Electromagnetic电磁的principle原则principal主要的macroscopic宏观的microscopic微观的differential微分vector矢量scalar标量permittivity介电常数photons光子oscillation振动density of states态密度dimensionality维数transver wave横波dipole moment偶极矩diode二极管mono-chromatic单色temporal时间的spatial空间的velocity速度wave packet波包be perpendicular to线垂直 be nomal to线面垂直isotropic各向同性的anistropic各向异性的vacuum真空assumption假设miconductor半导体nonmagnetic非磁性的considerable大量的ultraviolet紫外的diamagnetic抗磁的paramagnetic顺磁的antiparamagnetic反铁磁的ferro-magnetic铁磁的negligible可忽略的conductivity电导率intrinsic本征的inequality不等式infrared红外的weakly doped弱掺杂heavily doped重掺杂a cond derivative in time对时间二阶导数vanish消失tensor张量refractive index折射率crucial主要的quantum mechanics量子力学transition probability跃迁几率delve研究infinite无限的relevant相关的thermodynamic equilibrium热力学平衡（动态热平衡）fermions费米子bosons波色子potential barrier势垒standing wave驻波travelling wave行波degeneracy简并converge收敛diverge发散phonons声子singularity奇点（奇异值）vector potential向量式partical-wave dualism波粒二象性homogeneous均匀的elliptic椭圆的reasonable公平的合理的reflector反射器characteristic特性prerequisite必要条件quadratic二次的predominantly最重要的gaussian beams高斯光束azimuth方位角evolve推到spot size光斑尺寸radius of curvature曲率半径convention管理hyperbole双曲线hyperboloid双曲面radii半径asymptote渐近线apex顶点rigorous精确地manifestation体现表明wave diffraction波衍射aperture孔径complex beam radius复光束半径lenslike me
dium类透镜介质be adjacent to与之相邻confocal beam共焦光束a unity determinant单位行列式waveguide波导illustration说明induction归纳symmetric对称的steady-state稳态be consistent with与之一致solid curves实线dashed curves虚线be identical to相同eigenvalue本征值noteworthy关注的counteract抵消reinforce加强the modal dispersion模式色散the group velocity dispersion群速度色散channel波段repetition rate重复率overlap重叠intuition直觉material dispersion材料色散information capacity信息量feed into注入derive from由之产生mi-intuitive半直觉intermode mixing模式混合pul duration脉宽mechanism原理dissipate损耗designate by命名为to a large extent在很大程度上etalon标准具archetype圆形interferometer干涉计be attributed to归因于roundtrip一个往返infinite geometric progression无穷几何级数conrvation of energy能量守恒free spectral range自由光谱区reflection coefficient（fraction of the intensity reflected）反射系数transmission coefficient（fraction of the intensity transmitted）透射系数optical resonator光学谐振腔unity归
一optical spectrum analyzer光谱分析grequency parations频率间隔scanning interferometer扫描干涉仪sweep移动replica复制品ambiguity不确定simultaneous同步的longitudinal lar mode纵模denominator分母fines精细度the limiting resolution极限分辨率the width of a transmission bandpass透射带宽collimated beam线性光束noncollimated beam非线性光束transient condition瞬态情况spherical mirror 球面镜locus（loci）轨迹exponential factor指数因子radian弧度configuration不举
intercept截断back and forth反复spatical mode空间模式algebra代数in practice在实际中symmetrical对称的a symmetrical conforal resonator对称共焦谐振腔criteria准则concentric同心的biperiodic lens quence双周期透镜组序列stable solution稳态解equivalent lens等效透镜verge 边缘lf-consistent自洽reference plane参考平面off-axis离轴shaded area阴影区clear area空白区perturbation扰动evolution渐变decay减弱unimodual matrix单位矩阵discrepancy相位差longitudinal mode index纵模指数resonance共振quantum electronics量子电子学phenomenon现象exploit利用spontaneous emission自发辐射initial初始的thermodynamic热力学inpha同相位的population inversion粒子数反转transparent透明的threshold阈值predominate over占主导地位的monochromaticity单色性spatical and temporal coherence时空相干性by virtue of利用directionality方向性superposition叠加pump rate泵浦速率shunt分流corona breakdown电晕击穿audacity畅通无阻versatile用途广泛的photoelectric effect光电效应quantum detector量子探测器quantum efficiency量子效率vacuum photodiode真空光电二极管photoelectric work function光电功函数cathode阴极anode阳极formidable苛刻的恶光的irrespective无关的impinge撞击in turn依次capacitance电容photomultiplier光电信增管photoconductor光敏电阻junction photodiode结型光电二极管avalanche photodiode雪崩二极管shot noi 散粒噪声thermal noi热噪声
In this chapter we consider Maxwell’s equations and what they reveal about the propagation of light i
n vacuum and in matter. We introduce the concept of photons and prent their density of states.Since the density of states is a rather important property，not only for photons，we approach this quantity in a rather general way. We will u the density of states later also for other(quasi-) particles including systems of reduced dimensionality.In addition,we introduce the occupation probability of the states for various groups of particles.
