fdtd入门详细教程

ncslumerico 二零二三安装教程解压后看到的这些文件，先点到这个文件夹，右击以管理员身份运行点使开始安装。 同意下一步选择先安装位置，下一步下一个 到这个位置后 就是正在安装中，等一下，等到按钮可以点亮 下一个， 取消勾选， 再点一下 回到安装包，打开这个文件夹，把这两个复制一下， 打开 c 盘， 打开这个文件夹，我们在这个位置粘贴一下， 然后打开这个文件， 不要关闭这个界面， 我们打开这个程序， 把这个替换掉， 保存一下， 这个目前它是没有权限的，我们可以先令存为到桌面保存关闭， 我们回到这个地方，我们可以看一下它属性， 我们刚才保存的右复制粘贴替换一下，刚才是没有保存成功的， 所以我们先保存到桌面，然后再粘贴回来，替换一下， 我们再打开这个界面，我们点， 然后这个可以放大一下， 选择文件 c 盘这个文件夹下边刚才这个文件， 点这个按钮， 我们看到它显示已经成功了， 然后我们打开任务管理器， 找到服务，我们看到这两个已经正在运行了， 我们再回到安装包， 双击是是确定 右击属性属性， 然后系统高级设置， 然后点环境变亮 系统变量这一块， 我们新建一个变量名， 变量直视变量直视这个点，两名输入这些点，确定 确定，我们回到 安装包第三个文件夹，右击以管理员身份运行式 点安装 下一步。同意下一步注意安装的位置，下一步安装， 我们回到安装包，打开这个文件夹， 打开安装位置， 找到这个路径，粘贴， 从开始菜单 找到这个图标，拖出来 双击运行， 允许 我们的软件已经可以正常使用了。

the standard workplow is to first create the materials needed in the simulation if the material data isn't hard to available from the default material database once the materials are defined the structures and fdt simulation region are set up the simulation region is where the boundary conditions mesh simulation time are set next sources are added to inject fields into the simulation region and monitors are added to the coordinator before running the simulation checks can be done to make sure the material properties are simulated accurately and that the computer has sufficient memory to run the simulation after running data can be collected for monitors and the results this can be analyzed by plotting the data or by performing additional post processing using scripts in the process of designing a device the geometry of the device will usually be modified many times meaning that this process is repeated until the optimal design parameters are found the built in parameter sweep and optimization tool can also be used to help on this process convergence testing is the final step done to obtain high accuracy results convergence testing involved running the simulation while varying in t simulation settings to quantify the amount of numerical error in the simulation。

