毕业设计英文翻译.doc

本 科 毕 业 论 文 英文翻译English translation学生学号： 学生姓名： 专业班级： 指导教师姓名： 指导教师职称： 2023 年 3 月无损接口模式在两个周期性介电结构之间的边界 光塔姆状态是无损的接口模式在周边介质呈指数衰减。我们证明它们可以被形成在2周期性介电结构，具有周期接近1之间的边界处到的光的波长，另一种具有周期接近的波长的两倍。顺序层界面处对塔姆状态有决定性影响。的面内分散这些状态是抛物线与有效质量为TE和TM偏振略有不同，两者的10-5的顺序自由电子的质量。 表面波是一种特定类型的波,是被限制在两个不同媒体之间的界线。他们用于波长显微镜、分子化学、癌症研究等1-3。最受欢迎的类型的表面波是一个边界等离子体形成的金属介质媒体。最近,组织无损的也许性表面波在两种介质之间的界面已经被讨论了。Artigas和Torner4建议使用特别设计的二维光子晶体进行观测所谓的Dyakonov modes5本地化的表面的晶体。光子结构起到的作用单轴的电介质在可控的折射指数对普通和特殊光模式。在这简短的报告,我们提出另一种类型的无损耗接口模式,我们称之为光学OTSs都状态通过与著名的比方都为电子晶体的边界6。 波导管表面模式7相反和Dyakonov模式,都保持本地化任何平面波矢量的价值涉及零波向量。OTSs内形成“光锥”有限由一个k =w / c条件,k的波矢量光和频率。与电子相反都州,光都无法形成表面,但只有在两个光子之间的界面结构有重叠的带隙。我们提出一个简朴的平面多层结构允许OTSs的观测。十年前,我们开发了一种理论,都半导体电子承压边界的两个超晶格8。现在我们有扩展的方法来描述OTSs。我们表白,它们可以形成的之间的接口两个周期性介电结构不同的时期。OTS在于光学停止的两个部分的结构。其平面分散是抛物线的有效质量的顺序105自由电子质量。TE和TM极化都之间的分裂州增长与平面波矢量构造。我们提出基于多孔现实的多层结构硅让OTSs的观测。让我们考虑两个期刊介质之间的界面结构由双层厚度、和折射率,注在右边的接口和厚度,提单和指数,左边的界面图1。 图1布洛赫定理允许代表本征模光无限期刊作为期刊布洛赫振幅的产品结构和包络函数,要么是平面波或真正的指数函数的坐标。光能量的波段形式成倍增长被称为阻带衰落或增长信封在光子结构完整的类比与能量差距在固体晶体。在我们的模型结构,两个不同的半无限周期子结构有共同接口。我们的目的是在这找到光的模式本地化OTSs接口。显然,他们的精力应当在于停止子结构的波段。在OTS他们每个恰逢本征模也成倍增长或成倍减少。在接口、连续性的平面组件电场和磁场的这些模式必须得到保证。 自Born and Wolf后9,我们引入转移矩阵和描述矢量的转移。整个时期的左翼和右翼子结构,这里E和H平面组件的电力和磁场。2x2这些矩阵的元素依赖于厚度和折射率层、频率、平面波矢量和极化光。周期性的光学模式的色散方程结构为 （1）其中q是布洛赫光导向的伪波失常量，d为平面距离，T11，T12为结构周期。阻带是由给定的条件 （2) 及在两者之间的界面结构规定 （3） 让XL_和XR+是本征值相应于这些模式的转移矩阵，以便和。表达的组成部分通过特性值和两个矩阵的特性向量的元素，。很容易地从（3）获得 （4）方程(4)产生的OTSS和在平面内的能量这些国家的分散。为了找到OTSS ， 应求解方程(4)的两个部分的带隙内的结构。什么样的结构可以表现出塔姆状态？为了得到关于它的想法，让我们表达的电场和磁场式。( 1 )通过反射系数入射的光向左（向右）左侧的接口端（右端）的一部分的结构。在垂直入射 , (5)在阻带内，反射系数写入 (6) (7) 由于我们的左，右子结构是半无限大，在其阻带的重叠部分 解决式。（3）与使用方程的（ 5 ）-（7 ）可以得到等式为OTSS的以下形式的本征频率： （8）这个方程是相对易于分析的各阶段周期性结构的反射系数是众所周知的10。由于它的右边是一个有限的负数，二在左侧部分切线应采用相反的值签署但同样的顺序。让我们强调这一点，即在一维光子晶体的光学间隙可以无论是出现在中心或在布里渊边界区，即，在任q = 0时或q = / D 。反射的相位该结构的系数等于0处的中心停带在q = 0时，可以是0或在该中心阻带在Q = / D依赖于是否在第一层该结构具有比更低或更高的折射率第二层。在所有情况下，相位是一个缓慢光的频率的增函数。显然，这是不也许兼得和接近 ，具有介意，不一定在一个子结构的第一层高折射率和在此外一个第一层具有低折射率。另一方面，有也许兼得和接近于0 ，这是假如，比如说 ，并且在q = 0的左侧下部重叠的间隙与在Q = / D右子结构的差距。可以实现这种重叠的，例如，间第一站带一个完美的布拉格反射镜的，有和几乎两倍的结构的第二止动带较大的层所在的布拉格条件几乎是满意的，为了在q = 0时打开该间隙被引入11结构的两部分的光子能带示图。我们使用了以下的一组参数： 和。折射率的选择值是容易可实现的，例如，在多孔硅结构12.设计对的的子结构，我们已经略微的失谐厚度的层的从那些由布拉格条件定（ 9 ）为了调，可以允许使OTS靠近两个子结构的阻带的中心。图1通过使用闪光灯OTS的能量显示了我们模型结构。图2显示了电的强度这种模式下的字段作为坐标的函数。事实上，一位可以看出，模式指数衰减都在负和从接口正方向。的参数在塔姆的衰减状态向左（向右）子结构，是由相应的本征值给定的转移矩阵图2，固体粗线示出的电场强度在拟议的结构内轮廓的在职培训计划。固体细线为相应的折射率分布。虚线为对于两个子之间的接口。有趣的是，假如顺序层反转塔姆状态消失。例如，假如在左（右）结构，该层与折射率先行。这可以很容易地从公式的理解。 （ 8 ）中层的数目的反转改变由 ，而几乎保持不变。显然，等式的左侧部分。 （8 ）急剧的变化在这情况下，与溶液不能再找到。在塔姆态的能量，反射率光谱该表现出大幅下降的阻带内，作为图3所示。图3我们的模型结构3。在计算光谱反射率不同的入射角。人们可以观测到内畅游和锋利的峰停止结构有关OTS的波带。这样算来已进行了有25层对有限尺寸结构，其左部和12对层在其右侧部分。在这种差异需要对的数目，以平衡反射系数为了达成最高的两个子结构振幅OTS功能。改变入射角推塔姆状态向着更高的能量也可以看到从图的光谱。 图3，图4示出了计算面内分散的OTSS在我们的结构为TE-和TM极化模式（即具有模式电场向量和分别在层的平面内的磁场矢量）它本质上是抛物线两种极化并且可以特性的顺序的有效质量，其中m0为自由电子质量。在图的插图4显示了TM和TE偏振OTSS之间的分裂。它增长了二次作为在平面波的幅度的函数矢k 。我们检查了所获得的色散曲线解方程（ 3 ）和提取的反射光谱模型的结构是完全同样的。为了解析来估计有效群众表面模式，我们已经扩大式。 （2 ）成泰勒数列K和，其中是本征频率在OTS的。我们假设 (12)在这种情况下，为有效群众紧凑的表达式TE和TM极化可以得到 (13) (14)比重约5 TM在我们的例子。值非常接近那些从图中可以提取。图4在OTS4。能源作为平面波函数Vector中的TE实线和TM虚线极化。该插图示出了TM和TE模式之间的能量差。总之，光塔姆状态是一个有价值的替代到Dyakonov表面模式实现无损的局部光子态在介电结构。他们出现在常规周期之间的接口多层结构，不需要在平面调制介电常数。我们提出的方法设计适于观测塔姆的结构状态。