Influence of Primary Coma on the Tightly Focusing Characteristics of Circular Basis Hybrid Order Poincaré Sphere Beams

Abstract

Analogous to the Poincaré sphere, a hybrid order Poincaré sphere is used to represent the ellipse field singularities (C-points). We study the tight focusing properties of generic bright and dark hybrid order Poincaré sphere beams in the presence of primary coma. The role of the polarization singularity index and handedness of the polarization of the hybrid order Poincaré sphere beams on the focused structure has been discussed. Results have been presented for the total intensity, component intensities, and component phase distributions for left- and right-handed bright and dark star and lemon types singularities. The presence of primary coma distorted the focal plane intensity distributions for both positive and negative index generic C-points. Coma is known to disturb the circular symmetry of the focal plane intensity distribution. Similarly in tight focusing polarization is known to disturb the symmetry. Therefore, a beam with structured and inhomogeneous polarization distribution tightly focused under the influence of coma is a fit case to study. It is found that the presence of primary coma aberration in the focusing system produces a positional shift of the high-intensity peaks and a reduction of the intensity on one side of the center. As the strength of the primary coma increases, the focal plane intensity distributions shift more and more toward the right from the initial position. Unlike the scalar vortex case, in the case of hybrid order Poincaré sphere beams, the focal plane intensity distribution undergoes rotation, as the helicity of the hybrid order Poincaré sphere beams is inverted, in addition to shifting. All the component phase distributions are found to be embedded with phase vortices of charge ±1.

Keywords

• laser beam shaping
• Debye-Wolf Integral
• high numerical aperture optics
• hybrid order Poincaré sphere
• polarization
• singular optics