在本章中，我们讨论麦克斯韦方程和他们显示的有关光在真空中传播的问题。我们介绍了光子的概念以及光子态密度。由于态密度是很重要的属性，不单对光子而言，我们会经常用到态密度。我们将在之后用态密度描述其他（准）粒子包括降维系统。此外，我们介绍各种粒子态的占有率。
Now we tre
at Maxwell’s equations in matter.Doing so we have in principle to u the equations in their general from the equation (1.1).However we will still make some assumptions which are reasonable for miconductors:we assume that there are no macroscopic free space charges and that we have a nonmagnetic material.Actually,all matter has some diamagnetism.But this is a rather small effect of the order of 10-6 so it can be neglected for our purpos.Paramagnetic and especially ferromagnetic contributions can be significantly larger for low frequencies.However,even the contributions dimini
西加一笔是什么字sh rapidly for higher frequencies.Conquently the assumption of a nonmagnetic material is a good approximation in the visible range of the electromagnetic spectrum even for ferromagnetic materials.Furthermore,the more common miconductors are not ferro-,ferri- or antiferromagnetic and have only a small concentration of paramagnetic centres with negligible influence on the optical properties.The only exceptions are miconductors which contain a considerable amount ,Mn or Fe ions as does Zn1-yMnySe.帅气的句子
现在我们讨论麦克斯韦方程组问题。这样我们原则上可以使用方程的一般形式如方程（1,1）但是我们仍要对半导体进行一些合理的假设：我们假设没有宏观自由空间电荷而且是非磁性物质。其实所有的物质具有一定的抗磁性。但是对于10-6的数量级来说这个影响很小可以忽略不计。顺磁性特别是铁磁性对低频的贡献特别大。然而这些贡献会在高频率时迅速减弱。所以假设为非磁性材质在电磁频谱的可见光波段范围内对铁磁性物质具有良好的近似。此外比较常见的半导体不是铁，含铁或反铁磁性物质，而且具有一个小的集中顺磁性中心和稳定的光学性质。唯一例外的是半导体含有相当数量的如锰或铁离子比如Zn1-yMnySe。
For intrinsic or weakly doped miconductors,the carrier density is small and conquently σ is as well.Then the following inequality holds.
对于本征半导体或者弱掺杂半导体而言，载流子密度小因此σ也小，那么下面的不等式成立。
玉米粒怎么炒
This linear relation is the reason why everything that is treated in the following is called linear optics.A linear relation is what one usuallyassumes between two physical quantities as long as one does not have more preci information.In principle we can also consider (1.26a) as an expansion of P(E) in a power ries in E which is truncated after the linear term,The quantities ε and χ are called the dielectric function and the susceptiility,respectively.They can be considered as linear respon functions.
