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

We theoretically show that an astigmatic transformation of an 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 the cylindrical lens, located on a straight line perpendicular to the edge dislocation, at points whose coordinates are the roots of an $n$th- order Hermite polynomial. The orbital angular momentum of the edge dislocation is proportional to the order $n$.