TY - JOUR

T1 - Polarization singularity indices in Gaussian laser beams

AU - Freund, Isaac

PY - 2002/1/15

Y1 - 2002/1/15

N2 - 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 Poincaré-Hopf index η, with generic value η = ±1, while C-points are characterized by the conserved half-integer singularity index IC, with generic value IC = ±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-lines 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.

AB - 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 Poincaré-Hopf index η, with generic value η = ±1, while C-points are characterized by the conserved half-integer singularity index IC, with generic value IC = ±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-lines 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.

KW - Paraxial beams

KW - Polarization singularities

KW - Topological indices

KW - Vortices

UR - http://www.scopus.com/inward/record.url?scp=0037081190&partnerID=8YFLogxK

U2 - 10.1016/S0030-4018(01)01725-4

DO - 10.1016/S0030-4018(01)01725-4

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AN - SCOPUS:0037081190

SN - 0030-4018

VL - 201

SP - 251

EP - 270

JO - Optics Communications

JF - Optics Communications

IS - 4-6

ER -