Parameterization and orbital angular momentum of anisotropic dislocations

Waves that have an isotropic intensity distribution about the propagation axis may carry well-defined, quantized orbital angular momentum. The angular momentum is nonzero in the presence of screw dislocations. It is shown that these dislocations can be represented by a complete orthogonal set of functions (such as the Gauss–Laguerre set, which is valid for the paraxial approximation). Representing anisotropic dislocations by a superposition of isotropic ones provides easy derivation of various quantities related to the angular momentum, such as its expectation value and the uncertainty. Concentrating on dislocations that are solutions of the Laplace equation, we propose two natural and convenient ways of parameterization that bring forth their isotropic components as well as the geometrical properties of their phase map.  1996 Optical Society of America