COMSOL光学案例

Modeling of Pyramidal Absorbers for an Anechoic Chamber

Introduction

In this example, a microwave absorber is constructed from an infinite 2D array of pyramidal lossy structures. Pyramidal absorbers with radiation-absorbent material (RAM) are commonly used in anechoic chambers for electromagnetic wave

measurements. Microwave absorption is modeled using a lossy material to imitate the electromagnetic properties of conductive carbon-loaded foam.

Perfectly matched layers

Port

Conductive pyramidal form

Unit cell surrounded by periodic conditions

Conductive coating on the bottom

Figure 1: An infinite 2D array of pyramidal absorbers is modeled using periodic boundary conditions on the sides of one unit cell.

Model Definition

The infinite 2D array of pyramidal structures is modeled using one unit cell with Floquet-periodic boundary conditions on four sides, as shown in Figure 1. The

geometry of one unit cell consists of one pyramid sitting on a block made of the same

material. There are perfectly matched layers (PMLs) above the pyramid and the remaining space between the pyramid and the PMLs is filled with air.

The pyramidal absorber is made of a conductive material (σ = 0.5 S/m). At the interface of the conductive material and air, the incident field is partially reflected and partially transmitted into the pyramid. The transmitted field is attenuated inside of the lossy material. For angles within a particular range of normal incidence, the propagation direction of the reflected field is not back towards the source, but instead towards another surface of the conductive material. The process of partial reflection and partial transmission with subsequent attenuation is repeated until the field reaches the base of the pyramid. The amplitude of the field at the base of the pyramid is drastically reduced and so the reflection from the absorber at this point is marginal. The process is illustrated in Figure 2.

Incident wave

Conductive foam

Noise from outside the chamber is

blocked by a highly conductive layer

Figure 2: The incident wave is partially transmitted into the conductive foam where it is subsequently attenuated. For angles within a particular range of normal incidence, the reflected component of the field propagates towards another conducting surface where the process is repeated.

The bottom of the absorber has a thin highly conductive layer to block any noise from outside the anechoic chamber. Before mounting absorbers on the walls of the anechoic

chamber, it is necessary to apply a conductive coating on the walls, which is modeled as a perfect electric conductor (PEC).

The model domain immediately outside of the conducting foam is filled with air. Perfectly matched layers (PMLs) above the air at the top of the unit cell absorb higher order modes generated by the periodic structure ? if there are any ? as well as the upwards traveling excited mode from the source port. The PMLs attenuate the field in the direction perpendicular to the PML boundary. Since the model is solved for a range of incident angles, the wavelength inside the PMLs is set to 2π/|k0cosθ|, which, in some sense, is the wavelength of the normal component of the wave vector.

A port boundary condition is placed on the interior boundary of the PMLs, adjacent to the air domain. The interior port boundaries with PML backing require the slit condition. The port orientation is specified to define the inward direction for the

S-parameter calculation. Since higher order diffraction modes are not of particular interest in this example, the combination of Domain-backed type slit port and PMLs is used instead of adding a Diffraction order port for each diffraction order and polarization.

The periodic boundary condition requires identical surface meshes on paired boundaries. An identical surface mesh can be created by using the Copy Face operation from one boundary to another boundary.

Results and Discussion

Figure 3 shows the norm of the electric field and power flow in the case where the elevation angle of incidence is 30 degrees and the azimuth angle is zero. The intensity of the illuminating wave is strong near the tip of the absorber. It decreases towards the base of the pyramid, where it is ultimately very weak.

The S-parameter for y-axis polarized incident waves is plotted in Figure 4. The plot shows quantitatively that the absorber performs well for a range of incident elevation angles less than 40 degrees.

case where the elevation angle of incidence is 30 degrees and the azimuthal angle is zero.

Figure 4: The S-parameter is plotted as a function of incident angle.

Application Library path: RF_Module/Passive_Devices/pyramidal_absorber

Modeling Instructions

From the File menu, choose New.

N E W

1In the New window, click Model Wizard.

M O D E L W I Z A R D

1In the Model Wizard window, click 3D.

2In the Select physics tree, select Radio Frequency>Electromagnetic Waves, Frequency Domain (emw).

3Click Add.

4Click Study.

5In the Select study tree, select Preset Studies>Frequency Domain.

6Click Done.

G E O M E T R Y1

1In the Model Builder window, under Component 1 (comp1) click Geometry 1.

2In the Settings window for Geometry, locate the Units section.

3From the Length unit list, choose mm.

G L O B A L D E F I N I T I O N S

Parameters

1On the Home toolbar, click Parameters.

