GROUP THEORY SYMBOL
GTPhPermittivityMatrix
GTPhPermittivityMatrix[reciprocal basis,cutoff,objects,background]
gives the complete matrix 
i.e. the Fourier transform of 
. The reciprocal lattice vectors are defined by the reciprocal basis and vectors with 
< cutoff for a structure in the unit cell defined by objects. The structure is embedded in a dielectric background.
Details
- Two methods of the construction of the master equation, i.e. the eigenvalue problem to calculate photonic band structures are possible. First, the Fourier transform of ϵ(r) is calculated on the fly during the construction of the eigenvalue problem, second the
is calculated beforehand. GTPhPermittivityMatrix allows to calculate the matrix in two ways. First, it can be calculated directly by Fourier transform of 
r), the so called direct method. In the second method, so called Ho’s method (method of matrix inversion), the Fouriert ransform of ϵ(r) is calculated. The corresponding matrix is inverted. - The following options can be given:
-
GODCMethod "Direct" Method to calculate the matrix 
GOPixel False Decides the type of calculation: pixelmap or list of objects 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 10.4
- K. M. Ho, C. T. Chan, C. M. Soukulis, Existance of a Photonic Gap in Periodic Dielectric structures. Phys. Rev. Lett. 65, 3152 (1990).
Examplesopen all
Basic Examples (1)
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As an example dielectric rods in a square lattice in air are considered. The structure is defined:
| In[2]:= |
The Fourier transform of 
is calculated.
| In[3]:= |
The eigenvalue problem is constructed for the TM polarization.
The path in the Brillouin zone is fixed.
| In[5]:= |
The band structure is calculated and plotted.
| In[6]:= |
