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cover_picture_mie_3d_dgtd_small_zoom15This example has been updated. Find the latest version at Mie Scattering (DGTD).

 

 

 

 

 

This page provides step by step instructions on how to create the 3D simulation setup in the mie_example_3d.ldev project file.  The instructions below also highlight the general workflow of running a DGTD simulation.

1. Add Material Models

Open up a blank project in DGTD.  The first step in setting up the simulation is to add the necessary material models to the objects tree under the "materials" folder.  There are two separate material database in DGTD.  The electrical/thermal material database and the optical material database.  The optical material database can be opened by clicking the arrow beside the "Materials" button DEVICE_materials_icon and selecting the "optical material database".  Select the "Au (Gold) - Johnson and Christy" material from the list and click the "Create" button.  This creates a copy of the material in the "materials" folder in the Objects Tree.  Next select the "Vacuum" material and use the "Create" button to create a copy of the material in the objects tree.

optical_database_mie_3d_zoom26vacuum_material_mie_3d_zoom27

 

Alternatively the two material copies can also be created by clicking on the "New Material" button icon_DESIGN_newmaterial in the "Design" tab of the tabbed toolbar.  The newly created material can have electrical, thermal, and optical properties assigned to it.  Right-click on the "New Material" and select "Add optical property".  This will open the optical material database.  Select the "Au (Gold) - Johnson and Christy" material from the list and click OK.  Next right-click on the material again and select "rename".  Set the name of the material to "Au (Gold) - Johnson and Christy".  Follow the same steps to create a second material, set the optical property to the Vacuum material, and set the material name to "Vacuum".

 

Check Material Fit

For dispersive materials it is important to check the material fit.  Expand the property list of the "Au (Gold) - Johnson and Christy" material in the Objects Tree by clicking on the arrow on its left.  The list should only contain the optical properties (Em) of the material.  Right-click on the optical model (also named "Au (Gold) - Johnson and Christy") and select "Edit material properties".  This will open up the property editor (Fig. below-left).  To see the material fit click on the "Go to Material Explorer" button at the bottom right corner of the window.  This will open up the material explorer (Fig. below-center).  Set the "Fit range" from 0.3 um to 1.1 um (wavelength) and click on the "Fit and plot" button to see the material fit.  The green dots show the measurement data and the blue line shows the fitted material that will be used in the simulation.  The default fitting parameters do not give a good fit within the wavelength range of interest so edit the value of "max coefficients" to 8 and "imaginary weight" to 5 and click "Fit and plot" again.  The material fit should be better (Fig. below-center).  To check the fit in terms of the permittivity go to the "View Settings" tab and change the "vertical axis" to "permittivity" (Fig. below-right).  Click "Fit and plot" again to see the permittivity plot.  Click on "Close" to close the material explorer and save the material fit.

 

mie_3d_dgtd_au_property_zoom20

mie_3d_dgtd_material_explorer_zoom20

mie_3d_dgtd_au_permittivity_zoom21

2. Create Geometry

The "Structures" section in the "Design" tab of the tabbed toolbar contains multiple buttons to add different geometries into the simulation space.  The available options vary from simple rectangles and spheres to complex waveguides and planar solids.  In this example, we use one sphere to create the gold nanoparticle, one sphere to assign the source and the EM field monitor and one sphere to define simulation volume.  We also use three 2D rectangles to assign three additional EM field monitors so record the electric field profile on the XY, YZ, and XZ planes.

 

Sphere

Click on the "Sphere" button icon_strucs_sphere in the tabbed toolbar to add a sphere to the simulation region. This will act as the nanoparticle in our simulation.  Select the sphere in the Objects Tree and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value


name

sphere

Geometry

x (um)

0


y (um)

0


z (um)

0


radius (um)

0.05

Material

material

Au (Gold) - Johnson and Christy


mesh order

2

 

Source

Click on the "Sphere" button icon_strucs_sphere in the tabbed toolbar to add a sphere to the simulation region. This will act as the source injecting surface as well as the monitor surface for an EM field monitor to record the scattering and absorption cross-section of the nanoparticle.  Select the sphere in the Objects Tree and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value


name

source

Geometry

x (um)

0


y (um)

0


z (um)

0


radius (um)

0.07

Material

material

Vacuum


mesh order

3


preserve surface

enabled

Graphical rendering

override color opacity from material database

enabled


alpha

0.5

 

NOTE: The mesh order is set to a higher value than the default '2' so that the "source" sphere does not overwrite the "sphere" sphere.

NOTE:  The preserve surface option is enabled so that the simulated structure preserves the surface of the sphere.

