Polarization singularities of Gaussian vortex beams diffracted at a half-plane screen beyond the paraxial...

On the basis of the vector Rayleigh-Sommerfeld diffraction integrals, the analytical expression for Gaussian vortex beams diffracted at a half-plane screen beyond the paraxial approximation is derived and used to study the polarization singularities formed by the transverse and longitudinal electric field components in the diffracted field. It is shown that there exist C-points and L-lines that depend on the off-axis parameters in the x and y directions, waist width, wavelength, and topological charge of diffracted Gaussian vortex beams, as well as on the position parameter. By a suitable variation of the off-axis and position parameters, the creation, motion, and annihilation of polarization singularities may take place, and the topological relationship holds true. Therefore, the nonparaxial beam diffraction and propagation provide a method for generating polarization singularities.