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.
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:
Numerically, the scattering problem reduces to a periodic unit cell of a 2D computational domain, see example Line 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.