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A central subject of interest in the study of the singular optics of completely coherent but inhomogeneously polarized light fields (resulting, e.g., from stationary multiple scattering of laser radiation) involves the C points (the points where a field is circularly polarized and the azimuth of polarization is undetermined) and the L lines [the lines along which polarization is linear with a smoothly changing azimuth of polarization, and the direction of rotation of the electrical vector (handedness) is undetermined] at the transversal crosssection of a ‘beamlike’ (paraxial) field. Snakelike C lines and L surfaces correspond to such singularities in three dimensions. The set of C points and L lines obeys well-known sign principles and forms the vector skeleton of a coherent, inhomogeneously polarized beam. As such, knowing the characteristics of the field at C points and L lines, one can predict in a qualitative manner the field behavior (e.g., changing the state of polarization) in other regions of the beam. This property of polarization singularities follows from their genericity, i.e., their structural stability with respect to small perturbations of the initial conditions or perturbations of a freely propagating beam. Nongeneric polarization singularities resulting from coherent mixing of weighted orthogonally polarized Laguerre–Gaussian (LG) modes with different radial indices have also been reported. The universal theoretical and experimental approach for investigating vector (polarization) singularities involves determining the Stokes parameters as a function of spatial coordinates at the analyzed transversal cross-section of a beam, followed by determining the spatial distributions of the azimuth of polarization and the angle of ellipticity, and identifying the singular elements of a field.
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