numerical fdtd fdtd algorithm sour numerics the fttd method， solve or numerics as mentioned in the introduction， the finite difference time domain fttd method is used to solve maxwell's equations in the time domain， the equations are solved numerically on a discrete grid in both space and time this means that the electric and magnetic fields e and h respectively are discrete in space and time the grid step in space is generally called delta x or delta y or delta z and in time it is called delta t for convenience of notation we often drop the delta x and delta t and simply refer to the spatial grid as i or j or k and the time step as n furthermore we often use a subscript and superscript notation for the spatial position and time step respectively the e fields are solved at time and plus one half well， the h fields are solved at time n the derivatives in both space and time are handled with finite differences and are second order accurate when the grade is uniform the electric and magnetic field components are distributed in space over a unit cell called the e cell this staggering of the fields in space is ideal for calculating spatial derivatives of the curl terms at the correct positions in space at the beginning of the simulation the e and h fields are typically zero from here we update e at time n plus 1 half which is a function of e at the previous time step plus a turn proportional to the curl of h at time step n once， we have the e field updated to time n plus 1 half we can proceed to update h at time n plus 1 which is a function of h at the previous time step and the curl of e taken at time step n plus 1 half in this way， we can leap frog the update of e then h then e and so on until we choose to stop the simulation it is important to understand that we do not ever calculate enh at the same point in time they are offset by one half time step in fact if you record the e field as a function of time with a monitor and plotted the monitor will interpolate the original fdtd e fields to the same time step as h， so you may never notice this offset despite this issue this leapfrog approach has the advantage of allowing us to obtain second order accuracy in time which means that the error between the electromagnetic fields calculated by fdtd and the correct solution scales with the time step squared this means for example that if we reduce the time step by a factor of two are error diminishes by a factor of four the simulation geometry is discritized into ye cells which as mentioned previously of the fundamental unit of the fdtd method as mentioned before the enh field components are all located at different positions within the e cell this allows us to calculate spatial derivatives by finite differences at the optimal spatial locations and gives us second order accuracy in space on a uniform mesh still it is important to understand that the e and h components are never known at the same spatial location which can have consequences for many types of results which we may wish to calculate such as energy density by default monitors that record these fields will automatically interpolate all field components to the corner of the e cell so， that you can visualize and analyze your results at the same spatial location however， this interpolation can be disabled and and this is useful for some advanced calculations such as determining the optical absorption in a metal， near a metal dielectric interface in addition to e and h， we must also discritize the electric permitivity epsilon in most regions this is very straightforward because we can assign a permativity of either material a or material b however， it gets much more complicated near interfaces because the interface can pass through a e cell at any position and orientation and furthermore each electric field component is in a different spatial location as a result we need a different value for the x， y and z components of the permativity even if all materials are isotropic once， we have discritized the permitivity in this manner there are still challenges first the position of the interfaces is not well defined within the e cell for example if we have a yeast cell with a spatial grid of 40 nanometers and we move an interface by as much as 20 nanometers we may not see any difference in the fttd results because the primitivity dyscritization could be identical second， we do not treat the normal e field components which are discontinuous any differently than the tengential ones， which are continuous third we can experience staircasing effects when interfaces are on an angle with respect to the cartesian axes， which can lead to problems such as unphysical hotspots in plasmonic devices the conformal mesh technology is a method to deal with these issues by modifying the standard fdtd update， near interfaces to use an integral solution to maxwell's equations this is equivalent to introducing an effective primitivity that is antise a tropic and can provide a much more accurate solution we will discuss the conformal mesh technology in more detail later， fttd simulations can be run in 3d or in 2d it is important to remember that for 2d simulations the structure is infinite in the z dimension in some cases， 2d simulations are an approximation that can be run quickly， but in other cases they can be a fully accurate solution to the problem for example simulating line gratings like the one shown here on the right illuminated by plane waves should be be done in 2d because 2d fttd simulations make the assumption that the structure is infinite in the z dimension we know that the permativity in fields are the same for all values of z this allows us to separate maxwell's equations into two independent polarization states often called transverse electric or t e with fields e， x， e， y and h c， and transverse magnetic or t m with fields e， z， h， x， and h y in fttd solutions we try to avoid the terms te， and tm because they can lead to a great deal of confusion instead， it is best to look at the blue arrows of sources in the fttd design environment to see the direction of e field colarization in certain cases such as anacetropic materials with off diagonal elements this separation of polarizations is no longer valid in general you simply set your desired source polarization and in 2d fttd solutions will run a tetm or combined te and tm simulation as required it is important to think about how the memory and simulation time scale with the grid size if we assume that the spatial grid size is uniform and that delta x is the same as delta y and delta z the memory requirements for 3d scale like one over delta x cubed in 3d and one over delta x squared in 2d this is obviously expected， but what is surprising is that the simulation time increases like one over delta x to the fourth power in 3d and to the third power in 2d the reason for this which we will discuss in more detail later is that you cannot reduce the spatial grid size without also reducing the size of the time step delta t this means that there is a big penalty to pay for using a smaller grid step for example if you reduce your grid size by a factor of two your simulation time will increase by a factor of 16， also we often discuss the grid size not in absolute terms， but relative to the wavelength of light we call the ratio of the wavelength lamda to the grid size delta x the number of grid points per wavelength or sometimes just the points per wavelength this is a key factor that determines the accuracy of the fdtd simulation the course rule of thumb you can get initial fdtd results with six points per wavelength and many results such as transmission and reflection will be within 10 or 20 percent of the correct answer by 10 points per wavelength many results will be within one to two percent of the correct result and it is rare to require more than 20 points per wavelength i should note that this is a rule of thumb only and sometimes much smaller meshes are required to resolve geometric features or to correctly simulate plasmonic effects where highlight confinement can occur it is also important to note that the points per wavelength should be defined with respect to the wavelength in the medium and not free space wavelength therefore for similar accuracy a smaller grid size should be used in materials with higher refractive index lumericals fttd solutions provides a simple mesh actressy setting that targets a minimum points per wavelength in all regions of the simulation and automatically adapts to the refractive index of the different materials the mesh accuracy of one through eight corresponds to points per wavelength targets of six ten 14， 18 and so on up to 34 the default value is two and this is appropriate for most simulations initially you may want to even use a setting of one until everything else is set up properly it is rarely useful to use values of larger than three or four as there is typically something else that limits the accuracy of the simulation at that point for find geometric structures or situations such plasmonic structures where you know the light confinement will be high the mesh can be controlled locally using mesh override regions in the two figures on the lower right hand side， you can see some results of convergence testing for a 3d simmos image sensor application the first figure shows the fraction of source light that is incident on the silicon surface and the fraction incident under the green pixel as a function of mesh accuracy you can see that good results can be obtained with a mesh accuracy setting of one that by two you have almost achieved a converge result and that there is no point in going beyond a setting of four in the second figure， you can see the cost in time and memory of the higher mesh accuracy setting normalized to a mesh accuracy setting of one you can see that it takes almost 600 times longer to run with a mesh accuracy setting of 8 compared to one in this application where a mesh accuracy setting of one can run on a single workstation in a minute or less this can be the difference between waiting one minute and waiting ten hours for your simulation to complete yet the results are almost identical clearly you want to be working where each simulation takes only one minute， which makes it easy to perform complex， parameter， sweeps and optimization。

