FDTD Getting Started Manual

Getting StartedFDTD

Release 8.6

Solutions

1Contents

2003 - 2013 Lumerical Solutions, Inc

Table of ContentsPart I Introduction 2

............................................................................................................ 31 What is FDTD?

............................................................................................................ 42 FDTD Solutions GUI

............................................................................................................ 73 Running Simulations and Optimizations

............................................................................................................ 94 Analyzing simulation data

Part II Silver Nanowire Tutorial 12............................................................................................................ 131 Discussion and results............................................................................................................ 172 Modeling instructions

Part III Ring Resonator Tutorial 26............................................................................................................ 271 Discussion and results............................................................................................................ 342 Modeling instructions

Part IV PC Micro Cavity Tutorial 44............................................................................................................ 441 Discussion and results............................................................................................................ 522 Modeling instructions

Getting Started2


1 IntroductionThe goal of the Getting Started Guide is to introduce FDTD Solutions and demonstrate howit can be used to model a number of simple systems.

The FDTD algorithm is useful for design and investigation in a wide variety of applicationsinvolving the propagation of electromagnetic radiation through complicated media. It isespecially useful for describing radiation incident upon or propagating through structureswith strong scattering or diffractive properties. The available alternative computationalmethods - often relying on approximate models - frequently provide inaccurate results.

FDTD Solutions is useful for numerous engineering problems of commercial interestincluding:

integrated optical componentsdisplay technologiesoptical storage devicesOLED designbiophotonic sensorsplasmon polariton resonance devicesoptical waveguide devicesphotonic crystal devicesLCD devices

FDTD Solutions is an accurate and easy to use, versatile design tool capable of treatingthis wide variety of applications. This introductory chapter of the Getting Started Guideintroduces the general FDTD method and provides a basic overview of the product usage. The final sections contain examples that are accompanied by step-by-step instructions sothat you can set up and run the simulations yourself.

Application Type Description Example

Particle Scattering Calculation of the absorption,scattering and extinction cross-sections of a sub-wavelengthparticle.

Silver nanowire resonantscattering

Waveguide Devices Determination of the insertion lossor return loss, and frequencyresponse of waveguide-basedcomponents. Manufacturingtolerances are also calculated.

Ring resonator design forchannel drop filter

Cavities and Resonators Analysis of resonant modes andthe corresponding decay

Photonic crystal microcavity design

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Introduction 3


constants for cavities andresonators.

1.1 What is FDTD?The Finite Difference Time Domain (FDTD) method has become the state-of-the-art methodfor solving Maxwells equations in complex geometries. It is a fully vectorial method thatnaturally gives both time domain, and frequency domain information to the user, offeringunique insight into all types of problems and appFDTDlications in electromagnetics andphotonics.

The technique is discrete in both space and time. The electromagnetic fields and structuralmaterials of interest are described on a discrete mesh made up of so-called Yee cells.Maxwells equations are solved discretely in time, where the time step used is related tothe mesh size through the speed of light. This technique is an exact representation ofMaxwells equations in the limit that the mesh cell size goes to zero.

Structures to be simulated can have a wide variety of electromagnetic material properties.

Light sources may be added to the simulation. The FDTD method is used to calculate howthe EM fields propagate from the source through the structure. Subsequent iteration resultsin the electromagnetic field propagation in time. Typically, the simulation is run until thereare essentially no electromagnetic fields left in the simulation region.

Time domain information can be recorded at any spatial point (or group of points). This datacan be recorded for the duration of the simulation, or it can be recorded as a series of"snapshots" at times specified by the user.

Frequency domain information at any spatial point (or group of points) may be obtainedthrough the Fourier transform of the time domain information at that point. Thus, the

Getting Started4


frequency dependence of power flow and modal profiles may be obtained over a wide rangeof frequencies from a single simulation.

In addition, results obtained in the near field using the FDTD technique may be transformedto the far field, in applications where scattering patterns are important.

More information about the FDTD method, including references, can be found in the Physics of the FDTD Algorithm section of the reference guide.

1.2 FDTD Solutions GUIThis section discusses useful features of the FDTD Solutions Graphical User Interface(GUI).

In this topicGraphical User Interface: Windows andToolbarsAdd Objects to the simulationEdit ObjectsStart a new 2D/3D simulation

Graphical User Interface: Windows and Toolbars

The graphical user interface contains useful tools for editing simulations, including

a toolbar for adding objects to the simulationa toolbar to edit objectsa toolbar to run simulationsan objects tree to show the objects which are currently included in the simulationa script file editor windowan object librarya window to set up parameter sweeps and optimizationsa results view that shows all the current results for the selected simulation objecta script workspace that shows all the variables in the current scripting environmenta script favorites window that stores the user's favorite script commands

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Introduction 5


In the default configuration some of the Windows are hidden. To open hidden windows,click the right mouse button anywhere on the main title bar or the toolbar to get the pop upwindow shown in the screen shot below. The visible windows/toolbars have a check marknext to their name; the hidden ones do not have check marks. A second way to obtain thepop up window is to go to the main title toolbar and select VIEW->WINDOWS.

For more information about the toolbars and windows see the Layout editor section of thereference guide.

Add Objects to the simulation

The Graphical User interface contains buttons to add objects to the simulation. Click on thearrow next to the image to get a pull down menu which shows all the available options in agroup. The screenshot below shows what happens when we click on the arrow next to theCOMPONENTS button. Note that the picture on the button is the same as the MORECHOICES option in the list. If we click on the button itself (instead of the arrow) we will godirectly to the MORE CHOICES section of the object library.

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Also notice that the picture for the COMPONENTS button will change depending on whatthe last component that was added to the simulation was. Finally, the ZOOM EXTENT

button in the toolbar will resize the viewports to fit all the objects currently includedin the simulation.

Edit objectsTo edit an object, select the object and press E on the keyboard or press the EDIT button

on the toolbar. The easiest way to select an object is to click on the name of theobject in the objects tree. However, objects can also be selected by clicking on thegraphical depiction of them when the SELECT button is pressed. For more information seethe Layout editor section of the reference guide.

When we edit objects in FDTD, we get an edit window. The edit windows have units for thesettings; in the GEOMETRY tab, the x, y and z location will be in m by default. The unitscan be changed to nm if we choose SETTINGS->LENGTH units in the main menu. Fieldsin the edit windows act like calculators, so that equations can be entered in the fields. Seethe y span field below for an example.

Introduction 7


Start a new 2D/3D simulation

By default, the FDTD simulation region is 3D. In the following Getting Started Examples,we often begin with a 2D simulation, which can be obtained by setting the dimension of thesimulation region to 2D.

