Converting an nth-order edge dislocation to a set of optical vortices

Abstract

We show theoretically that an astigmatic transformation of an edge dislocation (a straight line of zero intensity) of the n-th order forms n elliptical optical vortices (screw dislocations) with a unit topological charge at twice the focal distance from a cylindrical lens. The vortices are located on a straight line perpendicular to the edge dislocation at points with coordinates equal to the roots of an n-th order Hermite polynomial. The orbital angular momentum of an edge dislocation with an astigmatic phase is found to be proportional to n.