meep简介

MeepMeepMeepMeep（或MEEP ）是一个免费的有限差分时域（FDTD）模拟软件包在麻省理工学院开发 的模型电磁系统，伴随着我们MPB的本征模包。 Its features include:它的功能包括： MeepMeepMeepMeepMeepMeepMeepMeep Download 下载 Release notes 发行说明 FAQ 常见问题 Meep manual Meep手册 Introduction 简介 Installation 安装 Tutorial 教程 Reference 参考 C++ Tutorial C + +教程 C++ Reference C + +参考 Acknowledgements 致谢 License and Copyright 许可和版权 • FreeFreeFreeFree softwaresoftwaresoftwaresoftware under the GNU GPL .根据 GNU GPL 的免费软件。 • Simulation in 1d,1d,1d,1d, 2d,2d,2d,2d, 3d3d3d3d , and cylindricalcylindricalcylindricalcylindrical coordinates.模拟一维，二维，三维，圆柱坐 标。 • Distributed memory parallelismparallelismparallelismparallelism on any system supporting the MPI standard.在任何支持 的系统内存并行分布式的 MPI标准。Portable to any Unix-like system ( GNU/Linux is fine). 移植到任何类 Unix系统（ GNU / Linux的是罚款）。 • Arbitrary anisotropicanisotropicanisotropicanisotropic electric permittivity ε and magnetic permeability μ, along with dispersivedispersivedispersivedispersive ε(ω) and μ(ω) (including loss/gain) and nonlinearnonlinearnonlinearnonlinear (Kerr & Pockels) dielectric and magnetic materials, and electric/magnetic conductivitiesconductivitiesconductivitiesconductivities σ.任意各向异性介电常数ε和磁导 率μ，随着分散 ε（ω）和μ（ω）（包括损耗/增益）和非线性 （克尔电光）介电和磁材 料，电/ 磁导率σ 。 • PMLPMLPMLPML absorbing boundaries and/or perfect conductor and/or Bloch-periodicBloch-periodicBloch-periodicBloch-periodic boundary conditions. PMLPMLPMLPML吸收边界和/或完善指挥和/或布洛赫周期性边界条件。 • Exploitation of symmetriessymmetriessymmetriessymmetries to reduce the computation size — even/odd mirror symmetries and 90°/180° rotations.剥削的对称性 ，以减少计算的大小-奇/偶镜像对称和90 ° / 180 °旋转。 • Complete scriptabilityscriptabilityscriptabilityscriptability— either via a Scheme scripting front-end (as in libctl and MPB ), or callable as a C++ library; a Python interface is also available.也可完成 scriptabilityscriptabilityscriptabilityscriptability -无论 是通过一个前端的计划脚本（ libctl 和 MPB），或作为一个可调用的 C + +库; 一个 Python接口。 • Field output in the HDF5 standard scientific data format, supported by many visualization tools.场输出的 HDF5的科学数据的标准格式，由许多可视化工具支持。 • Arbitrary material and source distributions.任意材料和源代码分发。 • Field analyses including flux spectra, frequency extraction, and energy integrals; completely programmable.场分析，包括通量光谱，频率提取和能源积分，完全可编程。 • Multi-parameter optimization, root-finding, integration, etcetera (via libctl ).多参数优化， 求根，整合，等等（通过 libctl ）。 Meep officially stands for MIT Electromagnetic Equation Propagation , but we also have several unofficial meanings of the acronym. Meep正式代表麻省理工学院电磁方程传播 ，但我们也有 一些非官方的含义的缩写。 [ edit ] [ 编辑 ] Time-domainTime-domainTime-domainTime-domain simulationsimulationsimulationsimulation时域仿真 A time-domain electromagnetic simulation simply takes Maxwell's equations and evolves them over time within some finite computational region, essentially performing a kind of numericalnumericalnumericalnumerical experimentexperimentexperimentexperiment .时域电磁模拟简单的麦克斯韦方程和一些有限的计算区域内随时间的演变，基 本上执行了一种数值试验。 This can be used to calculate a wide variety of useful quantities, but major applications include:这可以用来计算一个有用的数量种类繁多，但主要应用包括： • TransmissionTransmissionTransmissionTransmission andandandand reflectionreflectionreflectionreflection spectraspectraspectraspectra — by Fourier-transforming the response to a short pulse, a single simulation can yield the scattering amplitudes over a wide spectrum of frequencies. 