Synthesizing polarization singularity lattices using phase ramps.

In this paper, a novel methodology for generating polarization singularity lattices using ramp phase structures in a polarization interferometer is presented. By applying differential tilts to distinct regions within the wavefront using a spatial light modulator, a phase-discontinuity line separating the two regions is formed. During propagation along this line, phase vortices are formed at discrete points about which the phase difference on either side of the ramp is π. This wavefront with phase vortices is superimposed with a plane wave in orthogonal polarization in a polarization interferometer, giving rise to polarization singularities. A common-path polarization interferometer is constructed using a spatial light modulator to reduce errors and complexity. Polarization fringes instead of intensity fringes obtained in this interferometer host polarization singularities. Lattices made up of a linear chain of polarization singularities-unusually of the same index polarity-are found here. Experimental results corroborate the theoretical predictions. This study shows that singularities can be produced with non-spiral phase plates by using linear phase ramps. The method discussed in this paper may find potential applications in optical trapping and particle steering.

Evolution of coherence singularities in polarization singular beams.

The evolution of correlation singularities in partially coherent polarization singular beams (PC-PSBs) is investigated. Since PSBs are the superposition of two orthogonally polarized vortex beams, the occurrence of coherence singularities in PC-PSBs is strongly governed by the topological charge of the component vortex beams and the spatial coherence length. Coherence singularities appear in the form of ring dislocations in the modulus of the spectral degree of coherence (SDoC) profile, and the number of ring dislocations is equal to the higher value of the topological charge of the superposing vortex beam. Furthermore, the SDoC phase profile can be used to determine the polarity of a PC-PSB. The findings of the study could be valuable in various applications that rely on the spatial coherence of beams, such as free-space communication and imaging.

Detecting topological index of randomly scattered V-point singularities using Stokes correlations.

Topological defects in vector fields constitute polarization singularities that have numerous applications in classical and quantum optics. These beams are inhomogeneously polarized and are shown to self-heal under symmetric amplitude perturbations. Polarization singular beams are characterized using a singularity index that can be detected using Stokes polarimetry or other interferometric and diffraction approaches. However, the information about the singularity index is lost when these beams travel through random scattering media; this results in a spatially fluctuating polarization pattern known as polarization speckle. This paper proposes and experimentally demonstrates a new method to detect the topological index of these randomly scattered V-point singularities using higher-order Stokes correlations in a lensless condition. A detailed theoretical basis is developed, and the performance of the technique is demonstrated by retrieving the signature of polarization singularities with Poincaré-Hopf index |η|=1 and |η|=2. We also demonstrate that by studying the intensity-intensity correlations of the polarization speckle, it is possible to differentiate between different vector beams having the same magnitude as the Poincaré-Hopf index.

Coherence-induced depolarization effects in polarization singular beams.

We demonstrate theoretically and experimentally coherence-induced depolarization effects in generic and higher index polarization singular beams endowed with C-point (or V-point) polarization singularity. The irradiance profiles and degree of polarization (DoP) distributions are found to be governed by spatial coherence length, polarization singularity index, and orbital angular momentum (OAM) of the superposition states of the beams. On reducing the coherence length, the DoP distribution in the V-point deteriorates uniformly. In contrast, C-point beams resist depolarization exhibiting anti-depolarization around the central core of the beam due to the nonzero net OAM of the beam. Interestingly, the polarization vortex structure remains preserved on reducing the spatial coherence length.

Generation of Stokes singularities using polarization lateral shear interferometer.

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.

Investigation of partially coherent vector vortex beams with non-isotropic states of spatial correlation.

In this work, the far-field properties of non-isotropic partially coherent vector vortex beams (PCVVBs) are investigated both theoretically and experimentally. The term non-isotropic signifies that the spatial correlations between the parallel and orthogonal electric field components are distinguishable. It is found that self-orientation and shaping of intensity profile, correlation-induced polarization and depolarization are highly dependent on both the non-isotropic correlation parameters and Poincaré-Hopf index (PHI) of the beam. The simultaneous depolarization and polarization effects are due to the difference in the input correlation parameters that alter the state of polarization (SOP) and degree of polarization (DOP) distributions. The experimental results are in good agreement with the theoretical predictions. The distinguishability of correlation parameters at the source plane leads to significant changes on its intensity profile, DOP, and SOP distributions on far-field propagation, which may found potential applications in beam shaping, detecting and imaging atmospheric lidar, optical imaging and directional transportation where the self-rotation characteristic of beam plays an important role.

Young's double-slit experiment with vector vortex beams.

In this Letter, Young's double-slit experiment with vector vortex beams is investigated. We present the results for various Poincaré-Hopf index beams of this class considering all four major types. Polarization associated morphological changes in the far-field interference pattern are studied both theoretically and experimentally. The Fraunhofer pattern consists of lattices of polarization singularities of the generic type, located on a line, in a direction perpendicular to the slit. The number of linear lattices varies as a function of Poincaré-Hopf index η of the beam that is diffracted, and the number of intensity nulls occurring along the vertical line is equal to |η|.

