Unveiling locally linearly polarized vector fields with broken axial symmetry

We explore how the focusing of axial-symmetry-broken vector fields is associated with a sector aperture whose apex coincides with the field axis. Its focused field is azimuthally split into a pair of orthogonal right- and left-handed circularly polarized partial rings which are rotated by angles of {+-}{pi}/2 with respect to the input vector field carrying no orbital angular momentum (OAM) and no spin angular momentum (SAM), respectively. Each member of the pair of partial rings carries not only the opposite OAM but also the opposite SAM. We unveil the underlying physics behind such an effect.