透射和反射光谱 -傅立叶转化一个短脉冲响应，一个单一的模拟，可以产生 较广泛的频率散射振幅。 • ResonantResonantResonantResonant modesmodesmodesmodes andandandand frequenciesfrequenciesfrequenciesfrequencies — by analyzing the response of the system to a short pulse, one can extract the frequencies, decay rates, and field patterns of the harmonic modes of a system (including waveguide and cavity modes, and including losses). 谐振模式和频率 -通过分析系统的响应一个短脉冲，可以提取的频率，衰减率和领域的系统（包括波导和 腔模式，包括损失）的谐波模式模式。 • FieldFieldFieldField patternspatternspatternspatterns (eg Green's functions) in response to an arbitrary source, archetypically a CW (fixed-ω) input. 场模式 （如格林函数），archetypically一个 CW （固定ω）输入一 个任意源。 Using these results, one can then compute many other things, such as the local density of states (from the trace of the Green's function).利用这些结果，可以计算许多其他的事情，如国家的局 部密度（从跟踪的格林函数）。 Meep's scriptable interface makes it possible to combine many sorts of computations (along with multi-parameter optimization etcetera) in sequence or in parallel. Meep编写脚本的界面，使人们有可能结合序列或平行许多各种各样的计算（多参数优化等 耳熟能详的乐曲）。 The Meep manual gives examples of all of these kinds of computations. Meep手册提供了所有这 些类型的计算的例子。 [ edit ] [ 编辑 ] DownloadDownloadDownloadDownload下载 Please see the Meep Download page to get the latest version of Meep; the differences between versions are described in the Meep release notes .请参阅 Meep下载页面，以获取最新的 Meep 版本，版本之间的差异是在描述Meep发行说明。 The installation instructions can be found in the installation section of the Meep manual .安装说明可以发现在安装部分 Meep手册 。 [ edit ] [ 编辑 ] DocumentationDocumentationDocumentationDocumentation文档 See the Meep manual , and also the navigation sidebar at right.见Meep手册 ，并在右边的导航 侧边栏。 In particular, the Meep Introduction and Meep Tutorial are the most important things to read.特别是， Meep介绍和Meep教程阅读的最重要的事情。 See also the list of Meep examples .另见列表Meep例子 。 We also have a Meep FAQ .我们也有一个Meep常见问题 。 Please cite Meep in any publication for which you found it useful.请举出 Meep在任何刊物中， 您发现它有用。 [ edit ] [ 编辑 ] MailingMailingMailingMailing ListsListsListsLists邮件列表 The Meep mailing lists (and their archives) are another source of information about Meep. Meep 邮件列表（和他们的档案）的有关Meep信息的另一个来源。 Subscribe to the (read-only) meep-announce mailing list to receive an email when Meep is updated in the future. （只读） meep - announce邮件列表收到一封电子邮件时 Meep是在未 来的更新。 Subscribe to the (unmoderated) meep-discuss mailing list for discussion of questions and ideas about using Meep. （无监管） meep讨论邮件列表 ，讨论有关使用 Meep的问题 和想法。 Announcements are notnotnotnot always sent to meep-discuss; you should subscribe to meep-announce for that. Archives of meep-discuss are available online.公告并不总是发送 meep 讨论，你应该订阅 meep宣布。 meep -讨论可在网上。 (You can also read & post to the list via the gmane.comp.science.electromagnetism.meep.general newsgroup from Gmane ). （您还可以 阅读和后通过列表，gmane.comp.science.electromagnetism.meep.general从新闻组 Gmane）。 [ edit ] [ 编辑 ] AcknowledgementsAcknowledgementsAcknowledgementsAcknowledgements致谢 Meep was initiated by David Roundy when he was at MIT in JD Joannopoulos' group, and David was soon joined by Mihai Ibanescu, Peter Bermel, and later by Steven G. Johnson and Ardavan F. Oskooi. Meep大卫 Roundy发起 JD Joannopoulos“组中，当他在麻省理工学院和大卫很快就 被米哈伊 Ibanescu，彼得 Bermel加入，后由 Steven G. Johnson和 Ardavan楼 Oskooi。