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

Abstract

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.