参考文献1.Near-Field Optics and Surface Plasmon Polaritons, edited by S.Kawata Springer, Berlin, 2023.2.M. M. Bask, M. Jaros, and J. T. Groves, Nature London 427,304 2023.3.N. Kedei, D. J. Lundberg, A. Toth, P. Welburn, S. H. Garfield, andP. M. Blumberg, Cancer Res. 64, 3243 2023.4.D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 2023.5.M. I. Dyakonov, Sov. Phys. JETP 67, 714 1988.6. I. E. Tamm, Sov. Fiz. Zhurn. 1, 733 1932.7. See, e.g., J. D. Joannopoulos, R. D. Meade, and J. N. Winn,Photonic CrystalsPrinceton University Press, Singapore,1995, Chap. 4.8.M. R. Vladimirova and A. V. Kavokin, Fiz. Tverd. Tela Leningrad37, 1178 1995 Phys. Solid State 37, 1178 1995.9.M. Born and E. Wolf, Principles of Optics Pergamon, Oxford,1980.10 .See, e.g., G. Panzarini, L. C. Andreani, A. Armitage, D. Baxter,M. S. Skolnick, V. N. Astratov, J. S. Roberts, A. V. Kavokin, M.R. Vladimirova, and M. A. Kaliteevski, Phys. Solid State 41,1223 1999.11. Perfect Bragg mirrors have no gap at q=0.12.V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin,D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil,Phys. Rev. Lett. 92, 097401 2023.Lossless interface modes at the boundary between two periodic dielectric structures Tamm states of light are lossless interface modes decaying exponentially in the surrounding media. We showthat they can be formed at the boundary between two periodical dielectric structures, one having a period closeto the wavelength of light and another one having a period close to the double of the wavelength. The order oflayers at the interface has a crucial effect on the Tamm states. The in-plane dispersion of these states isparabolic with effective masses slightly different for TE and TM polarizations, both of the order of 105 of thefree electron mass. Surface waves are a specific type of waves that are confined at the boundary between two different media. They are used in subwavelength microscopy, molecular chemistry,cancer research, etc.13 The most popular kind of surface wave is a plasmon formed at the boundary of metallic and dielectric media. Recently, the possibility to organize lossless surface waves at the interface between two dielectric media has been discussed. Artigas and Torner4 have proposed to use specially designed two-dimensional photonic crystals for observation of the so-called Dyakonov modes5 localized at the surface of the crystal. The photonic structure plays the role of a uniaxial dielectric medium having controllable refractive indices for ordinary and extraordinary light modes. In this Brief Report we propose another type of lossless interface modes, which we call optical Tamm states OTSs by analogy with well-known Tamm states for electrons at crystal boundaries.6 Contrary to waveguided surface modes7and to Dyakonov modes, Tamm states remain localized for any value of the in-plane wave vector including the zero wave-vector. OTSs are formed inside the “light cone” limited by a k=w/c condition, where k is the wave vector of light and w is its frequency. Contrary to electronic Tamm states, optical Tamm states cannot be formed at the surface,but only at the interface between two photonic structures having overlapping band gaps. We propose a simple planar multilayer structure allowing for observation of the OTSs.Ten years ago, one of us developed a theory of Tamm states for electrons confined at the boundary of two semiconductor superlattices.8 