1.3 Running Simulations and OptimizationsThis section discusses important checks which should be made before running asimulation (memory requirements, material fits) and gives links to more information aboutrunning simulations and parameter sweeps or optimizations.

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In this topicCheck memory requirementsCheck material fitsSetup parallel optionsRun simulationRun parameter sweeps and optimizations

Check memory requirements

To check the memory requirements, press the CHECK button If this is not thecurrent icon, you can find it by pressing the arrow. Note that the memory report indicatesthe amount of memory used by each object in the simulation project as well as the totalmemory requirements. This allows for judicious choice of monitor properties in large andextensive simulations.

Check material fits

The CHECK button also contains a material explorer option . Many of thematerials used in FDTD Simulations come from experimental data (see the materialssection of the Reference Guide for references for the material data and descriptions of theFDTD material models). Before running a simulation, FDTD Solutions automaticallygenerates a multi-coefficient model fit to the material data in the wavelength range for thesource. It is a good idea to check and optimize the material fit before running a simulation.

Setup the resource configuration

Before running any simulations, the resource options must be set up. These options can

be accessed by pressing the Resources button . In most cases, the defaultsettings should be fine. The 'number of processes' is typically set to the number of coresin your computer.

Run simulation

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Introduction 9


You can run simulations by pressing the RUN button on the mail toolbar. For moredetails, such as how to run multiple simulations in distributed mode, please see the RunSimulations section in the online User Guide, or the Running simulations and analysissection of the Reference Guide.

Run parameter sweeps and Optimizations

FDTD Solutions also has a built in parameter sweep and optimization window. This windowcan be seen at the top of the page, and can be opened using the instructions in theGraphical User Interface discussion just prior to this topic.Optimization Window includesbuttons to add a parameter sweep and add an optimization. Parameter sweeps andoptimizations can include multiple parameters, or be nested. Each optimization or sweepcan be run by pressing the right-most button.

1.4 Analyzing simulation dataThis section discusses the tools used to analyze simulation data: the Results Managerand Visualizer, the script environment and data export to third party software such asMATLAB. For more details please see the Analysis tools and the Scripting languagechapters in the Reference Guide.

In this topicResult analysisScriptingData export

Result analysisThe Results Manager is a tool for analyzing simulation data. The Results View windowshows all the results for the simulation object that is currently selected in the Object Tree.The Script Workspace and Script Favorites windows work in conjunction with the scriptingenvironment to provide additional GUI-based functionalities.

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When used in conjunction with the Visualizer, the Results Manager provides a very usefuland intuitive way of analyzing and visualizing variables and results through the GUI.

More complex analysis can also be carried out in FDTD Solutions' powerful scripting

Introduction 11


environment.

Scripting

FDTD Solutions contains a built in scripting language which can be used to obtainsimulation data, and do plotting or post-processing of data. The script prompt can be usedto execute a few commands, or the built in script file editor can be used to create morecomplex scripts.

A thorough introduction to the Lumerical scripting language can be found in the Scriptingsection of the FDTD Solutions online user guide. Definitions for all of the script commandsare given in the Scripting language chapter in the Reference Guide.

Data Export

FDTD simulation data can be exported into text file format using the Visualizer, into aLumerical data file format (*.ldf) which can be loaded into another simulation, or into aMatlab data (*.mat) file. Instructions for exporting to these file formats can be found in thelinks under the Scripting section.

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2 Silver Nanowire TutorialProblem definition

For light incident on metallic nanoparticles, resonant interactions with the electronic chargedensity near the surface, called surface plasmon polaritons, play an important role. Herewe determine, for a silver nanowire with diameter 50 nm, the surface plasmon polaritonresonance and calculate the scattering, extinction and absorption cross sections as afunction of wavelength near this resonance.

Associated filesWe recommend downloading all associatedfiles before beginning the tutorial. Files canbe downloaded from the online help sectionof Lumerical's website, or from theexamples subdirectory of the FDTDSolutions installation directory.nanowire.fspplotcs.lsf, nanowire_theory.csvIn this topicSimulation set upResultsModeling instructions

See alsoOnline Help -> Surface Plasmons

Problem definition: More details

The scattering cross-section is defined as

)()()(

source

scatscat

IP

,where Pscat is the total scattered power [W] and Iinc is the incident intensity [W/m

2]. In 2D,power is described per unit length [W/m], and thus the scattering cross-section hasdimensions of length. The total scattered power can be calculated by summing the powerflowing outward through the four power monitors located in the scattered field region of theSimulation Area.

The absorption cross-section is similarly defined as

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Silver Nanowire Tutorial 13


)()()(

inc

absabs

IP

,where Pabs is the total power absorbed by the particle. The power absorbed by the particlecan be calculated by calculating the net power flowing inward through the four monitorslocated in the total field region of the Simulation Area.

The extinction cross-section is the sum of the absorption and scattering cross-sections)()()( scatabsext

.

2.1 Discussion and resultsSimulation set up

Once the simulation has been set up, it will look as in the screen shot below. The nanowireis the circle in the center of the simulation region. There are two yellow boxes of monitorswhich surround the nanowire. In between the two monitor boxes is a third box drawn with ofgrey lines. This box shows the Total-field scattered-field (TFSF) source.

TFSF sources are type of plane wave source, mostly used to particle scattering. The pinkarrow shows the direction of propagation (k vector), and the blue arrow shows thepolarization (E field vector). In the region inside the grey box, the total fields (incident planewave field + any fields scattered by particle) are calculated. At the boundary of the source,the incident plane wave fields are substracted, leaving only fields scattered by the particleinside the source. You can find more information about TFSF sources in the Sourcessection of the online user guide.

Because we use the TFSF source, the power scattered by the nanowire can be computedby measuring the power flow through a box of monitors located outside of the source (ie. inthe scattered field region). The power absorbed by the nanowire is equal to the powerflowing into the box of monitors in the total field region.

Getting Started14


In the graphical user interface (CAD), orange lines show the FDTD mesh if desired. Thereare two different regions: A graded mesh region (automatic mesh) and a mesh overrideregion. When using automatic meshing, the mesh size is based on the refractive index. Ahigher index material will have a smaller step size, inversely proportional to the index.When a material has a complex index, both the real and imaginary parts are considered bythe automatic mesh algorithm. However, accurate modeling of small geometric features,particularly when there is a high index contrast between materials combined with curved orangled interfaces, sometimes requires a finer mesh than is created by the automatic meshalgorithm. In these cases, a mesh override region can be used, as in this example, tomanually define a finer mesh where it is needed.

