Polarization singularity index sign inversion by a half-wave plate

Electrotunable 180° achromatic linear polarization rotator based on a dual-frequency liquid crystal

Linear polarization rotators have been widely used in optical systems. Commonly used polarization rotators are still beset by strong dispersion and thus restricted spectral bandwidth of operation. This leads to the development of achromatic or broadband alternatives, but most of them incorporate multiple waveplates for retardation compensation, which comes at the cost of increased complexity and reduced flexibility in operation and system design. Here, we demonstrate a single-element achromatic polarization rotator based on a thin film of dual-frequency chiral liquid crystal. The angle of polarization rotation is electrically tunable from 0° to 180° with low dispersion (±3°) in the entire visible spectrum, and a high degree of linear polarization (>95%) at the output.

Non-interferometric technique to realize vector beams embedded with polarization singularities: publisher's note

This publisher's note corrects the contents of references in J. Opt. Soc. Am. A37, 1043 (2020)JOAOD60740-323210.1364/JOSAA.393027.

Detection of degenerate Stokes index states

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\phi _{12})$$\end{document}(ϕ12) represents polarization azimuth \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\gamma )$$\end{document}(γ) distribution and the singularities present in it are polarization singularities. Therefore, the charge of the Stokes vortices depicted as Stokes index \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _{12}$$\end{document}σ12 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.

Non-interferometric technique to realize vector beams embedded with polarization singularities

In this paper, we present a simple and flexible non-interferometric method to generate various polarization singularity lattice fields. The proposed method is based on a double modulation technique that uses a single reflective spatial light modulator to generate different lattice structures consisting of V-point and C-point polarization singularities. The present technique is compact with respect to previous experimental realization techniques. Different structures having star and lemon fields are generated without altering the experimental setup. In addition, the same setup can be used to obtain different types of inhomogeneous fields embedded with isolated polarization singularities even of higher orders. The Stokes polarimetry method has been used to obtain the polarization distributions of generated fields, which are in good agreement with simulated results.

Full Poincaré beam with all the Stokes vortices

In this Letter, we present a recipe for the generation of full Poincaré beams that contain all Stokes vortices (SVs), namely ϕ₁₂, ϕ₂₃, and ϕ₃₁ vortices. Superposition of two scalar vortex beams with charges l₁ and l₂ (where |l₁|≠|l₂|) in orthogonal states of polarization (SOP) generates all three types of SVs, out of which two types of them are generic and always lie in a ring, with the third type at the center of the ring with index value (l₂-l₁). Thus, generation of hitherto unknown dark SVs is shown. The number of SVs in a ring is 4|l₂-l₁|. Index sign inversion for all SVs can be achieved by swapping l₁ and l₂. By changing the orthogonal pairs of SOPs of the interfering beams, the SV at the center of the ring can be changed from one to another type such that the other two types take part in the formation of the ring of generic SVs. We have also deduced the expressions for the location of all the SVs in the beam. Experimental results are presented.

Morphological transformation of generalized spirally polarized beams by anisotropic media and its experimental characterization

We present a generalization of the known spirally polarized beams (SPBs) which we will call generalized spirally polarized beams (GSPBs). We characterize in detail both theoretically and experimentally the streamline morphologies of the GSPBs and their transformation by arbitrary polarization optical systems described by complex Jones matrices. We find that the description of the passage of GSPBs through a polarization system is equivalent to the stability theory of autonomous systems of ordinary differential equations. While the streamlines of the GSPB exhibit a spiral geometry, the streamlines of the output field may exhibit spirals, saddles, nodes, ellipses, and stars as well. Using a novel experimental technique based on a Sagnac interferometer, we have been able to generate in the laboratory each one of the different cases of GSPBs and record their corresponding characteristic streamline morphologies.

Helicity dependent diffraction by angular momentum transfer

In this article we show that diffraction segregates the polarization singularities according to their handedness. Polarization singularities are superpositions of left and right handed circular polarization vortex states. In the superposition, the component states possess different orbital angular momenta depending on the type of the singularity. A fork grating that can generate different orbital angular momentum (OAM) states in different diffraction orders is shown to segregate right and left handed polarization singularities. A V-point polarization singularity that corresponds to one combination of OAM states incident on the fork grating is found to diffract in such a way that the same OAM combination does not occur in all the nonzero diffraction orders. As a result, each of the diffraction orders will have different polarization singularities. This OAM transfer by the fork grating segregates the right and left handed polarization singularities thereby, making the diffraction helicity dependent.

