GroupTheory`
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GTPhFields[file name,kpoint,band number,Gvectors,geometry]
calculates the electromagnetic field in a photonic crystal.
Details and Options
- 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.- 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
Examples
Basic Examples (1)
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.
The symmetry points Γ,X, and M are considered:
The reciprocal lattice will be defined and reordered in shells.
The matrix representation of the master equation will be set up. The calculation will done for TM polarization, if no option is given.
