Optical vortices produced by diffraction from dislocations in two-dimensional colloidal crystals

A dislocation in a crystal can be described by a Burger's vector b, whilst a screw dislocation in a laser mode can be described by a topological charge l. By illuminating both optically trapped and self-assembled two-dimensional ( 2D) colloidal crystals with a Gaussian laser beam, we show a correspondence between crystal and optical dislocations, where the first order diffraction pattern from a crystal with Burgers' vector b = na consists of vortex laser modes of topological charge l = +/- mn, ( n = integer, a = lattice constant and m = diffraction order).