2In the Settings window for Parameters, locate the Parameters section.

3In the table, enter the following settings:

Here, c_const is a predefined COMSOL constant for the speed of light in vacuum.

D E F I N I T I O N S

Variables 1

1On the Home toolbar, click Variables and choose Local Variables .2In the Settings window for Variables, locate the Variables section.3In the table, enter the following settings:

G E O M E T R Y 1

Block 1 (blk1)

1On the Geometry toolbar, click Block .

2In the Settings window for Block, locate the Size section.3In the Width text field, type 50.4In the Depth text field, type 50.5In the Height text field, type 280.

6Locate the Position section. In the x text field, type -25.7In the y text field, type -25.8In the z text field, type -90.

9Right-click Component 1 (comp1)>Geometry 1>Block 1 (blk1) and choose Build Selected .

Name Expression Value

Description theta 0[deg]0 rad Elevation angle phi 0[deg]0 rad Azimuth angle f05[GHz]5E9 Hz Frequency lda0

c_const/f0

0.05996 m

Wavelength

Nam e Expression Unit

Description

k_0emw.k0

rad/m Wavenumber, free space k_x k_0*sin(theta)*cos(phi)rad/m Wavenumber, x-component k_y k_0*sin(theta)*sin(phi)rad/m Wavenumber, y-component k_z

k_0*cos(theta)

rad/m

Wavenumber, z-component

10Click the Wireframe Rendering button on the Graphics toolbar.

Block 2 (blk2)

1On the Geometry toolbar, click Block.

2In the Settings window for Block, locate the Size section.

3In the Width text field, type 50.

4In the Depth text field, type 50.

5In the Height text field, type 180.

6Locate the Position section. From the Base list, choose Center.

Block 3 (blk3)

1On the Geometry toolbar, click Block.

2In the Settings window for Block, locate the Size section.

3In the Width text field, type 50.

4In the Depth text field, type 50.

5In the Height text field, type 25.

6Locate the Position section. From the Base list, choose Center.

7In the z text field, type -77.5.

Pyramid 1 (pyr1)

1On the Geometry toolbar, click More Primitives and choose Pyramid. 2In the Settings window for Pyramid, locate the Size and Shape section. 3In the Base length 1 text field, type 50.

4In the Base length 2 text field, type 50.

5In the Height text field, type 120.

6In the Ratio text field, type 0.

7Locate the Position section. In the z text field, type -65.

8Click the Build All Objects button.

The finished geometry should look like this.

Set up the physics based on the direction of propagation and the E-field polarization. Assume a TE-polarized wave which is equivalent to s-polarization and perpendicular polarization. E x and E z are zero while E y is dominant.

E L E C T R O M A G N E T I C W A V E S,

F R E Q U E N C Y D O M A I N(E M W)

1In the Model Builder window, under Component 1 (comp1) click Electromagnetic Waves, Frequency Domain (emw).

2In the Settings window for Electromagnetic Waves, Frequency Domain, locate the Physics-Controlled Mesh section.

3Select the Enable check box.

Set the maximum mesh size to 0.2 wavelengths or smaller.

4In the Maximum element size text field, type lda0/5.

5Locate the Analysis Methodology section. From the Methodology options list, choose Fast.

Periodic Condition 1

1On the Physics toolbar, click Boundaries and choose Periodic Condition.

2

Select Boundaries 1, 4, 9, and 18–20 only.

3In the Settings window for Periodic Condition, locate the Periodicity Settings

section.

4From the Type of periodicity list, choose Floquet periodicity .5Specify the k F vector as

Periodic Condition 2

1On the Physics toolbar, click Boundaries and choose Periodic Condition .

k_x x k_y y 0

z

2

Select Boundaries 2, 5, 10, 13, 14, and 16 only.

3In the Settings window for Periodic Condition, locate the Periodicity Settings

section.

4From the Type of periodicity list, choose Floquet periodicity .5Specify the k F vector as

Port 1

1On the Physics toolbar, click Boundaries and choose Port .

k_x x k_y y 0

z

2

Select Boundary 11 only.

3In the Settings window for Port, locate the Port Properties section.4From the Wave excitation at this port list, choose On .5Select the Activate slit condition on interior port check box.6From the Slit type list, choose Domain-backed .7From the Port orientation list, choose Reverse .

8Locate the Port Mode Settings section. Specify the E 0 vector as

9In the β text field, type abs(k_z).