The above screen shot does not show the full simulation region. Although we are notinterested in obtaining any data outside of the largest yellow monitor box shown above, thesimulation span is set to be much larger. We set the simulation to be larger because theboundaries are PML. PML absorbs incident radiation, but can also absorb energy fromevanescent fields. Hence, the PML should be placed far enough away from the structure sothat it does not interact with evanescent fields. In this case, the PML is about a fullwavelength from the structure.

The Ag (Silver) material used for the nanowire is defined with experimental data, rather thanan analytic model. A material model is automatically calculated based on the experimentalrefractive index data over the source bandwidth. We can check the material fit (see imagebelow) in the Material Explorer before running the simulation. The material fit, named FDTDmodel in the legend, can be adjusted by changing the Max coefficients and Toleranceparameters in the Material Explorer.



We can see from the above plot that the material data has an index that is on the sameorder of magnitude as the background index of 1. Also, we are able to simulate thisproblem at a small mesh size of 1nm or less. For this reason, we can change the meshrefinement option to "conformal variant 1" to take full advantage of the conformal meshingfeature, even for a metal like silver. Note that "conformal variant 1" is a good option herebecause there is low index contrast, however "conformal variant 1" is not always a goodoption for metals (the default conformal mesh will revert to staircasing for interfacesinvolving metals and PECs). Please see Mesh refinement and Conformal mesh for moredetail.

Note that in the screenshot of the simulation above, there is a yellow cross. This crossgives the location of a time domain monitor. Time domain monitors are used in FDTDsimulations to check that the fields have decayed by the end of the simulation. If the fieldshave not properly decayed, the simulation results can be incorrect. By default, FDTDSolutions has a simulation time of 1000fs and shuts off the simulations early if the fieldstrength has decayed to a user defined fraction of the peak field strength. Below, you cansee a plot of the x component of the E field. Notice that the simulation shut off early at32fs.

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Results

Scattering, absorption and extinction cross-sections can be computed analytically for thenanowire. We have precalculated the theory for this specific material and saved it in theassociated file, nanowire_theory.csv, from the first page of this getting startedexample.

Below, the leftmost figure shows the cross-sections obtained with from the FDTDsimulation in comparison with the analytic results. Clearly there is very good agreement. The second figure shows the same results from FDTD, but analytic results for a radius of24 and 26 nm. Since the simulation used a 1nm mesh, it is reasonable to expect theFDTD results to be accurate to within these results. We can see from the figure that this istrue.



The above image shows that the maximum extinction occurs near 345nm. We can plot theintensity of the y component of the E field as shown in the image below calculated with a0.5nm mesh.

2.2 Modeling instructionsThis page contains 2 independent sections. The simulation can be set up from a new 2Dsimulation, beginning at the Set up Model section. Otherwise the associated files (whichyou can find at the locations given on the first page of the tutorial) can be used to start atthe second section.

In this topic

Getting Started18


Set up modelRun simulation, plot cross sectionsCompare with theoretical resultsPlot near field data

Set up modelOpen a blank simulation file. For instructions see the FDTD Solutions GUI page in theIntroduction to the Getting Started Examples.

Press the arrow on the STRUCTURES button and select a CIRCLE fromthe pull-down menu. Set the properties of the circle according to the following table.

tab property value

name nanowire

Geometry x (nm) 0

y (nm) 0

z (nm) 0

radius (nm) 25

Material material Ag (Silver) - Palik (0-2um)

Press the SIMULATION button to add a simulation region. Note that if yourbutton does not look like the button to the left, you will need to press on the arrow to getthe simulation region. Set the properties according to the following table.

tab property value

General simulation time (fs) 200

dimension 2D

Geometry x (nm) 0

y (nm) 0

z (nm) 0

x span (nm) 800

y span (nm) 800

Mesh Settings mesh accuracy 4

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mesh refinement conformal variant 1

Note that since we are using a 2D simulation region, properties such as "z span" areirrelevant. The setting for these properties will be omitted for the remainder of themodeling instructions, and the default values (at z = 0) can be used.

Press the arrow on the SIMULATION button and select the MESH region

from the pull-down menu. Set the properties according to the following table.tab property value

General dx (nm) 1

dy (nm) 1

Geometry x (nm) 0

y (nm) 0

x span (nm) 110

y span (nm) 110

Press the arrow on the SOURCES button and select the Total-field scatter-field (TFSF) source from the pull-down menu. Set the properties according to thefollowing table:

tab property value

General polarization angle 0

Geometry x (nm) 0

y (nm) 0

x span (nm) 100

y span (nm) 100

Frequency/Wavelength Wavelength start (nm) 300

Wavelength stop (nm) 400

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Press the arrow on the ANALYSIS button and select OPTICAL POWER fromthe pull-down menu. This will open the object library window.Insert a CROSS SECTION analysis group and set the properties of this group accordingto the following table.

tab property value

name scat

Setup Variables x (nm) 0

y (nm) 0

x span (nm) 110

y span (nm) 110

z span (nm) 110** The Z span value is not important, since this is a 2D simulation in the XY plane.

Make a copy of "scat" with the COPY button and set the properties of this groupaccording to the following table.

tab property value

name total

Setup Variables x (nm) 0

y (nm) 0

x span (nm) 90

y span (nm) 90

Press the arrow on the MONITORS button and select GLOBALPROPERTIES from the pull-down menu. Set the FREQUENCY POINTS to 100.Press the arrow on the MONITORS button and select the FIELD TIME monitor from thepull-down menu. Set the monitor properties according to the following table.

tab property value

name time

Geometry x (nm) 28



y (nm) 26

Run simulation, plot cross sections.

Press on the CHECK button to open the MATERIAL EXPLORER. To obtain aplot of the refractive index as a function of wavelength, press the FIT AND PLOT button.Press the arrow next to the CHECK button and select the "Check simulation and

memory requirements" button to view the simulation and memory report.Next, check if the mesh is fine enough using the VIEW SIMULATION MESH button

and ZOOM button in the toolbars. For more information about how to use thesetools, see the Layout editor section of the reference guide.

Press the Resources button and check the number of processes (number ofcores) for the local machine. Then, press the "Run Tests" button to make sure thesimulation engine is configured correctly. The first time you run this test, it may fail andask you to register your username and password for your operating system account. If itdoes, fill in the appropriate text fields, press "Register", then "OK", and re-run the tests.

Run the simulation by pressing the RUN button . Once the simulation finishes running, all the monitors and analysis groups in the objecttree will be populated with data. The Results View window will show all the results andtheir corresponding dimensions/values for the selected object. Plot the time domain databy right-clicking on the time monitor and selecting Visualize -> E.

Getting Started22


You can then select which components of the E field data you want to plot in theVisualizer. The screenshot below shows how to plot the real part of the x component ofthe electric field.

