Polarisation singularities of non-paraxial Gaussian vortex beams diffracted by an annular aperture

Based on the vectorial Rayleigh-Sommerfeld diffraction integrals, the propagation expressions for non-paraxial Gaussian vortex beams diffracted by an annular aperture are derived, and are used to analyse polarisation singularities of non-paraxial Gaussian vortex beams in the diffraction field. It is shown that there exist polarisation singularities including C-points (S(12) vortices), S(23) vortices, and S(31) vortices. The number and position of polarisation singularities depend on the waist width of the beam, the off-axis distance of the vortex and the aperture parameter. The creation and annihilation of polarisation singularities appear as a controlling parameter - including the waist width, off-axis distance and aperture parameter - varies. When compared with the free-space propagation, more polarisation singularities may take place in the diffraction field.