NCyclicSymmetry¶

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

Note

JCMsuite automatically scans over this parameter for scattering problem. This paramater is only required when one intentionally restricts the fields to a specific symmetry index.

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.