Reduced Problem

In this tutorial example we utilize the fourfold symmetry of the geometrical layout of previous example to reduce the computational domain to a quarter of its original size:

The symmetry axes of the computational domain are so-called domain boundaries which need user-defined boundary conditions. In the layout file we assign BoundaryIds to the boundary segments, which refer to entries in the boundary_conditions.jcm file. For electromagnetic simulations there are two possible choices: either the tangential component of the electric or magnetic field is set to zero. These combinations on the two symmetry axes can be used to compute modes of accordingly different symmetries. Here we choose

BoundaryCondition {
  BoundaryId = 1
  Electromagnetic = TangentialElectric
}

BoundaryCondition {
  BoundaryId = 2
  Electromagnetic = TangentialElectric
}

Below we show the intensity and vector field of one computed mode:

In the vector plot we observe that the electric field vectors on the boundary are normal to the symmetry planes, hence their tangential component is zero as specified by the ‘’TangentialElectric’’ boundary condition.