Recent versions also include work by Alejandro W. Rodriguez and Alexander P. McCauley.最新版本还包 括由 Alejandro W.罗德里格斯和 Alexander P.麦考利的工作。 This work was supported in part by the Materials Research Science and Engineering Center program of the National Science Foundation under Grant No. DMR-9400334, and also by Dr. Dennis Healy of DARPA MTO, under award N00014-05-1-0700 administered by the Office of Naval Research.这项工作是支持 部分材料研究科学与工程研究中心计划，国家科学基金会批准号 DMR - 9400334下，也谭维 义 DARPA的MTO的希利奖 N00014 - 05 - 1 - 0700管理海军研究办公室。 Please see the Meep Acknowledgements for a more complete listing of those to whom we are grateful.请看到一个更完整的上市，那些我们感谢 Meep致谢。 [ edit ] [ 编辑 ] ContactsContactsContactsContacts andandandand FeedbackFeedbackFeedbackFeedback联系与反馈 If you have questions or problems regarding Meep, you are encouraged query the meep-discuss mailing list (see above); please search the meep-discuss archives as your first resort.如果您有任 何疑问或问题Meep的，我们鼓励您查询 meep讨论邮件列表（见上文）;请搜索 meep讨论 档案作为您的第一家度假村。 For professional consulting support of Meep, and photonic band-gap applications in general, contact Prof. Meep专业咨询支持，并在一般，接触的光子带隙应用教授 John D. Joannopoulos of MIT (phone: (617) 253-4806, fax: (617) 253-2562).麻省理工学院的约翰 D Joannopoulos（电 话：（617）253-4806，传真：（617）253-2562）。 Alternatively, you may directly contact Steven G. Johnson at stevenj@alum.mit.edu .另外，您也 可以直接联系史蒂芬 G. 约翰逊 stevenj@alum.mit.edu 。 Retrieved from " http://ab-initio.mit.edu/wiki/index.php/Meep " 取 自 “ http://ab-initio.mit.edu/wiki/index.php/Meep “ MeepMeepMeepMeep简介 FromFromFromFromAbInitioAbInitioAbInitioAbInitio从 AbInitioAbInitioAbInitioAbInitio Jump to: navigation , search跳转到： 导航 ， 搜索 Meep Meep Download 下载 Release notes 发行说明 FAQ 常见问题 Meep manual Meep手册 IntroductionIntroductionIntroductionIntroduction 简介 Installation 安装 Tutorial 教程 Reference 参考 C++ Tutorial C + +教程 C++ Reference C + +参考 Acknowledgements 致谢 License and Copyright 许可和版权 Meep implements the finite-differencefinite-differencefinite-differencefinite-difference time-domaintime-domaintime-domaintime-domain ( FDTDFDTDFDTDFDTD ) method for computational electromagnetism. Meep实现的时域有限差分（FDTDFDTDFDTDFDTD）方法计算电磁。 This is a widely used technique in which space is divided into a discrete grid and then the fields are evolved in time using discrete time steps—as the grid and the time steps are made finer and finer, this becomes a closer and closer approximation for the true continuous equations, and one can simulate many practical problems essentially exactly.这是一种广泛使用的技术，在空间划分成一个独立的电 网，然后使用离散时间进化等领域的步骤网格和时间步骤作出更细和更精细的，这将成为一 个密切近似的真正的连续方程，和一个可以模拟许多实际问题基本上完全相同。 In this section, we introduce the equations and the electromagnetic units employed by Meep, the FDTD method, and Meep's approach to FDTD.在本节中，我们介绍的方程和电磁 Meep，FDTD 方法，Meep 的方法来的 FDTD 聘用单位。 Also, FDTD is only one of several useful computational methods in electromagnetism, each of which has their own special uses—we mention a few of the other methods, and try to give some hints as to which applications FDTD is well suited for and when you should consider a different method.此外，FDTD的电磁学中几个有 用的计算方法只有一个，每个人都有自己的特殊用途，我们提到了一些其他的方法，并尝试 应用的 FDTD非常适合一些提示，当您应考虑不同的方法。 