GROUP THEORY SYMBOL

GTPhFields

GTPhFields[file name,kpoint,band number,Gvectors,geometry]
calculates the electromagnetic field in a photonic crystal.

DetailsDetails

  • The matrix representation of the photonic master equation is constructed with GTPhMasterEquation. Afterwards the eigenvalues and eigenvectors are calculated at certain k points by means of GTBands and stored.
  • The stored eigenvalues in file name are read for k point and band number. To construct the field also the reciprocal lattice vectors (G vectors) have to be provided.
  • The list geometry = {xmin,xmax,nx,ymin,ymax,ny} defines a rectangular grid. The field is calculated at nx mesh points in [xmin,xmax] in x-direction and ny mesh points in [ymin,ymax] in y-direction.
  • is calculated for TM polarization and for TE polarization.
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    is restricted to two - dimensional photonic crystals.
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 10.4

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package:

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This example is discussed in Joannopoulos, Meade, Winn, Photonic Crystals, Princeton University Press 1995, p. 68.

Cylindrical pillars of permittivity estruc in a background eback with a radius ra are considered. Filling factor and radius define the list geom.

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The symmetry points Γ,X, and M are considered:

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The reciprocal lattice will be defined and reordered in shells.

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The matrix representation of the master equation will be set up. The calculation will done for TM polarization, if no option is given.

TM polarization:

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The band 2 at Γ investigated

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TE polarization:

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The band 2 at M is investigated

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The band 3 at M is investigated

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