Polarization singularity index determination by using a tilted lens.

The superposition of spin and orbital angular momentum states of light generates polarization singularities. By perturbing and disintegrating their component orbital angular momentum (OAM) states, the polarization singularity indices can be determined. The spatially varying polarization distribution of these beams possesses information about the helical wavefront structures of the component OAM states, although they have plane wavefronts. The polarization singular beam (PSB) is focused using a tilted lens, and the intensity distribution at a predicted position in the direction of propagation is used to determine the component OAM content in the beam. Astigmatism introduced by the tilt of the lens modulates the vortex beam to introduce intensity nulls in the propagated beam. We demonstrate by simulations and experiments the index determination of the V points and C points using a tilted lens. This method is effective in the index determination of V points and C points formed by the superposition of component scalar vortices having opposite-sign topological charges. The degeneracy of C points with the same Stokes indices can be lifted through this technique.

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 [Formula: see text] represents polarization azimuth [Formula: see text] distribution and the singularities present in it are polarization singularities. Therefore, the charge of the Stokes vortices depicted as Stokes index [Formula: see text] 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 for Stokes singularities: publisher's note.

This publisher's note contains corrections to Opt. Lett.45, 5136 (2020)OPLEDP0146-959210.1364/OL.394137.

Hybrid order Poincaré spheres for Stokes singularities.

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.

Coherence-induced polarization effects in vector vortex beams.

We demonstrate theoretically and experimentally coherence-induced polarization changes in higher-order vector vortex beams (VVBs) with polarization singularity. The prominent depolarization on decreasing the transverse correlation width in a focused partially coherent VVB provides a means to shape the intensity profile and degree of polarization (DOP) while preserving the polarization distribution. The intensity variation and DOP dip are found to be dependent on the polarization singularity index of the beam. Our results may provide an additional degree of freedom in myriad applications presently projected with VVBs.

Use of q-plate as a coupler.

A coupler is a device that allows interconversion of angular momentum of the optical beam among spin and orbital parts, without absorbing any angular momentum. In this paper, we demonstrate that a q-plate with q=1 can act as a coupler for any of the polarization distribution that can be represented by a point on a Poincare sphere (PS), or on a higher-order PS, or on a hybrid-order PS. A q-plate with any q-value can act as a coupler for polarization distribution that can be represented by an equatorial point on any of these spheres. It is also possible to find a q-plate with an appropriate q-value that can act as a creation or annihilation operator that raises or lowers the polarization singularity index. The q-plate being a coupler and made of half-wave plate segments, the singularity index change is concomitant with the helicity inversion of C-points. Interconversion of bright and dark C-points is possible by using a q-plate.

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.

Author Correction: Helicity dependent diffraction by angular momentum transfer.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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.

Propagation of converging polarization singular beams through atmospheric turbulence.

We report investigations on propagation of converging vector beams containing C-point and V-point polarization singularities through atmospheric turbulence. The C-point singularity is generated by superposition of the l=0 and l=1 orbital angular momentum (OAM) states, whereas the V-point singularity is generated by a superposition of the l=-1 and l=1 OAM states in orthogonal polarizations. The propagation of these beams through extended atmosphere is modeled by placing random phase screens along a 2 km propagation path. The random phase screens were generated using the FFT method with von Karman spectrum and Cn2=10-14 m-2/3. The quality of intensity profile of the focused vector beams after propagation through turbulence is assessed using the instantaneous signal-to-noise ratio and the on-axis scintillation index measurements. Our simulation results show that although both the C-point and V-point beams perform better than their scalar OAM components, C-point beams are seen to maintain much better beam intensity profile compared to the V-point beams. This observation is explained in terms of the OAM diversity of the individual polarization states and the correlation of their associated speckle patterns. The results presented here are important for engineering laser beams that can maintain a robust intensity profile on propagation through long-range atmospheric turbulence.

Helicity conservation in V-point diffraction.

In singular beams, topological charge is conserved during diffraction. Like scalar field diffraction, in vector field diffraction also, there are conserved quantities. A diffracting V-point disintegrates into a number of C-points of the same polarity in which the polarization singularity index is conserved. In this Letter, we show for the first time, to the best of our knowledge, that apart from the index, the helicity (handedness) is also conserved in V-point diffraction. Since V-point is devoid of any handedness, the helicity conservation entails that there is an equal number of opposite handed C-points in the diffracted field, which are interestingly also found to be orthogonal pairs. Further, coexistence of C-points of opposite handedness in the diffraction demands the presence of L-line, which is also shown. We experimentally demonstrate these by studying the diffraction phenomenon through two different types of apertures.

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.