To plot the cross section results, right-click on the "scat" and "total" analysis groups,



and select "Run analysis". This will run the analysis scripts in the analysis groups tocalculate the cross section results.Right-click again on the "scat analysis group, and you will see an option to Visualize->sigma, which will plot the scattering cross section as a function of frequency in theVisualizer. To plot the result as a function of wavelength, simply change the "Parameter"option (near the bottom of the Visualizer) from "f" to "wavelength". You can also changethe "Units" to nanometers on the right side of the Parameters section.Without closing the Visualizer, go back to the object tree and right-click on the "total'analysis group, and select add to visualize1->sigma, which will plot the 2 cross sectionresults in the same Visualizer. Note that the absorption cross section is actually the negative of the result returned by"total", since we want the power flowing into the box, rather than out of the box. You canadd a negative sign to the result in the Visualizer under "Scalar operation".

Compare with theoretical results

Even though we can plot everything we need with the Visualizer, comparisons with

Getting Started24


theoretical calculations will have to done through the scripting environment.Open the script file editor (for instructions on how to do this see the Introduction sectionof the Getting Started examples ).Get the "plotcs.lsf" script file from the first page of this application example.

Then use the OPEN SCRIPT button to browse to and open the "plotcs.lsf" scriptfile.

Run the script file using the RUN SCRIPT button which is found on the Script FileEditor window This will create the two plots of the cross sections seen in the discussionand results section.

Plot near field data

Switch the simulation back into layout mode the SWITCH button . Edit the mesh. Set dx = dy = 0.5nm.Press on the arrow on the MONITORS button and select a FREQUENCY DOMAINFIELD PROFILE monitor from the pull down menu. Set the properties according to thefollowing table.

tab property value

name profile

General override global monitor settings check

use source limits uncheck

frequency points 1

wavelength center (nm) 345

Geometry monitor type 2D Z-normal

x (nm) 0

y (nm) 0

x span (nm) 90

y span (nm) 90

Run the simulation again by pressing on the RUN buttonOnce the simulation has run to completion, plot the profile monitor data with theVisualizer (right-click -> Visualize -> E). You can plot the image in a new widow byclicking the "Plot in new window" button.Go to the SETTINGS menu in the new figure and set the colorbar limits. To obtain the

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exact same plot as in the discussion and results section, set the colorbar min was to 0,and the colorbar max to 5.

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3 Ring Resonator TutorialProblem definition

The device being studied in this example is a ring resonator filter. It consists of twowaveguides (through and drop channels) connected by a ring. As the input modepropagates past the ring, a fraction will couple into the ring. Due to the circular nature of aring, the mode will circulate around the ring many times. As the mode circulates, it willinterfere with itself. The interference pattern is strongly wavelength dependent, which iswhy these devices can be used as filters. Some wavelengths will pass through the device,while other wavelengths will be re-directed into the drop channel.

We will use FDTD Solutions to study the same ring resonator in 3D that was designed in a2.5D simulation using MODE Solutions, see Ring resonator. We will then show how wecan extract S parameters that can be used for circuit level simulations in INTERCONNECT.

We will start with the geometric parameters determined in the MODE Solutions gettingstarted example.

Associated filesWe recommend downloading all associatedfiles before beginning the tutorial. Files canbe downloaded from the online help sectionof Lumerical's website, or copied from theexamples subdirectory of the FDTDSolutions installation directory.ring.fspIn this topicSimulation set upResultsParameter extractionConvergence testing2D Approximation to 3D GeometriesModeling Instructions

See alsoOnline User Guide -> Monitors and AnalysisGroups -> Making a cw movie

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FDTD Solutions contains a mode source with an integrated mode solver. This source willbe used to inject a guided mode into the upper waveguide. The mode source is set tocalculate the fundamental TE mode of the waveguide.

In the screen shot shown to the left below, the mode source injection plane is drawn with awhite outline and grey shaded region where it is inside the FDTD simulation region. Theinjection direction is depicted with the pink arrow. The line on the image on the right showsthe mode profile |E| 2^ that will be injected by the mode source. The mode profiles can beviewed simply by right clicking on the mode source object, or using the Results Managerwindow when the mode source is selected. You can also view the mode profile by editingthe mode source object.

Notice that the mode profile goes to zero at each edge of the image. For accuratesimulations, it is important that the mode source be large enough to contain the entiremode. If the mode source is too small, the mode will be truncated, leading to simulationerrors. Similar rules apply to the FDTD simulation region, shown as an orange box. Theabsorbing PML boundaries of the simulation region can not be placed too close to thestructure, or they will clip the mode.

The ring resonator is a high Q device which traps the light for many round trips in the ring.These high Q devices require longer simulation times in the time domain than non-resonant

Getting Started28


devices. Based on the MODE Solutions example, we will start with a simulation time of4000fs, although more time may be necessary.

This is longer than our default simulation time (1000fs). It is important to increase thesimulation time because the frequency domain monitor results are incorrect if thesimulation time is not set long enough for the fields to decay. Further discussion based onthis example can be found in the our Online User Guide -> Monitors and Analysis Groups -> Simulation time and Frequency domain monitors.

Results

Initially, we set the mesh accuracy to 1 and run the simulation. It is a good idea to runsimulation at very low mesh accuracy while they run quickly to be sure that most settingsare correct and that we are obtaining reasonable results. The simulation will run in about 5minutes or less on a modern workstation. Please refer to the Modeling Instructionspage for detailed information on how to generate some of the plots below.

The plot to the left below shows the Ey field in the drop channel. Notice that the initialpeaks are rapidly distorted due to dispersion. The figure on the right shows the associatedspectrum at the drop channel. As expected, we see resonances approximately every25.6nm. We also notice that some of the resonances are split. This is in fact an effect ofcoupling between forward and backward propagating modes in the ring which are weaklycoupled and which leads to a Rabbi splitting. In principle, the backward propagating modesshould not be excited, however, there is some scattering to backward propagating modeseach time the waveguides are close together. This effect is made worse by the very lowmesh accuracy, which can also introduce backscattering throughout the ring due tostaircasing effects. We will see that these effects are significantly reduced as we increasethe mesh accuracy. Nonetheless, backscattering effects can have important consequencesin real devices.

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The figure below shows the magnetic field intensity at 1.52 microns in the device. Here weclearly see the standing wave pattern from forward and backward propagating modes, whichleads to the Rabbi splitting observed at the 1.53 micron resonance. Note that this causeslight to be reflected back into the source and to output both forward and backward at thedrop waveguide.

We can rerun the simulation with a mesh accuracy of 2. This will take 25 minutes or lesson a modern workstation to run the full 4000fs.

