Transformation of a high-order edge dislocation to optical vortices (spiral dislocations)

We theoretically show that an astigmatic transformation of nth-order edge dislocation (a zero-intensity straight line) produces n optical elliptical vortices (spiral dislocations) with unit topological charge at the double focal distance from cylindrical lens, located on a line perpendicular to dislocation, points whose coordinates are roots Hermite polynomial. The orbital angular momentum is proportional order n.