Optical vortices in a vector field : the general definition based on the analogy with topological solitons in a 2D ferromagnet, and examples from the polarization transverse patterns in a laser

New approaches to the characterization of the vector vortical structure of the paraxial monochromatic field are introduced using the analogy between vector field singularities in a distribution of the unit vector of normalized Stokes parameters m(X,Y,Z),m2 = 1 in the transverse plane and topological solitons in a 2D ferromagnet. In this approach the vector vortex of the first order appears as zero and pole of the complex homographic function w = (X + iY)(1-Z)-1. The application of the developed method to the results of numerical simulations of a large aperture Zeeman laser is presented.

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