When studying periodic systems, Periodic BC's allow you to calculate the response of the entire system by only simulating one unit cell. Periodic BC's are relatively straightforward to use in your simulation: simply set the simulation span to be one unit cell wide and select Periodic BC's for that boundary. When the simulation runs, the Periodic BC's simply copy the EM fields that occur at one side of the simulation and inject them at the other side.
The most important detail to remember is that when using Periodic BC's, everything in the system must be periodic: both the the physical structure AND the EM fields. A common source of error is to use periodic boundary conditions in systems where the structure is periodic, but the EM fields are not. Examples include:
- A periodic structure is illuminated by a plane wave propagating at an angle. The fields will not be quite periodic in this case, as there will be a phase difference between each period of the device. Use Bloch BC's instead.
- A periodic structure is excited by a single dipole source, such as in OLED simulations. In this case the system is not periodic because there is only one dipole, not one dipole per period.
Movie of Ex fields from a simulation of a plane wave propagating in the Z direction at normal incidence in free space. Periodic BC's are used in the X and Y directions.
- Periodic BC's are most often used with the planewave source.
- If the Plane wave source is injecting at an angle, then the fields will not be periodic (there will be a phase difference between each period). Use Bloch BC's instead to get single frequency result, or use BFAST to get broadband result.
- For systems that are both periodic and have symmetry, select symmetry (or anti-symmetry) on both boundaries. This allows you to simulate only 1/2 of one unit cell. See Symmetric and anti-symmetric BCs for details.
- For best performance, enough of the structure should be drawn in the CAD so that it extends through the boundary condition region (the one mesh cell thick boundary region drawn in a light blue color. This ensures that the material properties are correctly defined in the boundary condition region.
- PML boundaries are typically used on the 'non-periodic' boundaries (the Z direction in the above video). The 'Steep angle' PML profile is recommended for periodic simulations because the structure can scatter light at steep angles.
Bloch boundary conditions, Symmetric and anti-symmetric BCs, Metamaterial Parameter Extraction Example