这种线性关系就是为什么下面所有都被归为线性光学的原因。线性关系是人们通常在没有更精确信息时假定两个物理量之间的关系。原则上我们也可以将（1.26a）即P（E）对于E的幂级数展开式看做截止后线性项，
ε和χ的数量分别被称为介电函数和磁化率。它们可以被看作是线性响应函数。
院子设计实景图The longitudinal waves which we found in matter are not electromagnetic waves but pure polarization waves with E and P oppod to each other with vanishing D,B and H.Until now we were considering the properties of light in the bulk of a medium.The boundary of this medium will need some extra ,the interface between vacuum (air) and a miconductor.This interface is crucial for reflection of light.Here we only want to state that the boundary conditions allow
a surface mode, that is,a wave which propagates along the interface and had field amplitudes which decay exponentially on both sides.
我们在物质中发现纵波不是电磁波而是与E和P的纯偏振波与其他相反的消失的D,B,H。
到目前为止，我们正在考虑多数媒介的光特性。这种介质边界需要一些额外的考虑，比如真空（空气）和半导体之间的接口。这个接口对光的反射至关重要。在这里我们指出边界条件只允许一种表面模式，即波沿界面传播并且双方场振幅指数衰减。
周工作总结模板A quantity which is cruial in quantum mechanics for the properties of particles is their density of states.It ,in Fermi’s folen rule which allows one to calculate probabilities.We want to discuss this problem in a general way for systems of different dimensionalities d=3,2 and 1.We shall need the results later on for low-dimensional miconductor structures.The discussion of the density of states,especially in various dimensions,is not so commonly treated as the harmonic oscillator,and so we shall spend some time on this problem and delve more into details.At the end of this ction we shall also state the occupation probability in thermodynamic equilibrium for classical particles,for fermions and bosons.
态密度是量子力学中对粒子特性来说很关键的一个量。比如可以用费米黄金法则计算概率。我们将在赵月芳
不同维度系统d=3.2.1中讨论这个问题。我们需要这些结果为了之后的低维半导体结构。对于态密度的讨论，特别是各个方面的，我们不能笼统的当成谐振子对待，所以我们在这个问题上需要花更多的时间并且钻研更多的细节。在本部分结束时，我们要陈述经典粒子如费米子和波色子在热力学平衡状态时的占有率。
If we assume that we have an infinitely high potential barrier around the box,then the wavefunction must have nodes at the walls (Fig.1.3a).
如果假设有一个无限高势垒围绕的区域，那么波函数必须在壁有节点（图1.3a）。
Another approach is to impo periodic boundary conditions. Then the plane wave should have equal amplitude and slope on opposite sides of the cube according to Figure.1.3b.
另一种做法是外加周期性边界条件。如图1.3b所示平面波在腔体的边界上会有相同的振幅和斜
率。
In contrast to the ca of standing waves,we now have to consider positive and negative values of ni parately.This procedure results finally in the same density of sates.As a conquence we find that plane waves have in Cartesian coordinates in k-space a constane density on all axes.Often one wan
ts to know the number of states in a shell between k and k+dk independent of the direction of k. This question can be answered by introducing polar coordinates k-space.The differential volume dVk of a shell of thickness dk in a d-demensional k-space is given by (1.72).Depending on the boundary condition we have to take into account only positive (1.67),or positive and negative (1.70),values of k or ni.The number D(k) of states in k-space found between k and k+dk in polar coordinates is given by dividing dVk by the volume for each state and by multiplying by gs.The quantitu g considers degeneracies such as the spin degeneracy.For photons we have g=2 according to the σ+ and σ- polarizations (e above).
在对照驻波时，我们必须分别考虑ni 的正负值。这个步骤的结果最终会是相同的态密度。其结果我们发现平面波在k-空间直角坐标系所有轴上具有恒定的密度。我们经常需要知道的是在k方向上k到k+dk壳内的状态数目。这个问题可以通过引入k-空间极坐标来解决。在d维K-空间中壳为微分量dVk和dk的关系由(1.72)可知。根据不同的边界条件我们求k值或者ni值只考虑正值（1.67）或正负值（1.70）。k-空间中极坐标下k到k+dk之间的状态数D(K)等于每个状态值除以dVk乘以gs。gs量为简并度如自旋简并度。对于光子而言根据σ+偏振和σ-偏振有g= 2（见上文）。
10. We want to stress here that we assumed only plane waves but did not make any specific assumptions about which type of particles are reprented by the plane waves-photons,electrons
etc.Therefore this result is valid for all particles described by plane waves.