Scattering Boundary Condition 1

1On the Physics toolbar, click Boundaries and choose Scattering Boundary Condition .2Select Boundary 12 only.

x exp(-i*k_x*x)*exp(-i*k_y*y)[V/m]y 0

z

M A T E R I A L S

Material 1 (mat1)

1In the Model Builder window, under Component 1 (comp1) right-click Materials and

choose Blank Material .

2In the Settings window for Material, locate the Material Contents section.3In the table, enter the following settings:

Material 2 (mat2)

1In the Model Builder window, right-click Materials and choose Blank Material .2

Select Domains 1 and 3 only.

3In the Settings window for Material, locate the Material Contents section.4In the table, enter the following settings:

Property

Name

Value Unit

Property group

Relative permittivity epsilonr 11Basic Relative permeability mur 11Basic Electrical conductivity

sigma

S/m

Basic

Property

Name

Value Unit

Property group

Relative permittivity epsilonr 1

1Basic

D E F I N I T I O N S

Perfectly Matched Layer 1 (pml1)

1On the Definitions toolbar, click Perfectly Matched Layer .

2Select Domain 4 only.

3In the Settings window for Perfectly Matched Layer, locate the Scaling section.4From the Typical wavelength from list, choose User defined .5In the Typical wavelength text field, type 2*pi/abs(k_z).

Since the model is solved for a range of incident angles, the wavelength inside the PMLs is set to 2φ/|k 0cos(θ)|, which is the wavelength of the normal component of the wave vector.

M E S H 1

In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Build All .

Relative permeability mur 11Basic Electrical conductivity

sigma

0.5

S/m

Basic

Property Name Value Unit Property group

D E F I N I T I O N S

View 1

1On the View 1 toolbar, click Hide Geometric Entities.

2Select Domain 4 only.

3In the Settings window for Hide Geometric Entities, locate the Geometric Entity Selection section.

4From the Geometric entity level list, choose Boundary.

5Select Boundaries 4, 5, 9, and 10 only.

M E S H1

S T U D Y1

Step 1: Frequency Domain

1In the Model Builder window, under Study 1 click Step 1: Frequency Domain.

2In the Settings window for Frequency Domain, locate the Study Settings section. 3In the Frequencies text field, type f0.

Parametric Sweep

1On the Study toolbar, click Parametric Sweep.

2In the Settings window for Parametric Sweep, locate the Study Settings section.

3Click Add.

4In the table, enter the following settings:

Parameter name Parameter value list Parameter unit

theta range(0[deg],5[deg],85[deg])

5On the Study toolbar, click Compute.

R E S U L T S

Data Sets

1On the Results toolbar, click Selection.

2In the Settings window for Selection, locate the Geometric Entity Selection section.

3From the Geometric entity level list, choose Domain.

4Select Domains 1–3 only.

Electric Field (emw)

1In the Model Builder window, expand the Results>Electric Field (emw) node, then click Multislice 1.

2In the Settings window for Multislice, locate the Multiplane Data section.

3Find the z-planes subsection. In the Planes text field, type 0.

4In the Model Builder window, right-click Electric Field (emw) and choose Arrow Volume.

5In the Settings window for Arrow Volume, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component

1>Electromagnetic Waves, Frequency Domain>Energy and

power>emw.Poavx,...,emw.Poavz - Power flow, time average.

6Locate the Arrow Positioning section. Find the x grid points subsection. In the Points text field, type 21.

7Find the y grid points subsection. In the Points text field, type 1.

8Find the z grid points subsection. In the Points text field, type 21.

9On the Electric Field (emw) toolbar, click Plot.

10In the Model Builder window, click Electric Field (emw).

11In the Settings window for 3D Plot Group, locate the Data section.

12From the Parameter value (theta (rad)) list, choose 0.5236.

13On the Electric Field (emw) toolbar, click Plot.

14Click the Zoom Extents button on the Graphics toolbar.

See Figure 3 to compare the plotted results.

1D Plot Group 2

1On the Home toolbar, click Add Plot Group and choose 1D Plot Group.

2On the 1D Plot Group 2 toolbar, click Global.

3In the Settings window for Global, click Replace Expression in the upper-right corner of the y-axis data section. From the menu, choose Component 1>Electromagnetic Waves, Frequency Domain>Ports>emw.S11dB - S-parameter, dB, 11 component.

4On the 1D Plot Group 2 toolbar, click Plot.

The calculated S-parameters at the input port are shown as a function of the incident angle. Compare with that shown in Figure 4.

