Detection of degenerate Stokes index states

Taxonomy of hybridly polarized Stokes vortex beams

Structured beams carrying topological defects, namely phase and Stokes singularities, have gained extensive interest in numerous areas of optics. The non-separable spin and orbital angular momentum states of hybridly polarized Stokes singular beams provide additional freedom for manipulating optical fields. However, the characterization of hybridly polarized Stokes vortex beams remains challenging owing to the degeneracy associated with the complex polarization structures of these beams. In addition, experimental noise factors such as relative phase, amplitude, and polarization difference together with beam fluctuations add to the perplexity in the identification process. Here, we present a generalized diffraction-based Stokes polarimetry approach assisted with deep learning for efficient identification of Stokes singular beams. A total of 15 classes of beams are considered based on the type of Stokes singularity and their associated mode indices. The resultant total and polarization component intensities of Stokes singular beams after diffraction through a triangular aperture are exploited by the deep neural network to recognize these beams. Our approach presents a classification accuracy of 98.67% for 15 types of Stokes singular beams that comprise several degenerate cases. The present study illustrates the potential of diffraction of the Stokes singular beam with polarization transformation, modeling of experimental noise factors, and a deep learning framework for characterizing hybridly polarized beams.

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.

Self-referenced interferometry for single-shot detection of vector-vortex beams

Vector-vortex (VV) beams are of significant interest for various applications. There have been substantial efforts toward developing a fast and efficient method for the characterization of generated VV beams which is crucial for their usage. Polarimetric approaches are commonly used to identify unknown VV beams but require multiple intensity recordings. This paper demonstrates a technique to detect VV beams and identify their parameters using the concept of self-referenced interferometry. The approach uses a single recorded interferogram to determine the beam parameters that allow rapid detection. The method even enables detection of VV beams having high-order optical vortices.

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.

Production of orbital angular momentum states of optical vortex beams using a vortex half-wave retarder with double-pass configuration

Higher orders of orbital angular momentum states (OAMs) of light have been produced with a double-pass configuration through a zero-order vortex half-wave retarder (VHWR). This double-pass technique can reduce the number of VHWR plates used, thus reducing costs. The OAM states of the vortex beams are identified by the near-field Talbot effect. Polarization dependence of the vortex states can also be demonstrated with this VHWR using Talbot effect. Without using the Talbot patterns, this effect of the polarization on the vortex beam can not be recognized. A theoretical validation has also been provided to complement the experimental results. Our study gives an improved understanding of this approach to use a VHWR plate.

Sharp Focusing of a Hybrid Vector Beam with a Polarization Singularity

The key result of this work is the use of the global characteristics of the polarization singularities of the entire beam as a whole, rather than the analysis of local polarization, Stokes and Poincare–Hopf indices. We extend Berry’s concept of the topological charge of scalar beams to hybrid vector beams. We discuss tightly focusing a new type of nth-order hybrid vector light field comprising n C-lines (circular polarization lines). Using a complex Stokes field, it is shown that the field polarization singularity index equals n/2 and does not preserve in the focal plane. The intensity and Stokes vector components in the focal plane are expressed analytically. It is theoretically and numerically demonstrated that at an even n, the intensity pattern at the focus is symmetrical, and instead of C-lines, there occur C-points around which axes of polarization ellipses are rotated. At n = 4, C-points characterized by singularity indices 1/2 and ‘lemon’-type topology are found at the focus. For an odd source field order n, the intensity pattern at the focus has no symmetry, and the field becomes purely vectorial (with no elliptical polarization) and has n V-points, around which linear polarization vectors are rotating.

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.