The polarization of light can exhibit unusual features when singular optical beams are involved. In 3-dimensional polarized random media the polarization orientation around singularities describe 1/2 or 3/2 Möbius strips. It has been predicted that if singular beams intersect non-collinearly in free space, the polarization ellipse rotates forming many-turn Möbius strips or twisted ribbons along closed loops around a central singularity. These polarization features are important because polarization is an aspect of light that mediate strong interactions with matter, with potential for new applications. We examined the non-collinear superposition of two unfocused paraxial light beams when one of them carried an optical vortex and the other one a uniform phase front, both in orthogonal states of circular polarization. It is known that these superpositions in 2-dimensions produce space-variant patterns of polarization. Relying on the symmetry of the problem, we extracted the 3-dimensional patterns from projective measurements, and confirmed the formation of many-turn Möbius strips or twisted ribbons when the topological charge of one of the component beams was odd or even, respectively. The measurements agree well with the modelings and confirmed that these types of patterns occur at macroscopic length scales and in ordinary superposition situations.

We present the investigation of high-order disinclination patterns in the spatially variable polarization of a light beam. The beam was prepared by encoding two distinct high-order optical vortices on each of the circular polarization components of the beam. As a consequence, we were able to produce high-index lemon and star patterns, which have positive and negative indices, respectively. By varying the asymmetry of one of the vortices we were able to transform one symmetric pattern (lemon or star) into another (lemon or star). With one exception, monstar patterns always appear for specific ranges of asymmetry regardless of the end symmetric patterns. Mapping of all disclinations within each case is contained in a spherical space, where monstar regions are cusp-shaped. We found that high-order monstar patterns can have positive or negative index.

The control of spatial and polarization modes of optical beams enables the production of topological singularities encoded on the polarization of the light. This allows the study of topological disclinations not easily found in the natural setting. In this article we report on the observation of new features in disclinations realized with singular optical beams. They were prepared using three spatial modes bearing optical vortices in non-separable superpositions with circular polarization states. The disclinations involve asymmetric rotational dislocations, whose optical counterparts in the optical far field are known as C-points, and which are classified as monstars. They have been known to have a singularity index that can be positive, or negative as reported by us recently. Here we report on monstars with an index of zero. Monstars are characterized by having sectors bound by radial lines that involve curved lines radiating from the singularity. We found that kinks in otherwise smooth line patterns of asymmetric disclinations are scars of a separate but related pattern of line-slope discontinuities, carried optically by C-lines in the far field. These scars are indicative of the underlying structure or symmetry of the pattern. We present a general formalism to understand and generate monstars, along with measurements: the experimental results are in excellent agreement with theoretical modelings.

The topological charge of a beam carrying an optical vortex is an important parameter that specifies the amount of orbital angular momentum carried by the beam and the azimuthal order of the beam mode. We present an experimental method to determine the sign and magnitude of the topological charge using a wedged optical flat as a lateral shearing interferometer. When the curvature of the wavefront is adjusted to be planar, the fringe pattern generated by the shearing interferometer consists of two conjoined forks that unambiguously identify the topological charge of the beam. We also investigated the changes in the pattern when the wedged flat is rotated.