The RCWA solver can be used with a non-orthogonal unit cell where the lattice vectors defining the unit cell are not perpendicular to each other. For example, a non-orthogonal unit cell can be used with a hexagonal lattice structure, as shown below:

## Defining a Non-orthogonal Unit Cell

The RCWA unit cell is defined using two lattice vectors, \(\vec{v_1}\) and \(\vec{v_2}\), and the lattice vector angle \(\alpha\), as shown in the diagram below:

The lattice vector angle \(\alpha\) in degrees is set using the **lattice vector angle** property of the RCWA solver:

The lattice vector \(\vec{v_1}\) will remain fixed and the lattice vector \(\vec{v_2}\) will rotate based on the lattice vector angle. The lattice vector angle must be between 1 and 179 degrees.

The span of the unit cell for a non-orthogonal unit cell is defined as the distance between the edges of the unit cell. The definitions of the **x span** and **y span** in the case of an RCWA simulation with a propagation direction of Z are shown in the diagram below, along with the definitions of the **x/y max/min**:

**Note:** A non-orthogonal unit cell can only be used with **mesh refinement** set to **staircase**.

## Comparison Between Orthogonal and Non-orthogonal Unit Cells

The same structure may be simulated with either an orthogonal unit cell (with a mesh refinement set to conformal or staircase), or an non-orthogonal unit cell (only possible with a mesh refinement set to staircase).

Either option can be used, but they do not converge in the same way. Different results may be obtained if the max number of k vectors or the number of mesh cells is too low. It is expected that the non-orthogonal unit cell option will converge more efficiently to the result.