Abstract
Optical gratings can be used to produce more complex potentials than sinusoidal ones. In particular, graphene-like two-dimensional gratings can be produced, in which certain singular points of the Brillouin zone, known as Dirac points, appear. In the vicinity of these points, particle behavior is similar to that of ultra-relativistic particles, with a quasi-linear dispersion relationship. We have shown how controlling the lattice parameters can make Dirac points move within the Brillouin zone, or even disappear. We have described a recent experiment that brought these points into focus and exploited the control available over the topology of the Brillouin zone.