This introduction does not talk about the user interface with which you can tell Meep to perform these tasks.此次推出的不谈论的用户界面，使用它可以告诉 Meep执行这些任务。Instead, we focus here on the concepts that are being simulated.相反，我们这里的重点概念正在模拟。 The user interface is introduced in the Meep tutorial .在Meep教程的用户界面介绍。 ContentsContentsContentsContents目录 [hide] o 1 Maxwell's equations 1 麦克斯韦方程1.1 Units in Meep 1.1 单位在Meep • 2 Boundary conditions and symmetries 2 边界条件和对称性 o 3 Finite-difference time-domain methods 3 有限差分时域 方法3.1 The illusion of continuity in Meep 3.1 Meep连续性的 错觉 • 4 Other computational methods 4， 其他的计算方法 o 5 Applications of FDTD 5 FDTD 法的应用 5.1 Field patterns and Green's functions 5.1 现场模式和格林函数 o 5.2 Transmission/reflection spectra 5.2 传输/反射光谱 o 5.3 Resonant modes 5.3 谐振模式 [ edit ] [ 编辑 ] Maxwell'sMaxwell'sMaxwell'sMaxwell's equationsequationsequationsequations麦克斯韦方程组 Meep simulates Maxwell's equations , which describe the interactions of electric ( EEEE ) and magnetic ( HHHH ) fields with one another and with matter and sources. Meep 模拟麦克斯韦方程 组 ，这说明电（EEEE）和磁场（HHHH）与另一个与物质和来源领域的相互作用。 In particular, the equations for the evolution of the fields are:在特定领域的演变方程： Where DDDD is the displacement field, ε is the dielectric constant, JJJJ is the current density (of electric charge), and JJJJ B is the magnetic-charge current density. 其中 D为位移场，ε是介电常数，JJJJ是 电流密度（电荷 ）， J JJ J BBBB是磁充电电流密度。 (Magnetic currents are a convenient computational fiction in some situations.) BBBB is the magnetic flux density (often called the magnetic field), μ is the magnetic permeability, and HHHH is the magnetic field.（磁流在某些情况下是一种方便的的计算虚 构的。）BBBB是磁通密度（通常称为磁场），μ是磁导率，HHHH是磁场。 The σ B and σ D terms correspond to (frequency-independent) magnetic and electric conductivities, respectively.的 σB 和 σD 项 对应（频率独立）的磁性和电导率，分别。 The divergence equations are implicitly:隐式的 分歧方程： Most generally, ε depends not only on position but also on frequency (material dispersion) and on the field EEEE itself (nonlinearity), and may include loss or gain.最普遍，ε依赖不仅立场，但也频（材 料色散）和电场 E（非线性），并可能包括损耗或增益。 These effects are supported in Meep and are described in Materials in Meep .这些影响都在Meep支持，并在材料 Meep 。 Meep supports simulation in cylindrical coordinates: see Cylindrical coordinates in Meep . Meep 支持模拟圆柱坐标：见Meep圆柱坐标 。 [ edit ] [ 编辑 ] UnitsUnitsUnitsUnits inininin MeepMeepMeepMeep在MeepMeepMeepMeep单位 You may have noticed the lack of annoying constants like ε 0 , μ 0 , and c — that's because Meep uses "dimensionless" units where all these constants are unity (you can tell it was written by theorists).您可能已经注意到，缺乏像恼人的常数 ε0，μ0 ， C -的，因为Meep使用“无量纲”的 单位，所有这些常量的统一（你可以告诉它是由理论家书面）。 As a practical matter, almost everything you might want to compute (transmission spectra, frequencies, etcetera) is expressed as a ratio anyway, so the units end up cancelling.作为一个实际问题，几乎所有的东西，你可能想 计算（透射谱，频率，等等）作为一个比例来表示，无论如何，这样的单位最终取消。 In particular, because Maxwell's equations are scale invariant (multiplying the sizes of everything by 10 just divides the corresponding solution frequencies by 10), it is convenient in electromagnetic problems to choose scale-invariantscale-invariantscale-invariantscale-invariant unitsunitsunitsunits (see our online textbook , ch. 2).特别 是，由于麦克斯韦方程组是规模不变的一切大小乘以10只是分成10的相应解决 方案 气瓶 现场处置方案 .pdf气瓶 现场处置方案 .doc见习基地管理方案.doc关于群访事件的化解方案建筑工地扬尘治理专项方案下载 的频率， 它是电磁问题的方便来选择尺度不变的单位（见我们的在线教科书，CH。