We can select the through and drop channels to quickly plot the transmission in thesewaveguides using a visualizer. The ripples in the result are an indication that the fields inthe ring have not fully decayed before the end of the simulation, as these ripples arecharacteristic of the fourier transform of a time signal that is truncated. We also notice thatthe splitting of the peaks has disappeared, indicating that the coupling to backwardpropagating modes was artificially large due to the extremely coarse mesh used. However,we will see that there is still backward propagating light generated and it would be worthdoing some convergence testing of the mesh size, particularly around the waveguidecoupling region, to determine how significant a problem this might be for an actual device.

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The following lines of script will also export the drop results in a format that can be used forMODE Solutions to compare with the MODE Solutions results.

Tdrop_3DFDTD = -transmission("drop");lambda_3DFDTD = c/getdata("drop","f");savedata("fdtd_results.ldf",Tdrop_3DFDTD,lambda_3DFDTD);

We can also obtain the spatial field profiles at various frequencies. The right image belowshows |E| 2^ at 1.6 microns, where almost all the light is transmitted to the through channel. The left image is shown at 1.5238 microns, where we begin to see light resonate morestrongly in the ring. Once the spectrum is determined of course, we can adjust thewavelength of our profile monitor to capture the fields precisely on and off resonance.



Parameter extraction

The ring resonator is a 4 port device, which we we can label 1 through 4, as shown below.We can use a mode expansion monitor to calculate the complex mode expansioncoefficient for both forward and propagating modes in each waveguide. This allows us toeasily construct the 16 parameter S matrix which can be exported for use inINTERCONNECT. In reality, this device is so symmetric, that only 4 coefficients of the Smatrix need to be calculated - for example, S11=S22=S33=S44.

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The mode expansion monitor is setup to calculate the amount of forward and backwardpropagating power in the fundamental TE mode for the 4 monitors at the input and outputports. First, we can look at this in the Visualizer. Note that this analysis takes severalseconds because each waveguide mode is recorded over 500 frequency points. To speedup the calculation, we have used a single mode at the center frequency for the expansion,however we could calculate more mode profiles over the device bandwidth to obtain a moreaccurate expansion. Once calculated, the expansion is stored in memory and will be savedto the fsp file for quick future reference. The figure below shows the amount of powerreflected in port 1 and transmitted through ports 2, 3 and 4. It is interesting to note theresonant reflection and transmission that is occurring at port 1 and port 4. The powerreflected and leaking out port 4 is equivalent. As discussed above, these are due to weakcoupling between forward and backward propagating modes in the ring, which can have asubstantial effect due to the high Q of the device.

The model itself is an analysis group that is setup to calculate the S parameters. Selectthe model and use the Results Manager to calculate the S matrix. During the calculation,S11, S21, S31 and S41 are saved to the text file FDTDtoINTERCONNECT.txt which canbe used to create a ring resonator element in INTERCONNECT. The different S parameters



can be easily visualized. For example, below we see the phase of S21 and S31. We cansee the effect of the resonances which lead to sudden changes in the slope of the phasewhich indicates the sudden change in group delay at resonance. There is still a reasonableamount of ripple in S21 that could clearly lead to incorrect interpretations of the group delayof the ring, these could be removed by running a longer simulation.

Note on convergence testing

The following issues may affect the convergence and should be investigated moreextensively:

The proximity of the PML. To save time, the simulation uses very little space verticallybetween the waveguide layer and the PML. The z span of the simulation region should beincreased.The simulation time should be increased. Once the correct time of the simulation hasbeen determined to achieve convergence of key results, time apodization of thefrequency domain monitors may be used to remove any ripple that remains in thespectra.

Getting Started34


The mesh size should be tested at a mesh accuracy of 3 and possibly even 4. It mayalso be necessary to use a mesh override region near the waveguide coupling regions toforce a fine mesh in those regions because the coupling of the forward and backwardpropagating modes appears to be sensitive to the mesh used in this region.

2D Approximation to 3D Geometries

3D simulations are much more CPU-time and memory intensive than 2D simulations. Thering resonator example we reference using MODE Solutions collapses the z dimension in aphysically meaningful way and is then able to run a 2D FDTD simulation much morequickly, while still maintaining the accuracy of important results like the filter FSR. It is alsopossible run a 2D simulation in FDTD, using a material with the effective index of the slabmodes supported in the Si layer. However, using a constant effective index will not give thecorrect FSR for the device, which depends on the group index of the waveguide modes.Therefore, we recommend doing the initial design and optimization in MODE Solutions,then moving to 3D FDTD for final optimization and accurate parameter extraction.

3.2 Modeling instructionsThis page contains 4 independent sections. The first section (Object setup) describes howto setup the simulation from a blank simulation file. If you prefer to skip this section, acopy of the completed simulation file is provided on the first page of the tutorial. The finalthree sections describe how to run the simulation, plot simulation results like field profilesand transmission spectra, and calculate the S parameters for this ring resonator device.

In this topicObject setupRun simulationPlot resultsCalculate S parameters

Object setupWe will start with the geometric parameters determined in the MODE Solutions gettingstarted example.

StructureOpen a blank simulation file. For instructions see the FDTD Solutions GUI page in theIntroduction to the Getting Started Examples.Press on aarrow on the STRUCTURES button and select a RECTANGLE from the pull-down menu. Set the properties of the insulator substrate rectangle according to thefollowing table.

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tab property value

Geometry x ( m) 0

x span ( m) 22

y ( m) 0

y span ( m) 16

z ( m) -2

z span ( m) 4

Material material SiO2 (Glass) - Palik

Press on arrow on the COMPONENTS button and select INTEGRATEDOPTICS from the pull-down menu. This will open the object library window.Select RING RESONATOR from the list and press the INSERT button.Set the properties of the ring resonator according to the following table. The couplinglength and radius used for the first part of the simulation are just an initial guess and willbe modified to the correct values later. The value of the index property of the ringresonator is not used unless the material is specified as , soit's value can be arbitrary.

tab property value

Properties x, y ( m) 0

z ( m) 0.09

Lc ( m) 0

gap ( m) 0.1

radius ( m) 3.1

material Si (Silicon) - Palik

wg width ( m) 0.4

z span ( m) 0.18

x span ( m) 25

FDTD Region

Press on the SIMULATION button to add a simulation region. Note that if

Getting Started36


your button does not look like the button to the left, you will need to press on the arrowto get the simulation region. Set the properties according to the following table.

tab property value


Geometry x ( m) 0

x span ( m) 9

y ( m) 0

y span ( m) 10

z ( m) 0

z span ( m) 1

Mesh settings mesh accuracy 1 or 2

Source

Press the arrow on the on the SOURCES button and select the MODEsource from the pull-down menu. Set the properties according to the following table.

tab property value

General mode selection fundamental TE mode

Geometry x ( m) -4.5

y ( m) 3.6

y span ( m) 3

z (um) 0

z span (um) 2

Frequency/Wavelength

wavelength start ( m) 1.5

wavelength stop ( m) 1.6

Monitors

We will set up power monitors at the 4 ports of the ring resonator to calculate thetransmission through each port, and the S parameters.



