No abstract

Lateral shear interferometer, being a self-referenced interferometer, has proven to be an important tool in scalar optics. Here we employ a vectorial counterpart - polarization lateral shear interferometer, in which the two interfering beams apart from being derived from the test wavefront, are in orthogonal states of polarization. Therefore when the test wavefront has spatially varying phase gradient across the beam cross-section, the resulting shearogram produces polarization fringes instead of intensity fringes. Further, the shearogram becomes inhomogeneously polarized. This polarization lateral shear interferometer may have potential uses in metrology, but in this article we demonstrate the ability of the interferometer in the generation of all Stokes singularities in the single beam by launching a phase singular beam into it. It is found that a vortex dipole is formed along with other generic Stokes singularities. Experimental observations support the results and they are discussed in the article.

In this paper, we report the morphological transformations of vector-field singularities (V-points) under symmetric and asymmetric perturbation using a diamond-shaped diffracting aperture. The number of null intensity points in the diffraction pattern depicts the magnitude of the polarization singularity index. Also, under symmetric perturbation, a higher-order V-point singularity disintegrates into | η | number of unit-index singularities following the index conservation rule. Asymmetric perturbations, realized by laterally shifting the aperture, lead to the formation of pairs of generic elliptic-field singularities (C-points) that are more fundamental and stable. In this process, the helicity and polarization singularity index are both conserved. This may find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams [Phys. Rev. Lett. 109, 183903 (2012)PRLTAO0031-900710.1103/PhysRevLett.105.053904].

Stokes phase is the phase difference between orthogonal component states in the decomposition of any polarization state. Phase singularities in the Stokes phase distribution are Stokes singularities of an inhomogeneous polarization distribution. Under circular decomposition, Stokes phase distribution $$(\phi _{12})$$ ( ϕ 12 ) represents polarization azimuth $$(\gamma )$$ ( γ ) distribution and the singularities present in it are polarization singularities. Therefore, the charge of the Stokes vortices depicted as Stokes index $$\sigma _{12}$$ σ 12 is an important parameter associated with the polarization singularity. The Hybrid order Poincaré sphere (HyOPS)/Higher order Poincaré sphere (HOPS) beams, all having same Stokes index, contain a Stokes singularity at the center of the beam as these beams are constructed by vortex superposition. These beams, being superposition of orthogonal orbital angular momentum (OAM) states in orthogonal spin angular momentum (SAM) states can offer great multiplexing capabilities in communication. In this article, we identify these degenerate Stokes index states and discuss the ways and means of lifting this degeneracy. Otherwise, there are limitations on intensity based detection techniques, where demultiplexing or segregation of different HOPS/HyOPS beams is warranted. The method adduced here uses the diffraction of these beams through an equilateral triangular aperture in combination with polarization transformation as a probe to lift the Stokes index/Stokes phase degeneracy. Successively, the novelty of the detection scheme is discussed in the context of beams with alike polarization distributions where even the technique of Stokes polarimetry fails to predict the OAM and SAM content of the beam.

Hybrid order Poincaré spheres to represent more general Stokes singularities are presented. Polarization singularities form a subset of Stokes singularities, and therefore induction of these spheres brings completeness. The conventional understanding of Poincaré beams as hybrid order Poincaré sphere beams is also expanded to include more beams. Construction and salient properties of these spheres are explained with illustrations to show their ability to represent more exotic Poincaré beams that have zero total helicity irrespective of their size. Pancharatnam–Berry geometric phase formulation using these new spheres is also possible.