2 ）。 That means that we pick some characteristic lengthscale in the system, a , and use that as our unit of distance. 这意味着，我们挑一些，并使用我们的距离单位，在系统的特点 lengthscale， 。 Moreover, since c = 1 in Meep units, a (or a / c ) is our unit of time as well.此外，由于 C = 1 Meep 单位（或 A / C）是我们的，以及单位时间 。In particular, the frequency f in Meep (corresponding to a time dependence e − i 2π f t ) is always specified in units of c / a (or equivalently ω is specified in units of 2π c / a ), which is equivalent to specifying f as 1 / T : the inverse of the optical period T in units of a / c .特别是，在Meep 频率 f（对应一个时间依赖性 E - 我2πF T）始终是在单位指 定 C /A（或等价ω2πC /A指定的单位），这是等同于指定 f为1 / T的单位为 A / C的光周期 T 的倒数。 This, in turn, is equivalent to specifying f as a / λ where λ is the vacuum wavelength.这 反过来，相当于指定为 A /λ，其中 λ是真空中的波长 f 。 (A similar scheme is used in MPB .) （一个类似的计划是在使用了MPB的。 ） For example, suppose we are describing some nanophotonic structure at infrared frequencies, where it is convenient to specify distances in microns.例如，假设我们所描述的一些红外频率的 纳米光子结构，它是方便到指定微米的距离。 Thus, we let a = 1μm .因此，我们让一个 =1μm 的 。 Then, if we want to specify a source corresponding to λ = 1.55μm , we specify the frequency f as 1/1.55 = 0.6452.然后，如果我们要指定一个源对应λ=1.55μm，我们指定的频率 f为1/1.55 ​ ​ = 0.6452。 If we want to run our simulation for 100 periods, we then run it for 155 time units (= 100 / f ).如果我们想要我们的模拟运行100期，然后再运行155个时间单位（= 100 / F）。 A transmission spectrum, for example, would be a ratio of transmitted to incident intensities, so the units of EEEE are irrelevant (unless there are nonlinearities).一个透射谱，例如，将是一个比传送 到事件的强度，所以 EEEE的单位是不相关的（除非有非线性）。 The Bloch wavevector (see below) kkkk is specified in Cartesian coordinates in units of 2π / a .布洛 赫 wavevector（见下文）kkkk是在直角坐标系中指定单位2π/ 。 (This is different from MPB : it is equivalent to taking MPB's k-points and transforming them with reciprocal->cartesian .)（这是从 不同的 企划预算处 ：它是相当于到企划预算处的 K点和转化他们 reciprocal->cartesian笛 卡尔。 ） [ edit ] [ 编辑 ] BoundaryBoundaryBoundaryBoundary conditionsconditionsconditionsconditions andandandand symmetriessymmetriessymmetriessymmetries边界条件和对称性 On a computer, we can only simulate a finite region of space, which means that we must terminate our simulation with some boundaryboundaryboundaryboundary conditionsconditionsconditionsconditions .在一台电脑，我们只能模拟一个有限的空间区 域，这意味着我们必须终止与一些边界条件的模拟。 Three basic types of terminations are supported in Meep: Bloch-periodicBloch-periodicBloch-periodicBloch-periodic boundariesboundariesboundariesboundaries , metallicmetallicmetallicmetallic wallswallswallswalls , and PMLPMLPMLPML absorbingabsorbingabsorbingabsorbing layerslayerslayerslayers .在 Meep支持终端的三个基本类型：布洛赫周期性边界，金属墙壁，PMLPMLPMLPML吸收层。Also, one can exploit symmetriessymmetriessymmetriessymmetries of a problem to further reduce the computational requirements.同样的，一个 可以利用的一个问题的对称性，以进一步降低计算要求。 With ordinary periodic boundaries in a cell of size L , the field components satisfy f ( x + L ) = f ( x ) . BlochBlochBlochBloch periodicityperiodicityperiodicityperiodicity is a generalization where普通尺寸 L细胞周期边界，磁场分量满足 F （X + L）= F（X）。 布洛赫周期性泛化 for some Bloch wavevector一些布洛赫 wavevector . 。 This can be used to solve for the modes of photonic crystals, waveguides, and so on, much like in MPB (see our online textbook , ch. 3).