Press on the arrow on Monitors button and select the frequency domain field

and power monitor from the pull-down menu. Set the properties according to thefollowing table

tab property value

name drop

Geometry monitor type 2D X-normal

x ( m) -4.2

y ( m) -3.6

y span ( m) 3

z (um) 0

z span (um) 2

Use the DUPLICATE button to create three copies of the monitor. Set the

properties according to the following tables.

tab property value

name drop2

Geometry x ( m) 4.2

y ( m) -3.6

tab property value

name in


y ( m) 3.6

tab property value

name through

Geometry x ( m) 4.2

Getting Started38


y ( m) 3.6

We will also place time monitors at each port to study the field as a function of time.

Press on the arrow on the on the Monitors button and select the field time monitorfrom the pull-down menu. Set the properties according to the following table

tab property value

name t_drop


y ( m) -3.6

Use the DUPLICATE button to create three copies of the monitor. Set theproperties according to the following tables.

tab property value

Name t_drop2

Geometry x ( m) 4.2

y ( m) -3.6

tab property value

name t_in


y ( m) 3.6

tab property value

name t_through

Geometry x ( m) 4.2

y ( m) 3.6We will also add a profile monitor to study the field distribution at different frequencies.

Press on the arrow on the Monitors button and select the frequency domainfield monitor from the pull-down menu. Set the properties according to the following table.

tab property value



name full_profile

General override global monitor settings select check box

frequency points 5

Geometry monitor type 2D Z-normal

x ( m) 0

y ( m) 0

x span ( m) 16

y span (um) 12

z (um) 0

Lastly, we will add the Mode expansion monitor for the S parameters calculation. Presson the arrow on the Monitors button again and select the Mode expansion monitor fromthe pull-down menu. Set the properties according to the following table.

tab property value

name expansion

Geometry monitor type 2D X-normal

x ( m) -4.2

y ( m) 3.6

y span ( m) 3

z (um) 0

z span (um) 2

We have positioned this monitor directly in front of the MODE source, and we will use thefundamental mode of the top waveguide to expand the field at the 4 ports of the ringresonator.

In the Mode expansion tab, select the fundamental TE mode for "MODE calculation".You can use the Visualize Mode Data button to study the field profile for this mode.In the "Monitors for expansion tabl"e, select the 4 power monitors we have set up at the4 ports of the Ring Resonator as follows:

Getting Started40


Setup resources. Run simulation

Press the Resources button and check the number of processes (number ofcores) for the local machine. If you have additional computers on the network with FDTDinstalled as well as extra engine licenses, you can add them to the resource list. Click"Add" and set the appropriate properties.Press the "Run Tests" button to make sure the simulation engines on the resources areconfigured correctly. The first time you run this test, it may fail and ask you to registeryour username and password for your operating system account. If it does, fill in theappropriate text fields, press "Register", then "OK", and re-run the tests. If there are anyerrors or warnings, they will appear in the "Result" field.

Run the simulation by pressing the RUN button .

Plot resultsOnce the simulation finishes running, all the monitors and analysis groups in the objecttree will be populated with data. The Results View window (which can be opened byclicking on the "Show result view" button) will display all the results and theircorresponding dimensions/values for the selected object. Plot the time signal andspectrum Ey by right-clicking on the "t_drop" time monitor and selecting Visualize -> Eor spectrum.



You can then select which components of the E field data you want to plot in theVisualizer. The screenshot below shows how to plot the real part of the y component ofthe electric field.

To plot the transmission through the through monitor, right-click on the "through" powermonitor and select Visualize->T.To plot the magnetic field intensity at 1.52 microns, right-click on the full_profile monitorand select Visualize->H and select the appropriate wavelength.

Getting Started42


Calculate S ParametersThe model analysis group in the provided pre-made simulation file has been set up tocalculate the S parameters. Since the expansion monitor automatically returns theexpansion coefficients for the forward and backward propagating light (a and b), we cancalculate the S parameters very straightforwardly. The calculations can be found in thescript under the Analysis tab of the "model" group, this script will also export the Sparameter results into a .txt file, which can be imported directly by INTERCONNECT.



As shown in the figures above, the Results View will automatically show the Sparameters result returned by the model analysis group. One can then visualize thisresult by right-clicking on "S" and selecting Visualize.

Getting Started44


4 PC Micro Cavity TutorialProblem definition

The goal of this example is to demonstrate how FDTD Solutions may be used to analyzephotonic crystal cavities. We want to determine the resonant frequency, Quality factor, andmode profile of the cavity modes. Once we learn how to find the mode of interest andmeasure its Q-factor, we will use a particle swarm optimization to find the inner hole radiuswhich provides the maximum Q factor.

Note: The screen shots in this example were created with the Mac version of FDTDSolutions. The graphical user interface looks a slightly different than it does on Windowsand Linux.Associated filesWe recommend downloading all associatedfiles before beginning the tutorial. Files canbe downloaded from the online help sectionof Lumerical's website, or from theexamples subdirectory of the FDTDSolutions installation directory.ppc_cavity.fspIn this topicSimulation set upSimulation resultsFurther analysis: SymmetryFurther analysis: Optimization of inner holeradius

See alsoOnline help -> Cavities and ResonatorsOnline help -> Photonic Crystals


The cavity is constructed by perforating a slab of Ta2O5 (which has an index of 2.0995) withair holes forming a hexagonal lattice. The lattice constant is 575 nm, and the air holeradius within the photonic crystal lattice is 194 nm. The cavity itself is formed by removinga central hole, by reducing the radius of the inner six holes to 100 nm, and by removingholes along the outer edge of the cavity to form the structure shown in the figures below.

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PC Micro Cavity Tutorial 45


When we construct this structure in FDTD Solutions, we create the slab out of a rectangle.Then we add cylinders to the simulation for the holes. In the locations where the holes andthe slab overlap, we use the mesh order property to make sure that FDTD Solutions usesthe refractive index data from the holes (cylinders) instead of from the slab (rectangle). Formore details about mesh order, refer to the mesh order page in the Reference Guide.

Two dipole sources (depicted with green arrows to show the direction of the H field) areused to excite the modes of the cavity. These dipoles are not located in the center of thePC structure in order to reduce the chance that they are located at a zero of the cavitymode. The dipole sources are used to inject energy into the simulation volume. Some ofthe dipole radiation will be coupled into the cavity modes and decay slowly. The radiationwhich does not get coupled into the cavity modes will be scattered and quickly exit thesimulation volume.

