GroupTheory`
GroupTheory`

GTPhDCObjects

GTPhDCObjects[reciprocal lattice vector,permittivity background,structure]

gives the Fourier transform of the inverse permittivity of an ensemble of geometric objects.

Details and Options

  • The Fourier transform of the inverse permittivity of objects with simple geometric forms can be found analytically. Based on the structure factors of such elements the Fourier transform of an ensemble of such elements can be easily found. If objects are present in the unit cell, the list structure contains elements.
  • structure = {object_1, object_2, ..., object_n}
  • The description object_i of an object has the following form:
  • object_i = {identifier, permittivity, geometry, shift}
  • The identifier can be: "CircularRod", "Cuboid", "EllipticRod", "PrismaticRod", "RectangularRod", "Slab", or "Sphere". A circular rod is a special case of an elliptic rod and a rectangular or square rod can be defined by PrismaticRod.
  • Permittivity defines the permittivity of the object.
  • Shift is a non-primitive vector of the direct lattice (with respect to the direct lattice vectors) defining the position of the object in the unit cell.
  • Finally, geometry defines the geometry of the object. The form of the list depends on the identifier. The list has to have the following structure
  • "Slab"{gamma,0,0,0,0}
    "CircularRod"{gamma,r,r ,0,phi}
    "EllipticRod"{gamma,a_e,b_e ,0,phi}
    "PrismaticRod"{gamma,a,b,alpha,phi}
    "RectangularRod"{gamma,a,b,pi/2,phi}
    "Sphere"{gamma,r,0,0,0}
    "Cuboid"{gamma,a,b,c,0,0}
  • is the filling factor in each case. The rotation angle can be used to rotate the object with respect to its original position. This option is only implemented for the two-dimensional cases.
  • The following option can be given:
  • GOVerbose FalseControls 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

Examples

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Basic Examples  (1)

First load the package:

A square lattice will be considered. The unit cell consists of a circular rod of radius 0.2 at the origin, an elliptic rod in the middle of the cell and a rotated prismatic rod in air.

To inspect the constructed structure GTPhShowStructure is used.

The Fourier transform is now calculated at a grid of reciprocal lattice vectors.

Options  (2)

GOVerbose  (2)

GOVerbose gives only information about the objects in the structure and the mean value of the inverse permittivity, if G={0,0,0}.