我们在这里强调的是，我们只假设是平面波但是没有假设是哪种粒子代表的平面波——光子，电子等等。因此这个结果对所有由平面波描述的粒子都有效。
桂花树种植技术
11. The next quantity,which we need is the occupation probabiltiy of the states discusd above.We restrict ourlves in the following to thermodynamic equilibrium.There are three types of statistics which can be considered:For classical,distinguishable particles,Boltzmann statistics apply:(1.80a).For bosons,i.e indistinguishable particles with integer spin,photones being an example,one must u the Bo-Einstein statistics (1.80b).Fermions,or indistinguishable particles with half-integer ,electrons obey the Fermi-Dirac statistics fFD (1.80c).The Boltzmann constant is kB and the chemical potential is μ which gives the average energy necessary to add one more partical to the system. For fermions μ is als
o known as the Fermienergy EF.The probability to find a particle in the interval from E to E+dE is then given by the product of the density of states D(E) and the occupation probability f (1.81).In figure.1.5 we plot fB,fBE and fFD as a function of (E-μ)/kBT.The Boltzmann statistics show the well-known exponential dependence.The Fermi-Dirac statistics never exceed one,realizing thus Pauli’s e
xclusion principle.The Bo-Einstein condensation,or in other words,a macroscopic population of a single state,if μ falls in a region with finite density of states.In this ca the species with energies E=μ and tho with E>μ must be considered parately. Furthermore it is obvious from Figure 1.5 that fBE and fFD converge to fB for (E-μ)/kBT>1.The chemical potential μ is zero for quanta who number is not conrved,,photons or phonons.
我们需要的下一个量是上面讨论过的状态占有率。我们限定在下热力学平衡中。有三种统计方式：经典粒子统计，可区分粒子统计，玻耳兹曼统计。（1.80a）对于波色子来说，即具有整数自旋的不可区分粒子，比如光子，必须用波色-爱因斯坦统计（1.80b）费米子，或半整数自旋的不可区分粒子，例如电子必须服从费米-狄拉克统计fFD（1.80c）玻尔兹曼常数kB和化学势μ是这个系统增加一个粒子所必须增加的平均能量。对于费米子μ也称为费米能EF。找到一个在间隔在E和E+dE之间的粒子的概率由态密度D(E)和占据概率f（1.81）而得。图1.5为fB,fBE 和fFD随(E-μ)/kBT变化的曲线。玻耳兹曼统计数据表明这众所周知的指数依赖关系。费米 - 狄拉克统计同状态粒子不能超过一个，从而实现泡利的不相容原理。玻色 - 爱因斯坦凝聚，或者说具有宏观数量达到单个状态。如果μ落在一个有限态密度区域。在这种情况下能量类型E =μ和E>μ必须分别考虑。此外由图1.5可见，在（E-μ）/ KBT>1时FBE和FFD收敛于FB。化学能μ为0的量子数量不守恒，例如声子或光子。
12. A cloly related topic of fundamental importance in lar electronics is the propagation of optical
beams.The beams usually take the form of planelike waves who energy density is localized,for reasonable propagation distances,near the propagation axis.The output of lar oscillators will be found to consist of one or more of such beams.This is also the form of the fields t up by feeding electromagnetic energy into a resonator formed by two curved reflectors.The understandingof the characteristics of the modes is thus a prerequisite to the study of many lar-related phenomena.
一个与激光电子学中根本重要性有密切相关的议题就是光束传播。这些光束采取局部能量密度的类平面波的性质，贴近传播轴传播合理的传播距离。激光振荡器的输出由一个或者多个光束组成。这也是由两个弧形反射谐振腔形成
叶圣陶名言名句
