GROUP THEORY SYMBOL

GTPhMasterEquation

GTPhMasterEquation[structure,permittivity structure, permittivity background,geometry,reciproval lattice vectors]
constructs the matrix formulation of the master equation to calculate photonic band structures.

Details Details

A linear combination of plane waves is used to transform the master equation of the photonic band structure problem into an eigenvalue problem. The eigenvalue problem can be constructed for two-dimensional and three-dimensional photonic crystals. The Fourier transform of the permittivity is given in analytic form, hence only a few model structures can be considered: CircularRod, EllipticalRod, RectangularRod, Sphere, Cuboid, EmptyLattice, One-Dimensional. The permittivity of the structure and the permittivity of the background define the dielectric contrast. The list geometry (see GTPhDielectric) contains the structural information with respect to structure. Several hundred reciprocal lattice vectors have to be used to get converged results.
The following option can be given:
GOPhPol "E" Selects the polarization in case of two-dimensional photonic crystals
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, chpter 11.1
This module will finally be substituted by GTPhMasterObjects and/or GTPhMasterPixel.

Examples Examples open all close 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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