The frequency domain monitors in FDTD simulations calculate the mode profile by taking adiscrete Fourier Transform of the time domain data. Obviously, we do not want to includethe portion of the time signal at the beginning of the simulation, since it contains radiationwhich does not excite the modes; we are only interested in the later portion of the timesignal when all the energy left in the cavity is in the resonant modes. As you can see in themodeling instructions on the next page, we can use monitor apodization to select only theportion of the time data at which all the energy left in the simulation is in the resonantmodes. A more in depth discussion of monitor apodization (also based on a PC cavity) canbe found in the Online User Guide->Monitors and Analysis Groups->Apodization.

The rest of this set up section discusses some important simulation settings, namely theboundary conditions, the mesh and the simulation time.

Getting Started46


Boundary Conditions

The orange boundaries which can be seen in the screenshot above are Perfectly MatchedLayer (PML) boundary conditions. PML boundaries absorb incident radiation, and areintended to absorb all radiation propagating away from the cavity. It is important to leavesome distance between the cavity and the PML boundaries. If the boundaries are too closeto the cavity, they will start to absorb the non-propagating local evanescent fields that existwithin the cavity. A simple rule is to leave at least half a wavelength of distance above andbelow the structure.

Next, notice that the lower half of the simulation (z



the simulation.

Before running simulations with periodic structures, it is good practice to use an indexmonitor to check that the structure actually looks periodic when it is meshed. The indexmonitor results below show that each of the holes looks like a cross. This is because themesh is a bit coarse. However, each cross (except for the 6 inner holes) looks identical. Itis important to make sure that the holes all are meshed the same way, if we want to obtaingood results. It is possible to view the meshed structure with the index monitor in layoutmode (i.e. before the simulation has been run).The modeling instructions section on the next page contains step by step instructions ofhow to create index monitor plots.

Getting Started48


Simulation time

To obtain accurate frequency domain data, it is generally required to run the simulation untilthe time domain fields have decayed to zero. High quality factor cavity simulations are oneexception to this rule. This is fortunate, since high Q modes decay very slowly. Runninghigh Q cavity simulations long enough for the fields to fully decay would be very slow.

A combination of time domain analysis and frequency domain apodization allow us toaccurately calculate the Q-factor and profile of cavity modes without running the simulationuntil the fields decay. However, some care should still be taken when using this technique. Other measurements like power transmission and field amplitudes will not necessarily becorrect when the simulation is stopped early.

Simulation Results

The simulation contains a Q analysis group, which contains a script that finds theresonance peaks and Q factors of the cavity modes. We have placed the Q factor group,which contains a time monitor, away from the origin of the simulation for exactly the samereason the dipoles are not placed at the origin.

We can use the analysis script to obtain the largest two resonance peaks in the sourcebandwidth and their Q factors. It is easy to obtain more resonance peaks: Simply changethe "number_resonances" parameter in the Analysis-> Variables tab of the Q analysisobject.



We can also obtain a plot of the E fields as a function of time (below right) and a plot of theresonance peaks. The Q factor calculations are discussed in detail in the Cavities andResonators section of the Online Help.

Once we know the resonance frequencies, the corresponding E field profiles can be plotted.

Getting Started50


The image below shows real(Ey) for the mode at 201 THz.

Further analysis: Symmetric boundary conditions

We will need to run quite a few simulations in order to find the inner hole radius whichmaximizes the Q factor of the mode at 201 THz. Since the mode profile possessessymmetry about the x and y axes, we can use anti-symmetric/symmetric boundaryconditions to reduce the simulation time by an additional factor of 4.

From the above image and the discussion on the Choosing between symmetric and anti-symmetric BCs page in the User Guide - Simulation section, we can see that the E fields



for the mode of interest have a plane of anti-symmetry at X=0, and a plane of symmetry atY=0.

Whenever the EM fields have a plane of symmetry through the middle of the simulationregion, using symmetrical boundary conditions will give the same results as running the fullsimulation. The plot below shows real(Ey) after we set the x min and y min boundaryconditions to anti-symmetric/symmetric. This plot looks identical to the one above exceptfor the magnitude. The change in magnitude arises because the sources have beenmirrored, i,e in the full simulation there are only two sources, but by using symmetry wehave mirrored these sources so that there are now 8.

Further analysis: Optimization of inner hole radius

FDTD Solutions contains a built in optimizer. We choose to use the particle swarmoptimization algorithm which is included with the optimizer, but it is also possible to definea different optimization algorithm. For more details about the optimizer, see the RunningSimulations and Analysis -> Optimization section of the online User Guide.

In this case, we choose to try to find the radius of the 6 inner holes of the PC Cavity whichoptimizes the Q factor of the first resonance. The sweep below shows an optimal radiuscorresponding to 0.167*0.575 um = 96 nm.

Getting Started52


4.2 Modeling instructionsThis page contains 4 independent sections. The first section describes how to setup thecavity structure and the FDTD simulation region. Section 2 describes the source andmonitor setup, and some initial analysis. Section 3 provides further information on usingsymmetry boundaries, and section 4 describes how to use the optimization feature ofFDTD Solutions.

In this topicCreate PC and check material indexAdd sources and monitors. Run simulation and get data.SymmetryOptimize inner hole radius

Create PC and check material indexOpen a blank simulation file. For instructions see the FDTD Solutions GUI page in theIntroduction to the Getting Started Examples.

Press on arrow on the STRUCTURES button and select a RECTANGLE

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from the pull-down menu. Set the properties of the ring according to the following table. tab property value

Geometry x ( m) 0

y ( m) 0

z ( m) 0

x span ( m) 10

y span ( m) 10

z span ( m) 1

Material index 2.0995

Press on arrow on the COMPONENTS button and select PHOTONICCRYSTALS from the pull-down menu. This will open the object library window.Select HEXAGONAL LATTICE PC H-CAVITY from the list and press the INSERT button.Set the properties of the PC Cavity according to the following table.

tab property value

Properties x ( m) 0

y ( m) 0

z ( m) 0

material etch

H number 2

z span ( m) 1

n side 6

a ( m) .575

radius .194

Press the DUPLICATE button to create a second copy of the hexagonal lattice PCcavity. Edit the properties according to the following table

tab property value

Getting Started54


name inner

Setup Variables x ( m) 0

y ( m) 0

z ( m) 0

H number 1

n side 2

radius ( m) .100

Press on the SIMULATION button to add a simulation region. Note that ifyour button does not look like the button to the left, you will need to press on the arrowto get the simulation region. Set the properties according to the following table.

tab property value


Geometry x ( m) 0

y ( m) 0

z ( m) 0

x span ( m) 12 * .575

y span ( m) 12 * .575 * sqrt(3) / 2

z span ( m) 3

Boundary conditions z min bc Symmetric

Advanced options force symmetric x mesh check

force symmetric y mesh check

force symmetric z mesh checkNote: Forcing a symmetric x mesh ensures that a mesh line lies at x=0, and therefore themesh does not change when we switch the x min boundary condition from PML tosymmetric or anti-symmetric. Strictly speaking we do not need this option for this particularsimulation since we have set up the mesh in this example so that there will be a mesh lineat x=0 anyways.

