Gratings¶
An optical grating is a periodical structure for the diffraction of light. It can diffract an incoming light beam into several beam travelling in different directions.
1D grating
A 1D grating is periodic in one direction with lattice vector and geometrically invariant in the
-direction
(this follows the
JCMsuite
convention that the coordinate system for 2D setups is the plane),
Due to -invariance the structure appears as lines in 3D:
![_images/line_lattice_grating.png](_images/line_lattice_grating.png)
1D grating.¶
Numerically, the scattering problem reduces to a periodic unit cell of a 2D computational domain, see example Line Grating.
2D grating
A 2D grating is periodic in both horizontal directions. There exist two lattice vectors so that the geometry is when shifted by a lattice vector,
The following figures show a square lattice and a hexagonal lattice arrangement.
![_images/square_lattice_grating.png](_images/square_lattice_grating.png)
Square lattice arrangement. are orthogonal.¶
![_images/hexagonal_lattice_grating.png](_images/hexagonal_lattice_grating.png)
Hexagonal lattice arrangement. The lattice vectors form an angle of
and are of equal length.¶
For the simulation it is possible to restrict the computation on a unit cell (primitive unit cell), see examples Square Unit Cell and Hexagonal Unit Cell.