 

Outer

Click on the "Sphere" button icon_strucs_sphere in the tabbed toolbar to add a sphere to the simulation region.  This will define the extent of the simulation volume.  Select the sphere in the Objects Tree and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value


name

outer

Geometry

x (um)

0


y (um)

0


z (um)

0


radius (um)

0.4

Material

material

Vacuum


mesh order

4

Graphical rendering

override color opacity from material database

enabled


alpha

0.5

 

NOTE: The mesh order is set to a higher value than that of the "source" sphere so that it does not get overwritten.

 

 

XY Field

Click on the "2D Rectangle" button icon_strucs_2D_rect in the tabbed toolbar to add a 2D rectangle to the simulation region.  This will act as the monitor surface for an EM field monitor to record the electric field profile on a cross-section of the nanoparticle along the XY plane. Select the 2D rectangle in the Objects Tree and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value


name

XY field

Geometry

surface normal

z


x (um) / x span (um)

0 / 1


y (um) / y span (um)

0 / 1


z (um)

0

Graphical rendering

override color opacity from material database

enabled


alpha

0.2

 

YZ Field

Click on the "2D Rectangle" button icon_strucs_2D_rect in the tabbed toolbar to add a 2D rectangle to the simulation region. This will act as the monitor surface for an EM field monitor to record the electric field profile on a cross-section of the nanoparticle along the YZ plane. Select the 2D rectangle in the Objects Tree and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value


name

YZ field

Geometry

surface normal

x


x (um)

0


y (um) / y span (um)

0 / 1


z (um) / z span (um)

0 / 1

Graphical rendering

override color opacity from material database

enabled


alpha

0.2

 

XZ Field

Click on the "2D Rectangle" button icon_strucs_2D_rect in the tabbed toolbar to add a 2D rectangle to the simulation region. This will act as the monitor surface for an EM field monitor to record the electric field profile on a cross-section of the nanoparticle along the XZ plane. Select the 2D rectangle in the Objects Tree and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value


name

XZ field

Geometry

surface normal

y


x (um) / x span (um)

0 / 1


y (um)

0


z (um) / z span (um)

0 / 1

Graphical rendering

override color opacity from material database

enabled


alpha

0.2

 

 

3. Define Simulation Region

The next step is to define the 3D simulation region.  The Objects Tree in DGTD by default contains a simulation region.  Select the simulation region and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.  Note that all the simulation boundaries are set to "open" so that the simulation volume gets determined by the geometries themselves and not by the "simulation region" object.  This results in a spherical simulation region whose dimension is defined by the "outer" sphere.

 

tab

property

value


name

simulation region

General

dimension

3D


x min boundary

open


x max boundary

open


y min boundary

open


y max boundary

open


z min boundary

open


z max boundary

open

Geometry

x (um) / x span (um)

0 / 0.8


y (um) / y span (um)

0 / 0.8


z (um) / z span (um)

0 / 0.8

 

 

4. Add DGTD Solver

Next place a DGTD solver in the Objects Tree by clicking the "DGTD Solver" button icon_solver_dgtd in the tabbed toolbar.  Once in the Objects Tree, select the DGTD solver object and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value

General

simulation region

simulation region


simulation time (fs)

35

Mesh

edges per wavelength

5


refine based on material properties

enabled


polynomial order

2


dt stability factor

0.99

 

NOTE:  Once the DGTD solver gets added a new tab called "DGTD" will appear in the tabbed toolbar that contains all the necessary simulation objects for a DGTD simulation.

 

5. Add Boundary Conditions

The DGTD solver contains a folder names "boundary conditions" which contains all necessary boundary conditions.  In this example we will use the absorbing boundary condition.

 

Absorbing BC

Click on the "Absorbing boundary" button icon_absorbing_bc in the "DGTD" tab of the tabbed toolbar to place an absorbing boundary condition in the objects tree. Once the absorbing boundary conditions gets created select it (under the "boundary conditions" folder) and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value


name

absorbing

Geometry

surface type

solid


solid

outer


outer surface only

enabled

 

 

6. Add Source

The next step in the simulation setup is to add a source.  In this example we use a plane wave source and assign it to a sphere (closed surface) so that it acts as a total field scattered field (TFSF) source.

