Boundary conditions are a crucial aspect of any simulation.
The FDTD solver region supports PML, metal, periodic, symmetric, Bloch and PMC boundaries.
PML absorbing boundaries are the most common option.
Most simulations use PML on at least some boundaries.
These boundaries attempt to absorb all incident fields, without creating any back reflection,
as shown in the video.
Ideally, PML boundaries would absorb all incident light without creating any back reflections.
In practice, the performance of the PML depends on several factors.
The PML configuration profiles optimize the PML performance for the three most common
For most simulations, the standard PML profile is the best option, maximizing absorption
without significantly affecting the simulation speed.
The steep angle profile should be used when the fields are incident on the PML at a steep
or grazing angle, typically beyond 60 degrees.
To compensate for PML’s lower efficiency at absorbing fields at steep angles, the steep
angle profile uses more PML layers to absorb the fields.
The cost of using extra layers is the simulation requires a bit more memory and time to run.
The stabilized profile should only be used if your simulation is suffering from a numerical
divergence problem, where the divergence originates in the PML region.
Finally, the custom option allows expert users full access to adjust all the PML parameters.
Metal boundaries act very much like a mirror, reflecting 100% of the fields without any
Technically, the boundary acts as a perfect electrical conductor at the boundary.
Occasionally, you may encounter simulations where the choice of boundary condition doesn’t
For example, if the fields are zero at a boundary, then the boundary condition doesn’t matter.
In such cases, metal boundaries are the best choice, since they are the fastest of the
PMC, or Perfect Magnetic Conductor boundaries are very similar to metal, except the boundary
is implemented as a perfect magnetic conductor, rather than a perfect electrical conductor.
Periodic boundaries are used to simulate periodic structures, such as the array of circular
particles shown here.
This video shows a simulation that included three unit cells, to more clearly demonstrate
the periodicity of the simulation.
In your actual simulation, you should only include a single unit cell in the simulation,
as shown here.
With periodic boundaries, the periodicity is determined by the span of the simulation
It is very important to understand that both the structure, electromagnetic fields and
source must be periodic.
For this reason, plane wave sources are most often used with periodic boundary conditions.
Bloch boundaries are used for periodic simulations where the source is injected at an angle – they
are similar to periodic boundaries where light which exits one boundary is re-injected from
the opposite boundary, but they add the required phase difference to the light that is re-injected
corresponding to the phase accumulated between the unit cells due to the angle of the source.
Symmetric and anti-symmetric boundary conditions can be used to take advantage of any symmetry
in the simulation in order to reduce the volume that needs to be simulated.
When you have a structure and source that have a plane of symmetry through the middle
of the simulation region, symmetry boundaries allow you to reduce the size of the solver
region that needs to be simulated.
For example, this example has a plane of symmetry along the y-axis.
Therefore, there is no need to directly simulate the left half of the volume, since it will
be the same as the right half.
This example has two planes of symmetry, along with both the X and Y axis.
Using symmetry boundaries makes this simulation run four times faster.
Even though the fields are only computed in one-quarter of the full simulation region,
monitors will automatically by unfolding the electromagnetic fields to show the field profile
over the full volume.
The main challenge with using symmetry boundaries is determining which type of symmetry exists
in the system: Positive Symmetry, or Anti-Symmetry.
This choice must be manually made by the user.
To be sure that you have selected the correct boundary, run the simulation with and without
symmetry and ensure you get the same result.
Different results mean that you selected the wrong type of symmetry.
The figure of the left shows the non-zero field components at the boundary.
This information provides a simple rule of thumb for determining the symmetry to use
in your simulation.
In most cases, the type of symmetry can be determined from the source polarization.
If the source polarization arrow is tangential to the plane of symmetry, then the polarization
arrow and the boundary shading color should match.
If the polarization arrow is normal to the boundary, then the colors should not match.
This figure shows the field symmetries across the boundary.
In most cases, monitors automatically unfold field data according to these rules.
When using symmetry boundaries, the boundary should only be applied to the ‘min’ boundary.
The ‘max’ boundary should be set to whatever the boundary would be without symmetry; typically
The only exception is when using symmetry boundaries with periodic structures.
In such cases, set both the min and max boundaries in the periodic direction to use symmetric
or anti-symmetric boundaries.
You will need to enable the “allow symmetry on all boundaries” option.