NCyclicSymmetry¶

Type:	int
Range:	[0, 2147483647]
Default:	-/-
Appearance:	optional

Note

This paramater is not optional for eigenmode problems. In contrast to scattering problems JCMsuite does not automatically scan over this parameter for eigenmode problems.

The parameter NCyclicSymmetry selects the angular symmetry class of the solution.

In the presence of discrete rotational symmetries ( $C_n$ ) it is required to specify the phase relation of the electromagnetic field between adjacent symmetry sectors. A cyclic symmetry is defined by a rotation of angle $\Delta\varphi = 2\pi/n$ around a given symmetry axis.

For such a rotation, the electromagnetic fields satisfy a Bloch-type periodicity condition. Let $\mathcal{R}$ denote the rotation operator. Then the fields fulfill

$\begin{eqnarray*} \VField{E}(\mathcal{R}\pvec{x}) & = & \VField{E}(\pvec{x}) e^{i m \frac{2\pi}{n}},\\ \VField{H}(\mathcal{R}\pvec{x}) & = & \VField{H}(\pvec{x}) e^{i m \frac{2\pi}{n}}, \end{eqnarray*}$

where $m \in \{0,1,\dots,n-1\}$ is the cyclic symmetry index.

The parameter NCyclicSymmetry corresponds to this index $m$ and selects the angular symmetry class of the solution.

NCyclicSymmetry = 0 corresponds to fully symmetric modes with identical fields in all sectors.
NCyclicSymmetry > 0 introduces a phase shift between neighboring sectors and yields higher-order angular modes.

The cyclic symmetry index $m$ determines how the field transforms under rotation:

For $m = 0$ , the fields are invariant under rotation.
For $m \neq 0$ , the fields acquire a phase factor, leading to rotating or twisting field patterns across the structure.

This is analogous to cylindrical coordinates, where $m$ represents the azimuthal mode number.

JCMsuite automatically detects the cyclic rotation angle from a given grid.jcm and enforces the above phase relation across these boundaries automatically based on the specified value of NCyclicSymmetry. In the layout.jcm cyclic symmetry is activated by assigning Class = Cn to the corresponding boundary segments. These boundaries then form a pair of interfaces related by the rotation operator.