Is the boundary condition region important for simulations with Bloch/periodic boundary conditions?


#1

When you use periodic or Bloch boundary conditions for a particular direction, two blue regions at the edges of the simulation region will appear as shown below:

For periodic/Bloch boundary conditions these regions are always one mesh cell thick. The best practice is to extend your structure through the boundary condition area so that the piece of the structure in this area matches the corresponding piece in the mesh cells at the opposite end of the simulation region, as shown here for a periodic structure along the x direction:

The easiest way to ensure this is to draw at least one more unit cell of the structure on each side of the periodic boundary. In this example, since we have periodicity in one direction only, we draw 3 unit cells. For periodicity in two directions draw 3X3 unit cells and for periodicity in three directions draw 3X3X3 unit cells.

In any case, it is important to bear in mind that for any periodic direction the period is set by the distance between the inner boundaries, which corresponds to the span of the simulation window. Thus, in the example above the “x span” of the simulation region sets the period.


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Simulation of All-dielectric metasurface analogue of electromagnetically induced transparency
Transmission for finite number of cells
Bloch 혹은 주기 경계조건을 반영한 시뮬레이션에서 경계조건 영역의 중요성