GTPhSymmetryField[field,character table,number of points]
performs the symmetry analysis of an electromagnetic field. Character table corresponds to the group of the wave vector 
. Number of points fixes the number of interpolation points in the mesh.
Details and Options
- GTPhSymmetryField is the elementary command for the symmetry analysis of the eigenmodes of an photonic band structure calculation. The symmetry of the eigenmode of a special band at a special k-point will be analyzed. Therefore the character table of the corresponding group of the wave vector
has to be calculated before the analysis. Character projection operators are applied to field to figure out to which irreducible representation of 
the eigenmode belongs to. - GTPhSymmetryField can be used to analyse results from the external program MPB. It is also possible to investigate eigenmodes constructed by means of GTPhFields, resulting from calculations of photonic band structures within GTPack.
- The calculation of a Frobenius norm is used to decide at the end, which irreducible representation is the correct one. The norms of the deviation of the transformed mode with respect to the original mode are normalized in such a manner that 100% means that the eigenmode transforms like that irreducible representation. For all the other irreducible representations the norm should be approximately zero.
- The following options can be given:
-
GOPlot False Plots table and field GOPlotStyle "Re" Could be "Re" fot the real part, "Im" for the imaginary part or "Abs" for the absolute vaule of the mode GOVerbose False Controls the output of additional information - See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 11.2
Examples
open allclose allBasic Examples (1)
As an example an eigenmode calculated by means of MPB will be analysed. The data are stored in the subdirectory MPB of datasets.
A circular rod in a quadratic unit cell was considered in the MPB calculation. The radius of the rod is ra = 0.2 a. The real structure of the system is shown first.
The point group of the problem is 
. A field at the 
-point will be analysed. 
at the 
-point is the full point group 
. The character table of 
is calculated.
The field, calculated by MPB is read in. Due to the nomenclature used by MPB the z-component of the E-field of the third band - .b03. - at the first k-point - .k01. - is read. The MPB files are in hdf5 format. The objects "Bloch vector" and the real and imaginary part ("z.r-new", "z.i-new") of the mode after transformation with the tool mpb-data are necessary to prepare the mode for the symmetry analysis.
The first part of field is the wave vector. The second part is the eigenmode.
It can be seen clearly, that only the transformation according to the irreducible representation E leads to the original map of the field, i.e. the band #3 belongs to an E representation.
Options (3)
GOPlot (1)
GTPhSymmetryField is used internally in other commands. Therefore in the standard case the table and the fields are not given.
