Periodic Boundary Condition (PBC)

Use a periodic boundary condition (PBC) to analyse infinite periodic structures. A typical application of PBC is to analyse frequency selective surface (FSS) structures.

The unit-cell definition for the periodic boundary condition solution is based on vectors. For the one-dimensional case, the start point and end point of a single vector are required. Periodicity is defined based on two planes passing through these start point and end point, and normal to the vector formed between them. The vector used to define one-dimensional periodicity can have any orientation but must have a non-zero length.

For the two-dimensional case, two vectors are required. These vectors form the two boundaries of the unit cell which is infinite in the direction normal to the plane on which both vectors lie. The vectors that define the unit-cell for two-dimensional periodicity must have non-zero length, and cannot be oriented in the same direction.

Figure 1. The periodic boundary condition for two-dimensional periodicity.
A phase shift can be applied in the direction of the vectors defining the unit-cell. The specified values for the phase-shift are only used if a plane wave source is not present.
Note: If a plane wave source is present and a phase is specified, the Solver will return an error during the solution.

For array modelling using periodic boundary conditions, the beam (squint) angle is specified by defining the theta and phi angle. The phase along the periodic lattice vectors is computed automatically to ensure the specified beam direction.