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14. 右侧任务栏：预置研究→瞬态； 15. 研究2 →步骤1：研究设定； 16. 时间单位：可设置为ms；时间：设置仿真时间范围及步长； 17. 仿真完成后，结果下面自动出现“温度”； 18. 点击温度→表面。出现仿真结果图。可看到温升变化，和稳态保持一致； 19. 派生值，右键，“体最大值”，会在仿真图下方出现“表格2”，自动将时间和温度的对应变化列出来； 20. 在表格处，点击“表图”按钮，结果下面自动出现“一维绘图组”：会有温度

comsol单模光纤仿真案例

Step-Index Fiber Introduction The transmission speed of optical waveguides is superior to microwave waveguides because optical devices have a much higher operating frequency than microwaves, enabling a far higher bandwidth. Today the silica glass (SiO 2) fiber is forming the backbone of modern communication systems. Before 1970, optical fibers suffered from large transmission losses, making optical communication technology merely an academic issue. In 1970, researchers showed, for the first time, that low-loss optical fibers really could be manufactured. Earlier losses of 2000 dB/km now went down to 20 dB/km. Today’s fibers have losses near the theoretical limit of 0.16 dB/km at 1.55 μm (infrared light). One of the winning devices has been the single-mode fiber, having a step-index profile with a higher refractive index in the center core and a lower index in the outer cladding. Numerical software plays an important role in the design of single-mode waveguides and fibers. For a fiber cross section, even the most simple shape is difficult and cumbersome to deal with analytically. A circular step-index waveguide is a basic shape where benchmark results are available (see Ref. 1). This example is a model of a single step-index waveguide made of silica glass. The inner core is made of pure silica glass with refractive index n 1 = 1.4457 and the cladding is doped, with a refractive index of n 2 = 1.4378. These values are valid for free-space wavelengths of 1.55 μm. The radius of the cladding is chosen to be large enough so that the field of confined modes is zero at the exterior boundaries. For a confined mode there is no energy flow in the radial direction, thus the wave must be evanescent in the radial direction in the cladding. This is true only if On the other hand, the wave cannot be radially evanescent in the core region. Thus The waves are more confined when n eff is close to the upper limit in this interval. n eff n 2 >n 2n eff n 1 <<

comsol电场示例

Computing the Effect of Fringing Fields on Capacitance Introduction A typical capacitor is composed of two conductive objects with a dielectric in between them. Applying a voltage difference between these objects results in an electric field. This electric field exists not just directly between the conductive objects, but extends some distance away, a phenomenon known as a fringing field. To accurately predict the capacitance of a capacitor, the domain used to model the fringing field must be sufficiently large, and the appropriate boundary conditions must be used. This example models a parallel plate capacitor in air and studies the size of the air domain. The choice of boundary condition is also addressed. Air domain Metal discs Figure 1: A simple capacitor consisting of two metal discs in an air domain.

COMSOL3.5结构力学模型案例01

结构力学 : 结构力学模型案例 结构力学模型案例 通过以下两个不同情况来介绍如何进行线性静态应力分析。 这个案例来自NAFEMS 基本系列 (参考文献. 1). 锥形膜末端载荷 第一个案例介绍厚度为0.1mm 的膜的2D 平面应力。水平载荷沿右末端平均分布，为10 MN/m (也就是应力 为 100 MPa)。在左末端，x 方向位移零。左端的中间点固定在y 方向。 模型使用以下材料属性： 在COMSOL Multiphysics 中建模 使用平面应力模式的静态分析，这样可以直接进行应力分析。有限元模型使用拉格朗日二次三角单元。为了 ? 外边界的均布水平载荷 ? 重力载荷 ? 材料是各向同性的。 ? 杨氏模量（弹性模量）为210·103 MPa 。 ? 泊松比为0.3 。

确定结果已经收敛到基准值，细化网格然后再次计算结果。 结果 点（0，2）处x方向应力求解值和基准目标值61.3 MPa吻合很好。如果采用初始化网格，COMSOL Multiphysics 计算结果为61.41 MPa。两次连续的细化网格后计算值分别为T 61.36 MPa 和 61.35 MPa。 图8-1: 均布末端载荷下x方向的应力分布 模型库路径: COMSOL_Multiphysics/Structural_Mechanics/edge_load_2d 图形用户界面建模 建模导航 1 在空间维度下拉框中选择2D。 2 在应用模式树下，依次选择COMSOL Multiphysics>结构力学>平面应力>静态分析。 3 点击确定。 几何建模 1 在绘图菜单下，选择指定对象>线。 2 在线对话框中，在x编辑框中输入0 4 4 0 0，在y编辑框中输入 0 1 3 4 0。 3 点击确定。 4 点击主工具栏的缩放至窗口大小按钮。 5 点击绘图工具栏的强迫成实体按钮。

