GroupTheory`
GroupTheory`
GOPhPol
is an option to decide, which polarization has to be used in calculations of photonic band structures.
Details and Options
- In a 1D problem it is assumed, that the light is propagating perpendicular to the stack of layers. In such a case the problem is independent of the polarization.
- In a 3D case no separation of the polarization directions is possible in the definition of the eigenvalue problem.
- Two-dimensional photonic crystals are translational invariant in z-direction and are lattice periodic in the x-y-plane. Usually the light is considered to penetrate the structure in the x-y-plane. In this case the master equation separates for the two polarization directions. The two independent polarizations can be considered independently.
- Typical values for GOPhPol are:
-
"Automatic" No special definition necessary (1D and 3D problems) "E" or "TM" TM polarization "H" or "TE" TE polarization - See: J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals - Molding the Flow of Light, Princeton University Press, 1995
- W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica
Examples
Basic Examples (2)
A dielectric stack is considered.In this case it is not necessary to specify the polarization.
Calculate the path in k-space.
Calculate and plot the photonic band structure.
Two-dimensional photonic crystal
The structure is two-dimensional, i.e. the polarization has to be TE or TM. At first, the structure is defined.
The reciprocal lattice vectors are calculated.
The master equation is set up as an eigenvalue problem for TM polarisation.
The k-path is defined. The photonic band structure is calculated and plotted.
