In this video, we will get familiar with various boundary conditions available for the DGTD
In addition to providing a way to model various optical systems with different conditions,
in some cases, boundary conditions can be used to enhance the performance of the simulation.
We will use a metamaterial structure made of a periodic array of gold disks as an example
to demonstrate the application of different kinds of boundary conditions in DGTD simulations.
The first type of boundary condition is called Perfectly matched layer or PML in short.
PML boundaries absorb electromagnetic waves incident upon them.
They are essentially open boundaries that are intended to absorb all incident fields
without any reflection.
PML boundaries extend the simulation volume by a finite amount.
They basically add an absorbing material to the edge of the simulation region.
PML works best when the surrounding structures extend completely through the PML region.
In our metamaterial example, the PML boundary conditions are used along the light propagation
direction (top and bottom of the simulation region) since these boundaries are expected
to be open with no reflection.
The second type of boundary condition is absorbing, which is also intended to absorb incident
light without any reflection.
The difference is that absorbing boundary conditions are faster to process for simulation
and easier to setup.
In addition, unlike PML, they can be assigned to an arbitrarily shaped boundary but will
not be as accurate as PML when the light is incident at the boundary at a non-normal direction.
We typically recommend starting with Absorbing boundary conditions as they are faster and
easier to setup.
As part of your convergence testing, it’s a good idea to try PML to ensure you get the
The main exception to this rule is situations where the fields are propagating at non-normal
incidence to the boundary.
In such cases, PML should always be used.
Periodic structures, such as our meta-material example, can often scatter fields at non-normal
incidence and therefore PML is recommended for such structures.
Periodic boundary conditions should be used when both the structures and electromagnetic
fields are periodic.
These boundary conditions will allow you to directly simulate a single unit cell, but
still get the response of a periodic system.
In this example, periodic boundary conditions should be used in the X and Y directions.
Another type of boundary condition available in DGTD simulations is Perfect Electric Conductor
or PEC and Perfect Magnetic Conductor or PMC.
PEC boundary conditions are used to specify boundaries that behave as a Perfect Electric
Conductor such as metals.
For such a boundary, the component of the electric field parallel to the boundary is
The component of the magnetic field perpendicular to the boundary is also zero.
PEC boundaries are perfectly reflecting, allowing no energy to escape the simulation volume
along that boundary.
PMC boundary conditions are the magnetic equivalent of the PEC boundaries.
The component of the magnetic field parallel to a PMC boundary is zero and the component
of the electric field perpendicular to a PMC boundary is also zero.
In our metamaterial example, rather than using periodic boundary conditions to simulate a
single gold disk as shown on the right, we can reduce the required simulation time even
further by taking advantage of the symmetry of the structure.
In this case, only a quarter of a disk needs to be directly simulated due to the planes
of symmetry along the X and Y axes.
To take advantage of symmetry in your simulation, it is important to ensure that both the structure
AND the fields are symmetric.
For example, if your source is at an angle, the fields will not be symmetric.
The choice of PEC or PMC on the boundary depends on the source polarization.
Determining the correct option can be tricky.
To ensure you have the correct settings, run the simulation with and without taking advantage
of the symmetry.
You should get the same result in both cases.
You can download and run the provided simulation files for the metamaterial gold disk array
and compare the results and the time required for running the simulation with different
boundary condition options.
When using PEC & PMC, the simulation will run about four times faster.
You can also compare the result of using an absorbing or PML boundary condition.
In this case, the results will be very similar since the light is normally incident on these