这可以用来 解决光子晶体的模式，波导等很像，企划预算处（ 见我们的网上购书，CH 3 ）。 An even simpler boundary condition is a metallic wall, where the fields are simply forced to be zero on the boundaries, as if the cell were surrounded by a perfect metal (zero absorption, zero skin depth).一个更简单的边界条件是金属墙，领域的只是被迫零的界限，如果细胞的周围有 一个完美的金属（零吸收，皮肤的深度为零）。 More generally, you can place perfect metal materials anywhere you want in the computational cell, eg to simulate metallic cavities of an arbitrary shape.更普遍的是，你可以把任何你想要完美的金属材料在计算单元，如模拟任意 形状的金属模腔。 To simulate open boundary conditions, one would like the boundaries to absorb all waves incident on them, with no reflections.为了模拟开放边界条件，想的界限，没有反射，吸收所有这些波 事件。 This is implemented with something called perfectlyperfectlyperfectlyperfectly matchedmatchedmatchedmatched layerslayerslayerslayers (PML).这是一些所 谓的完全匹配层（PML）的实施。 PML is, strictly speaking, not a boundary condition—rather, it is a special absorbing material placed adjacent to the boundaries. PML的，严格来说，不是一 个边界条件，相反，它是一种特殊的吸波材料放在相邻的边界。 PML is actually a fictitious (non-physical) material, designed to have zero reflections at its interface. PML 的其实是一个虚 构的（非物质）的材料，在其界面零反射。 Although PML is reflectionless in the theoretical continous system, in the actual discretized system it has some small reflections which make it imperfect.虽然 PML的无反射在连续系统的理论，在实际的离散系统，它有它不完善的一些 小的反射。 For this reason, one always gives the PML some finite thickness in which the absorption gradually "turns on".出于这个原因，人们总是给人一些 PML的有限厚度吸收逐渐 “打开”。 For more information, see perfectly matched layer .欲了解更多信息，请参阅完全匹配 层 。 Another way in which the computational cell is reduced in size is by symmetrysymmetrysymmetrysymmetry .计算细胞体积缩 小的另一个方式是由对称性。 For example, if you know that your system has a mirror symmetry plane (both in the structure and in the current sources), then you can save a factor of two by only simulating half of the structure and obtaining the other half by mirror reflection.例如， 如果你知道你的系统有一个镜像对称平面（无论是在结构和电流源），然后您可以保存只模 拟结构的一半，另一半由镜面反射获得的两个因素。 Meep can exploit several kinds of mirror and rotational symmetries — it is designed so that the symmetry is purely an optimization, and other than specifying the symmetry your computation is set up in exactly the same way. Meep 可 以利用镜像和旋转对称的几种 - 设计，对称，纯粹是一种优化，比其他指定你的计算是完 全相同的方式设置的对称。 See: Exploiting symmetry in Meep .见：利用对称性在Meep 。 [ edit ] [ 编辑 ] Finite-differenceFinite-differenceFinite-differenceFinite-difference time-domaintime-domaintime-domaintime-domain methodsmethodsmethodsmethods时域有限差分方法 FDTD methods divide space and time into a finite rectangular grid. FDTD的方法划分成有限的 矩形网格的空间和时间。 As described below , Meep tries to hide this discreteness from the user as much as possible, but there are a few consequences of discretization that it is good to be familiar with.正如下文所述 ，Meep试图隐藏用户尽可能离散，但也有几个后果的离散，这 是很好的熟悉。 Perhaps the most important thing you need to know is this: if the grid has some spatial resolution Δ x , then our discrete time-step Δ t is given by Δ t = S Δ x , where S is the Courant factor and must satisfy也许最重要的事情，你需要知道的是这样的：如果电网有一些空间分辨率ΔX，那么 我 们 的 离 散 时 间 步 长 Δt 是 由 Δ 吨 =ΔX ， 其 中 S 是 柯 朗 因 素 ， 必 须 满 足 , where n min is the minimum refractive index (usually 1), in order for th