comsol案例——肖特基接触

肖特基接触 本篇模拟了由沉积在硅晶片上的钨触点制成的理想肖特基势垒二极管的行为。将从正向偏压下的模型获得的所得J-V（电流密度与施加电压）曲线与文献中发现的实验测量进行比较 介绍 当金属与半导体接触时，在接触处形成势垒。这主要是金属和半导体之间功函数差异的结果。在该模型中，理想的肖特基接触用于对简单的肖特基势垒二极管的行为进行建模。使用“理想”这个词意味着在这里，表面状态，图像力降低，隧道和扩散效在界面处计算半导体与金属之间传输的电流应被忽略。 注意，理想的肖特基接触的特征在于热离子电流，其主要取决于施加的金属- 半导体接触的偏压和势垒高度。这些接触通常发生在室温下掺杂浓度小于1×1016 cm-3的非简并半导体中。 模型定义 该模型模拟钨 - 半导体肖特基势垒二极管的行为。图1显示了建模设备的几何形状。它由n个掺杂的硅晶片（Nd = 1E16cm-3）组成，其上沉积有钨触点。该模型计算在正向偏压（0至0.25V）下获得的电流密度，并将所得到的J-V曲线与参考文献中给出的实验测量进行比较。该模型使用默认的硅材料属性以 及一个理想的势垒高度由下列因素定义： ΦB=Φm-χ0（1） 其中ΦB是势垒高度，Φm是金属功函数，χ0是半导体的电子亲和力。选择钨触点的功函数为 Φm = 4,72V （2） 其中势垒高度为ΦB= 0.67V。 结果与讨论 图2显示了使用我们的模型（实线）在正向偏压下获得的电流密度，并将其与参考文献中给出的实验测量进行比较ref. 1（圆）。

建模说明 从文件菜单中，选择新建NEW。 N E W 1在“新建”窗口中，单击“模型向导”。 MODEL WIZARD 1 在模型向导窗口，选择2D轴对称 22在选择物理树中，选择半导体>半导体（semi）。 3单击添加。 4点击研究。 5在“选择”树中，选择“预设研究”>“稳态”。 6单击完成。 D E F I N I T I O N S 参数 1在“模型”工具栏上，单击“参数”。 2在“参数”的“设置”窗口中，找到“参数”部分。3在表格中，输入以下设置： 选择um做长度单位

COMSOL动网格案例

COMSOL动网格案例 有限元方法是一种基于网格的数值计算方法，其一般流程为： 剖分网格是在几何模型的基础上进行的，但是我们在仿真过程中经常会遇到几何模型随着计算过程变化的情况，例如模拟电机转动、固体在流体中运动等，这时候，基于原来网格的方程就不再准确，而需要重新划分网格，即引入动网格的概念。 动网格是相对于传统“静”网格而言，一般仅在有运动物体参与的仿真模型中使用。引入动网格的概念之后，仿真流程就不再是单独的一条流水线，而变成了循环迭代模型。

动网格使用方法 根据重新划分网格的不同，动网格可以分为两种： 1用户提前知道运动物体的位移变化过程，从而可以手动指定网格的运动形式。 例如在下面的电动机案例中，中间部分的转子在不停转动，需要进行动网格的设置，但是由于其转速是固定的，因而网格的变换形式我们就可以预先指定。 2用户提前不知道运动物体如何运动，无法预先手动指定网格运动形式，需要软件自动重新绘制网格。 下面的案例模拟了管道中流体流过时，其中一个障碍物的变形情况。流体从管道的左侧向右流动，在流体压力作用下，原本直立在管道中的障碍物发生变形，向一侧倾斜。

由于我们无法事前了解网格的运动形式，所以也就无法指定网格运动，而交由软件自动划分，下图展示了这种情况下动网格的设置方案。 下面的图展示了网格变形情况。 与电动机的例子不同，我们在管道流动的案例中发现了网格的拉扯现象，即网格实际上没有重新划分，仅仅是网格单元的形状发生了变化，这仅适用于网格进行小范围变化的情形，当变形较大是，网格单元可能会被拉扯为畸形，从而降低计算精度，甚至导致模型不收敛。 我们可以很方便的验证一下，将障碍物的杨氏模量由200kPa改为2kPa，也就是将障碍物变得更软一些。 下面的图展示了此时的网格变形情况，实际上模型还没有算完，计算过程中由于不收敛停止了，我们仅展示了计算得到的部分结果。