Now we have extended the method of Ref. 8 to describe OTSs. We show that they can be formed at the interface between two periodic dielectric structures having different periods. The OTS lies in the optical stop bands of both parts of the structure. Its in-plane dispersion is parabolic with an effective mass of the order of 105 of a free electron mass. The splitting between TE and TM polarized Tamm states increases quadratically with the in-plane wave vector.We propose realistic multilayer structures based on the porous silicon allowing for observation of the OTSs. Let us consider the interface between two periodical dielectric structures composed by the pairs of layers of thicknesses ar, br and refractive indices na, nb on the right-hand side of the interface and thicknesses al, bl and indices na, nb on the left-hand side of the interface Fig. 1a. The Bloch theorem allows representing eigenmodes of light in any infinite periodical structure as products of periodical Bloch amplitudes and envelope functions, which are either plane waves or real exponential functions of the coordinate. The energy bands in which the eigenfunctions of light have exponentially decaying or increasing envelopes are called stopbands in photonic structures a complete analogy with energy gaps in solid crystals. In our model structure, two different semi-infinite periodic substructures have a common interface.Our goal is to find the modes of light localized at this interface OTSs. Evidently, their energies should lie in the stop bands of both substructures. In each of them the OTS coincides with one of the eigenmodes of light having an envelope either exponentially increasing in the left substruc-ture or exponentially decreasing in the right substructure.At the interface, continuity of the in-plane components of theelectric and magnetic fields of these modes must be assuredas the Maxwell boundary conditions require.FIG. 1. aSketch of the interface between the right and the left parts of our model structure. b The solid line shows the allowed photonic band in the right substructure. The dashed line shows the allowed photonic band in the left substructure. The energies are shown of the pseudowave-vector q expressed in /d units, d=al+bl for the left structure, and d=ar+br for the right structure. The flash shows the position of the OTS which is located within the gaps of the two substructures. Following Born and Wolf,9 we introduce the transfer matrices TL and TR describing the transfer of the vector across the periods of the left and right substructure, respectively.Here Et and Ht are in-plane components of the electric and magnetic field. The elements of these 22 matrices are dependent on the thicknesses and refractive indices of the layers, frequency, in-plane wave vector, and polarization of light. The dispersion equation for optical modes in periodic structures writes (1)where q is the Bloch pseudo-wave-vector of light oriented normally to the layer planes, d is the period of the structure,t11, t22 are diagonal elements of the corresponding transfer matrix. The stop bands are given by the condition (2) The matching of E and H at the interface between two structures requires (3)where the left right part is the eigenvector corresponding the mode decaying in