Press on the arrow next the the SIMULATION button and select MESH OVERRIDE fromthe pull-down menu. Set the properties according to the following table.



tab property value

General dx ( m) .575 / 8

dy ( m) .575 * sqrt(3) / 2 / 8

override z mesh uncheck

Geometry x ( m) 0

y ( m) 0

z ( m) 0

x span ( m) 10

y span ( m) 10

z span ( m) 1

Press on the arrow on the MONITORS button and select the INDEX monitorfrom the pull-down menu. Set the properties according to the following table.

tab property value

name index

Geometry x ( m) 0

y ( m) 0

x span ( m) 10

y span ( m) 10Get the index monitor data: Note that to do this we need to start running the simulation -index monitor data is collected during meshing so we just need to start simulation andget through meshing. Then we can exit:

To do this press the RUN button . This will start the simulation and show the jobmonitor window, which displays useful information about the current project. Initially thesimulation will be meshing. As soon as the progress bar starts, it has finished meshingand you will be able to press SAVE & QUIT button to stop the simulation.

Getting Started56


The index monitor data is collected during the initialization and meshing phase, and it willbe correct even if the simulation is not complete.To look at the index monitor results, simply right-click on the index monitor and selectVisualize->index.

Switch back to layout by pressing the SWITCH TO LAYOUT button. This is sothat we can continue setting up the rest of the simulation.

Add sources and monitors. Run simulation and get data.

Add sources and Q analysis object

Press the arrow on the on the SOURCES button and select the DIPOLEsource from the pull-down menu. Set the properties according to the following table.

tab property value

name dipole1

General dipole type Magnetic dipole

Geometry x ( m) .1

y ( m) .2

Frequency/Wavelength frequency start (THz) 160

frequency stop (THz) 250

While the dipole is still selected, click the DUPLICATE button on the toolbar (or,use the keyboard shortcut key D). Set the name to dipole2 and the x location of thedipole to 0.3 microns.



Press the arrow on the on the ANALYSIS button and select RESONATORSfrom the pull-down menu. This will open the object library window.Insert the Q ANALYSIS analysis group. Set the location of the monitor to x = .4 m, y= .2 m and z = 0 m.

Run simulation and get data: Get Q analysis data

Press the Resources button and check the number of processes (number ofcores) for the local machine. If you have additional computers on the network with FDTDinstalled as well as extra engine licenses, you can add them to the resource list. Click"Add" and set the appropriate properties.Press the "Run Tests" button to make sure the simulation engines on the resources areconfigured correctly. The first time you run this test, it may fail and ask you to registeryour username and password for your operating system account. If it does, fill in theappropriate text fields, press "Register", then "OK", and re-run the tests. If there are anyerrors or warnings, they will appear in the "Result" field.

Run the simulation by pressing the RUN button . For more information aboutsetting the parallel computing options see the Introduction section of the Getting Startedexamples .Switch to the objects tree window (for instructions on how to do this see the Introductionsection of the Getting Started examples ).To get the Q factor of the cavity, right-click on the Qanalysis group and select"runanalysis". Alternatively, open the edit window for the Qanalysis group, and under theAnalysis->Script window, press the RUN ANALYSIS button to run the script.

Add profile monitor (now that we know the resonance frequencies for the structure)

Press the arrow on the MONITORS button and select the FREQUENCYDOMAIN FIELD PROFILE monitor from the pull-down menu. Set the monitor propertiesaccording to the following table.

tab property value

name profile

General override global monitor settings check

use source limits uncheck

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4

Getting Started58


frequency points 2

minimum frequency (THz) 201

maximum frequency (THz) 209.5

Geometry x ( m) 0

y ( m) 0

x span ( m) 10

y span ( m) 10

Spectral averaging andapodization

apodization Full

apodization center (fs) 1000

apodization time width (fs) 250

Run simulation and get data: Get profile monitor data

Press the RUN button.Once the simulation has run to completion, plot the profile monitor data by right-clickingon the monitor and selecting Visualize->E. Set the scalar operation to "Abs 2^" to plot theelectric field intensity.This image corresponds to the result at the first frequency point. To plot the electric fieldintensity at other frequencies, simply move the frequency slider as shown below.



To plot real(Ey), simply select "Y" for Vector operation and "Re" for Scalar operation.

SYMMETRY

Press the SWITCH TO LAYOUT button. Edit the FDTD simulation region. In the BOUNDARY CONDITIONS tab, set "x min bc" tobe "Anti-Symmetric" and "y min bc" to be "Symmetric". Press the RUN FDTD button to re-run the simulation. Visualize real(Ey) as shown in the visualizer screenshot above.

For more information on using symmetry boundaries, see the Online help - User guide -Simulation - Symmetry boundaries page.

Getting Started60


Optimize inner hole radiusSet the following variables in the Q analysis group:

tab property value

Setup Variables make_plots 0

number_resonances 1Switch to/open the optimization and parameter sweep window

Press on the CREATE NEW OPTIMIZATION button . Set up the optimization asshown in the following screen shot. Warning: These settings will run MaximumGenerations*Generation size = 20*10 = 200 simulations (set the "make plot" option inQanalysis to 0 to avoid generating hundreds of figures). You can reduce the maximumgeneration size to run less simulations and therefore a faster optimization.

Each generation of the optimization will create a temporary set of simulations to be runbefore being replaced by the next generation. The job monitor will show the individualprogress for each simulation of a generation set. In the screenshot below, the simulation



is using both Local Host and Laptop to run through the iterations in parallel. Note that indistributed mode, the source fsp file must be stored on the network, accessible by all thecomputing resources.

IntroductionWhat is FDTD?FDTD Solutions GUIRunning Simulations and OptimizationsAnalyzing simulation data

Silver Nanowire TutorialDiscussion and resultsModeling instructions

Ring Resonator TutorialDiscussion and resultsModeling instructions

PC Micro Cavity TutorialDiscussion and resultsModeling instructions

Documents

FDTD Getting Started Manual