We present a convenient method to generate vector beams of light having polarization singularities on their axis, via partial spin-to-orbital angular momentum conversion in a suitably patterned liquid crystal cell. The resulting polarization patterns exhibit a C-point on the beam axis and an L-line loop around it, and may have different geometrical structures such as lemon, star, and spiral. Our generation method allows us to control the radius of L-line loop around the central C-point.

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... , we investigate the free-air propagation of these fields across a Rayleigh range.