 

Plane Wave

Click on the "Plane Wave" button icon_DEVICE_optical_source in the tabbed toolbar.  Once the plane wave source is in the Objects Tree, select it and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value


name

source

General

direction definition

axis


injection axis

z-axis


direction

forward


angle theta (degrees)

0


angle phi (degrees)

0


polarization angle (degrees)

0

Geometry

surface type

solid


solid

source


outer surface only

enabled

Frequency/Wavelength

wavelength start (um)

0.3


wavelength stop (um)

1.1

 

 

7. Add Mesh Constraint

For simulations with metals, mesh constraints are often used to more accurately resolve the locations of the metal interface, especially with curved surfaces.  For this simulation we therefore apply a mesh constraint to the surface of the gold nanoparticle.  Click on the "Mesh Constraint" button icon_CHARGE_constraint in the "DGTD" tab of the tabbed toolbar.  Once in the Objects Tree select the mesh constraint and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

 

tab

property

value


name

mesh

General

max edge length (um)

0.015

Geometry

geometry type

surface


surface type

solid


solid

sphere


outer surface only

enabled

 

 

8. Add Monitors

 

Monitors are used in DGTD simulations to record simulation results.  In this example we will use one EM field monitor (scat) to calculate the absorption and scattering cross-sections and additional three EM field monitors (field_XY, field_YZ, field_XZ) to record the field enhancement around the gold nanoparticle along the XY, YZ, and XZ planes.  We use 41 frequency points over the frequency span of the source to record the frequency domain result.

 

Scat

Click on the "Frequency Domain EM Field" monitor button icon_DEVICE_EM_monitor to add an EM field monitor.  Once in the Objects Tree select the monitor and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value


name

scat

General

use linear wavelength spacing

enabled


use source limits

enabled


frequency points

41

Geometry

geometry type

surface


surface type

solid


solid

source


outer surface only

enabled

 

Field_XY

Click on the "Frequency Domain EM Field" monitor button icon_DEVICE_EM_monitor to add another EM field monitor.  Once in the Objects Tree select the monitor and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value


name

field_XY

General

use linear wavelength spacing

enabled


use source limits

enabled


frequency points

41

Geometry

geometry type

surface


surface type

solid


solid

XY field

 

Field_YZ

Click on the "Frequency Domain EM Field" monitor button icon_DEVICE_EM_monitor to add another EM field monitor.  Once in the Objects Tree select the monitor and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value


name

field_YZ

General

use linear wavelength spacing

enabled


use source limits

enabled


frequency points

41

Geometry

geometry type

surface


surface type

solid


solid

YZ field

 

Field_XZ

Click on the "Frequency Domain EM Field" monitor button icon_DEVICE_EM_monitor to add another EM field monitor.  Once in the Objects Tree select the monitor and click on the "Edit Properties" button icon_edit to edit its properties according to the following table.

 

tab

property

value


name

field_XZ

General

use linear wavelength spacing

enabled


use source limits

enabled


frequency points

41

Geometry

geometry type

surface


surface type

solid


solid

XZ field

 

 

9. Check Partitioned Volume

The simulation is now set up.  Next click on the "Partition simulation region" button icon_partition to view the partitioned volume (Fig. below).  The partitioned volume mode shows the entire simulation volume and identifies the different domains and surfaces.  Each domain and surface has a unique identifier and they are listed under the "simulation region" in the Objects Tree.  As you select different domains and surfaces in the Objects Tree the corresponding volume or surface gets highlighted in the partitioned volume.  In the figure below "domain 16" is highlighted in the partitioned volume.

mie_3d_dgtd_partitioned_vol_zoom21

 

The partitioned volume mode also makes it simpler to see where each boundary condition or source or monitor is getting applied in the simulation region.  As you select each simulation object the corresponding surface or volume gets highlighted in the partitioned volume making it easier to identify its location.  For example the three figures below show the location of the absorption boundary condition (left), the source (center), and the field_XY monitor.  Note that in the case of the absorbing boundary conditions all the external surfaces of the simulation region are highlighted.  The view port was switched to the "Wireframe" mode by clicking the corresponding button icon_wireframe on the "Perspective View Toolbar" located at the top of the perspective view window to generate the following figures as the highlighted volumes and surfaces become more clearly visible in this mode.  You can switch back to the default "Shaded" mode later by clicking on the corresponding button icon_shaded in the same toolbar.

mie_3d_dgtd_absorbing_bc_zoom22mie_3d_dgtd_source_zoom22mie_3d_dgtd_xy_field_zoom22

10. Error Check

The project file is now set up.  Next check if there is any error in the simulation setup by clicking on the "Check" icon_DEVICE_check button.  This will open up the "Error Checking and Diagnostics" window that shows any error in the simulation setup as well information about the different simulation objects (Fig. below).  There should no warnings. Finally save the file using the "File" menu and run it by following the instructions provided in the main page.

mie_3d_dgtd_error_check_zoom30

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