GROUP THEORY SYMBOL

GTPhSymmetryPoint

GTPhSymmetryPoint[file,minb,maxb, objects,mesh size,point group,reciprocal basis]
performs the symmetry analysis of electromagnetic fields given in datasets defined by file. All bands between minb and maxb will be investigated. objects defines the objects from the hdf5 files which are necessary for the analysis. Mesh size defines the number of points used for interpolation. The system under consideration is characterized by point group and reciprocal basis.

DetailsDetails

  • It is assumed, that a series of eigenmodes are calculated at a special k-point in the Brillouin zone by means of MPB. file is a filename corresponding to the rules of MPB at this k-point. The filennames of the modes of the bands from minb to maxb will be constructed automatically. The files with the eigenmodes are stored in hdf5 format, containing several objects.
  • For the symmetry analysis the objects containing real and imaginary part of the field after transformation with mpb-data (cf. GTPhMPBFields) are necessary.
  • The fields are interpolated on a mesh defined by mesh size.
  • The point group of the photonic crystal has to be provided. The corresponding group of the wave vector and the corresponding character table are constructed internally. Projection operators to the irreducible representations of are used for the symmetry analysis.
  • The following options can be given:
  • GOIrepNotation"Mulliken"Defines the notation of the irreducible representations
    GOPlotFalseDecides, if table and eigenmodes are displayed
    GOPlotStyle"Re"Could be "Re" fot the real part, "Im" for the imaginary part or "Abs" for the absolute vaule of the mode
    GOVerboseFalseControls 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
  • J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals. Molding the flow of light, Princton 2008, p .70
  • for MPB: http://ab-initio.mit.edu

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package:

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The data are stored in the subdirectory MPB of datasets.

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A circular rod in a quadratic unit cell is considered. The radius of the rod is ra = 0.2 a. The real structure of the system is shown first.

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The point group of the problem is . The bands 1-8 at the -point of the BZ will be analyzed. This is point 52 in the MPB calculation. TM polarization was assumed. The point of the problem is .

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It is checked, which objects are contained in the dataset.

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Obviously it is a file at the -point.

The objects real and imaginary part ("z.r-new", "z.i-new") of the mode after formation with the tool mpb-data are necessary to prepare the mode for the symmetry analysis.

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A list of the irreducible representations to all the bands is provided.

Options  (4)Options  (4)

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