Polarization singularity indices in Gaussian laser beams

Two types of point singularities in the polarization of a paraxial Gaussian laser beam are discussed in detail. V-points, which are vector point singularities where the direction of the electric vector of a linearly polarized field becomes undefined, and C-points, which are elliptic point singularities where the ellipse orientations of elliptically polarized fields become undefined. Conventionally, V-points are characterized by the conserved integer valued Poincare-Hopf index eta, with generic value eta = +/-1, while C-points are characterized by the conserved half-integer singularity index I-C, with generic value I-C = +/-1/2. Simple algorithms are given for generating V-points with arbitrary positive or negative integer indices, including zero, at arbitrary locations, and C-points with arbitrary positive or negative half-integer or integer indices, including zero, at arbitrary locations, Algorithms are also given for generating continuous lines of these singularities in the plane, V-Iines and C-lines, V-points and C-points may be transformed one into another. A topological index based on directly measurable Stokes parameters is used to discuss this transformation. The evolution under propagation of V-points and C-points initially embedded in the beam waist is studied, as is the evolution of V-dipoles and C-dipoles. (C) 2002 Elsevier Science B.V. All rights reserved.