the negative positive direction in the left right substructure. Let XL and XR + be the eigenvalues of the transfer matrices corresponding to these modes, so that XL1 and XR + 1. Expressing the components of the eigenvectors via eigenvalues and the elements of both matrices,Ref. 8, one can easily obtain from(3), (4) Equation (4)yields the energies of the OTSs and the in-plane dispersion of these states. In order to find the OTSs, one should solve Eq. 4 within the band gaps of both parts of the structure.What kind of structures can exhibit Tamm states? To get an idea about it, let us express electric and magnetic fields in Eq. (1) via reflection coefficients for light incident from the right left side of the interface on the left right part of the structure. At normal incidence , (5) Within the stop bands, the reflection coefficients write (6) (7) As our left and right substructures are semi-infinite, in the overlapping part of their stop bands rR=rL=1. Resolving Eq. 3 with use of Eqs. (57)one can obtain the equation for the eigenfrequencies of the OTSs in the following form: (8) This equation is relatively easy to analyze as the phases of reflection coefficients of periodic structures are well known.10 As its right part is a finite negative number, two tangents in the left part should take values of the opposite sign but of the same order. Let us underline at this point, that in one-dimensional photonic crystals the optical gaps may appear either at the center or at the border of the Brillouin zone, i.e., at either q=0 or q=/d. The phase of the reflection coefficient of the structure equals to 0 at the center of the stop band at q=0 and can be either 0 or at the center of the stop band at q=/d dependent on whether the first layer of the structure has a lower or higher refractive index than the second layer, respectively. In all cases, the phase is a slowly increasing function of the frequency of light. Clearly, it is impossible to have both L and R close to , having in mind that necessarily in one substructure the first layer has the high refractive index and in the other one the first layer has the low refractive index. On the other hand, it is possible to have both L and R close to 0. It is realized if, say, nanb, and the gap at q=0 in the left substructure overlaps with the gap at q=/d in the right substructure.This kind of overlap can be realized, for example, between the first stop band of a perfect Bragg mirror, having and the second stop band of a structure with almost twice larger layers where the Bragg condition is almost satisfied, so that is introduced in order to open the gap at q=0 11The photonic bands of two parts of the structure are shown in Fig. 1b. We used the following set of parameters: na=1.4, nb=2, naal=384 nm, nbbl=437 nm, naar=95 nm, and nbbr=285 nm. The chosen values of refractive indices are easily achievable, for instance, in porous silicon structures.12 Designing the right substructure, we have slightly detuned the thicknesses of layers from those given by the Bragg condition9 in order to tune r, that allowed bringing the OTS closer to the center of the stop bands of both substructures.Figure 1b shows by a flash the energy of the OTS in ourmodel structure. Figure 2 shows the intensity of the electric f