click the show mesh button on the toolbar to see the generated simulation mesh in the drawing grid properties turn off the drawing grid to better see the mesh lines because we are simulating a device where there are plasmonic effects the results can be very sensitive to the meshing the 10 animator mesh set size is a starting point but for most accurate results we need to preform convergence testing by trying finer mesh set sizes next we will add and set up a plane wave source at normal incidents from the air above the structure add a plane wave source from the sources drop down menu set the source to inject in the backward direction along the z axis this means that the source will propagate in the minus z direction under the geometry tab set the source x and y positions to 0 and spans to 0.5 micro， so the source covers the full area of the simulation region set the set position to 0.3 micron so the source invention can be located in the air about destruction under the frequency weight points tab the source start and stop range are already set to 0.4 to 0.7 micron which is the range that we're interested on the right， we can see the automatically generated the source poles over time as well as the spectrum of the source poles you can click and drag an area on the plots to zoom in next， we'll set up monitors to accord data from the simulation we will be using monitors to accord the refractive index profile， reflection and transmission， spectrum， electric and magnetic field profile and a movie of the time to main fields start by adding， i will practice the next monitor from the monitors drop down the name edit the monitor and in the geometry tab set the monitor type to 2ds at the set the x and y spans to 0.5 micron and the zed position to 0.05 my so that the monitor is within the gold film set the monitor name to xy inx now add another refractive index monitor to see the field profile in the xzed plane， set the monitor name to xzed index under the geometry tab set the monitor type to 2d wine album and set the x pan to 0.5 micron and zedsman to one micron you can see the monitors in the viewports outlined in yellow， it's fine for the monitors to extend outside of the simulation region data is only recorded within the simulation region so the results returned are automatically trunated by the in no simulation region memories。

接下来是这个监视器的一个功能使用，我们是以超表面频率功率监视器设置为例，那么监视器它分好几种，包括 折射率监视器、时间监视器、影片监视器、场分布监视器，还有个功率监视器，还有模式扩展，全局属性这几个选项啊。大部分应该用的比较多的是这个 分布和功率显示器，我们一般用的比较多的是这款 c 多米 fl 的 and plus。 我们一个个来看，转射率显示器是在模拟过程中，他会将 nk 值单程频率波成的函数来记 记录，只有在二维或三维时，他的折射率监视器才是可以用的，没有点和线监视器，就这个折射率监视器只能用于二维或三维模拟的过程中， 如果是意味着它是不可以的。然后食欲监视器是同提供整个模拟 期间场分布剖量的信息，食欲监视器它是可以点线面都可以的，来捕获这个模拟区，放进去所有不同时空范围内的信息。电影监视器嘛，就是可以将这个监视器在 一段时间内的这个分布啊一这种动态显示，然后这个是频率监视器，可以通过复利液变化得到任意单色波长的稳态结果，虽然说它是频率的啊，可以用于透射、反射，吸收散射彩分布，原厂发射，还有经常放大一些 作用。那接下来就是频率分布监视器，他这个里面分了两个，一个是频率分布监视器，一个是频率功率分布监视器， 那么这俩之间又有什么区别呢？我们可以看看频率分布近视器是收集某些空间内的频率模拟结果的场分布是电场和磁场分布， 那么这个是功率了。接下来是模式扩展，模式扩展呢？就是广播导范围内的，然后这个就是一些设置，我们看看他这个监视器是怎么设的。

to start with we can check that the necessary materials for the simulation are available in the material database open the material database by clicking on the materials button in the main toolbar， the list of available materials is displayed in the material list we will be using gold， glass and edge materials click on a material to see the material data in the material properties section of the material database the etch material is a material with refractive index one and we will use this material to represent the etched holes in the gold film if the background index was not one then the refractive index of the etch material would need to be modified to match the background index we will use the materials available in the default material database so it's not necessary to add any new materials the next step is to set up the structures add a rectangle from the structures drop down menu to represent the gold film click the arrow next to the structures button to open the menu edit the rectangle there are several ways to open the edit window you can do this by selecting the object in the object tree and clicking on the edit button in the toolbar on the left or you can use the edit menu in the title bar menu here you can see that the keyboard shortcut to edit an object is e finally you can you can also right click on the object and select edit object from the context menu set the name of the structure to film in the geometry tab set the x and y position to zero and span to 1.2 microns the period of the device is 0.4 microns so this will represent three periods in each direction to set the device thickness set the zedmen position to zero and zed max position to 0.1 micron to simulate a 100 meter thick film in the material tab use the drop down menu to select the au goal crc material make a copy of the rectangle using the coffee and paste keyboard your cuts change the name to substrate set z max to zero and z min to minus one micron so the rectangle will be one micron thick in the material tab set the material to sio2 glass palette next add an array of circles from the object library to represent the array of holes etched in the gold film the object library contains a library of structure groups that can be used to set up more complex structures such as periodic rays。