Synthesis of Stokes vortices

Fields containing polarization singularities normally do not host all the Stokes vortices. For example, fields with S₁₂ Stokes vortices (C-points, V-points) in general do not contain S₂₃ Stokes vortices (Poincare vortices). In this paper, we demonstrate for the first time, to the best of our knowledge, synthesis of a structured field that hosts all three Stokes vortices, namely, S₁₂, S₂₃, and so far unexplored S₃₁ Stokes vortices. Only S₁₂ Stokes fields that host C-points and V-points have been experimentally realized by many research groups. Generation of S₂₃ Stokes fields that contain Poincare vortices have been proposed earlier but not experimentally demonstrated so far. There are no reports on the generation of S₃₁ Stokes field containing the third set of Stokes vortices.

Angular momentum switching and orthogonal field construction of C-points

In this Letter, we take on the non-trivial problem of transforming a C-point singularity into its orthogonal state by switching its angular momentum components. For homogeneous distribution, orthogonal transformation is a trivial operation using a single half-wave plate. For C-point singularity, this entails a change in the handedness without disturbing the index, followed by rotation of the state of polarizations in the distribution. Swapping the spin angular momentum (SAM) components of C-point singularities leads to index and handedness inversion, whereas, switching of orbital angular momentum (OAM) components results only in handedness inversion. By changing the SAM and OAM components in sequence, a C-point can be transformed into its orthogonal state. While experimentally demonstrating this, a spiral phase plate, which is a phase element, is shown to perform polarization transformation operation.

Edge enhancement by negative Poincare-Hopf index filters

Phase and polarization are interrelated quantities, and hence polarization elements that perform like phase elements can be designed. In this Letter, we show that a polarizing element producing a negative Poincare-Hopf (PH) index beam can be used as a spatial filter to perform edge enhancement. Either isotropic or anisotropic edge enhancement can be achieved by polarization selection of the light that illuminates the sample. A conventional microscope imaging system is modified into a polarization-selective optical Fourier processor. Experimental results are presented to show that negative PH index filters, producing a set of orthogonal polarization distribution and their superpositions, can also be used for edge enhancement in optical signal processing.

Hopping induced inversions and Pancharatnam excursions of C-points

In this Letter, we show the acquisition of the Pancharatnam phase by a C-point singularity when it is subjected to discrete cyclic polarization transformations. The changes in state of polarizations (SOPs) are mapped onto a Poincaré sphere as geodesical closed trajectories. The Pancharatnam phase acquired by a C-point is equal to the solid angle subtended by the closed trajectories at the center of the Poincaré sphere. We show this by considering index hopping induced inversions of C-points. For example, a lemon from the North Pole of a Poincaré sphere is first converted into a star whose location can be traced to the South Pole of the Poincaré sphere and retrieved back as a lemon at the North Pole to complete a closed geodesical trajectory on the Poincaré sphere. Depending on the trajectory, it is shown that the lemons (stars) acquire different amounts of the Pancharatnam phase, attributable to the amount of rotation in the SOP pattern of the lemons (stars).

Generation of V-point polarization singularity lattices

V-points normally do not occur in generic light fields as compared to C-points and L-lines. In structured optical fields, simultaneous existence of C-points, V-points and L-lines can be engineered in lattice forms. But lattices consisting only of V-points have not been realized so far. In this paper we demonstrate creation of lattices of V-point polarization singularities with translational periodicity. These lattice structures are obtained by the interference of four (six) linearly polarized plane waves arranged in symmetric umbrella geometry. The state of polarization of each beam is controlled by an S-waveplate. Since in a periodic lattice of polarization singularities the net charge in a unit cell is zero, the lattices are populated with positive and negative index V-point singularities. All the first order degenerate states of V-point singularities can be realized in the same setup by selective excitation of the S-waveplate.