GTPhMasterPixel
GTPhMasterPixel[reciprocal lattice vectors,pixelmap,basis]
constructs the master equation if the permittivity is given by a pixelmap. Basis describes the lattice in real space. A list of reciprocal lattice vectors is used.
Details
- Complicated distributions of the permittivity
do not lead to an analytic form of the the Fourier transform of the inverse permittivity. The Fourier transform can be calculated, if the permittivity distribution is expressed by a pixelmap. Each pixel is transformed separately. - The following options can be given:
-
GOPhPol "Automatic" Specifies the polarization. GOVerbose True Controls the output of additional information. - See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 11.1
Examplesopen all
Basic Examples (1)
| In[1]:= |
A pixel map of the permittivity distribution is defined.
| In[2]:= |
The structure is plotted. The unit cell is a square.
The reciprocal lattice vectors for the quadratic lattice will be calculated. A limited number of plane waves is used to show the principle.
The eigenvalue problem according to the master equation is constructed.
| In[5]:= |
The path in the Brillouin zone for the plot of the photonic band structure is calculated.
| In[6]:= |
The photonic bands for TE polarization are calculated and plotted.
| In[7]:= |
For the simple shape of the distribution of 
an analytical result exists. A rectangular rod in a quadratic unit cell is defined according to the rules in GTPhDCObjects.
| In[9]:= |
The photonic bands for TE polarization are calculated and plotted.
