GroupTheory`
GroupTheory`

GTPhMaster

GTPhMaster[background permittivity,reciprocal lattice vectors,Fourier transforms]

constructs the master equation for a structure with background permittivity, if the Fourier transforms of epsilon^(-1)(r) are calculated beforehand. The list of reciprocal lattice vectors is used in the construction.

Details and Options

  • Usually the Fourier transforms of are calculated on the fly during the construction of the eigenvalue problem for the master equation. This can be done also beforehand. The details of the structure under consideration determine the Fourier transforms, i.e. no structure specification is necessary calling GTPhMaster.
  • Warnings: The set of reciprocal lattice vectors used here, has to correspond to the reciprocal lattice vectors in the calculation of the Fourier transforms. GTPhMaster works only for the dimensions 2 and 3.
  • The following options can be given:
  • GOPhPol "Automatic"Specifies the polarization.
    GOVerbose TrueControls 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

Examples

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Basic Examples  (1)

First load the package:

A circular rod in a quadratic unit cell is defined.

The reciprocal lattice vectors for the quadratic lattice will be calculated.

The Fourier coefficients are calculated beforehand.

The eigenvalue problem of the master equation will be formulated.

The path in the Brillouin zone for the plot of the photonic band structure is calculated.

The photonic bands for TE polarization are calculated and plotted.

Options  (2)

GOPhPol  (1)

The Fourier transform of the permittivity is independent of the polarization, i.e. the master equation can be evaluated with those precalculated Fourier coefficients for TM polarization immediately.

GOVerbose  (1)

Additional information can be switched off.