes place, and it is the most important phenomenon for creating a highly directional and highly coherent light source (e.g. laser diode, fiber laser, and optical amplifier). The importance is quite evident from the fact that LASER is an abbreviation for Light Amplification by “Stimulated Emission” of Radiation.
It is the electronic noise generated by the thermal agitation of the charge carriers (usually the electrons) inside an electrical conductor at equilibrium, which happens regardless of any applied voltage.
Shot noise is a term describing the random fluctuations in a measurement signal due to the random arrival time of the signal carriers.
Relative intensity noise (RIN):It describes the instability in the power level of a laser. Phase induced intensity noise: Unwanted signal results from the phase incoherence of the overlapping signals on the same spectra, causing fluctuations of the total signal intensity.
STEP INDEX FIBER:
- The refractive index of the core is uniform throughout and undergoes on abrupt change at the core cladding boundary GRADED INDEX FIBER:
- The refractive index of the core is made to vary gradually such that it is maximum at the center of the core.
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