Robust laser beam engineering using polarization and angular momentum diversity

Twin-stagnation-free phase retrieval with vortex phase illumination

The recovery of a complex-valued exit wavefront from its Fourier transform magnitude is challenging due to the stagnation problems associated with iterative phase retrieval algorithms. Among the various stagnation artifacts, the twin-image stagnation is the most difficult to address. The upright object and its inverted and complex-conjugated twin correspond to the identical Fourier magnitude data and hence appear simultaneously in the iterative solution. We show that the twin stagnation problem can be eliminated completely if a coherent beam with charge-1 vortex phase is used for illumination. Unlike the usual plane wave illumination case, a charge-1 vortex illumination intentionally introduces an isolated zero near the zero spatial frequency region, where maximal energy in the Fourier space is usually concentrated for most natural objects. The early iterations of iterative phase retrieval algorithms are observed to develop a clockwise or anti-clockwise vortex in the vicinity of this isolated zero. Once the Fourier transform of the solution latches onto a specific vortex profile in the neighborhood of this intentionally introduced intensity zero in early iterations, the solution quickly adjusts to the corresponding twin (upright or inverted) and further iterations are not observed to bring the other twin into the reconstruction. Our simulation studies with the well-known hybrid input-output (HIO) algorithm show that the solution always converges to one of the twins within a few hundred iterations when vortex phase illumination is used. Using a clockwise or anti-clockwise vortex phase as an initial guess is also seen to deterministically lead to a solution consisting of the corresponding twin. The resultant solution still has some faint residual artifacts that can be addressed via the recently introduced complexity guidance methodology. There is an additional vortex phase in the final solution that can simply be subtracted out to obtain the original test object. The near guaranteed convergence to a twin-stagnation-free solution with vortex illumination as described here is potentially valuable for deploying practical imaging systems that work based on the iterative phase retrieval algorithms.

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.

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.

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.

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.

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.

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.

Polarization singularity index sign inversion by a half-wave plate

Inhomogeneous polarization distributions can host polarization singularities such as lemons, monstars, stars, flowers, spider webs, and higher-order C-points in optical beams. Singularities in ellipse fields are characterized by a C-point index and singularities in vector fields by the Poincare-Hopf index. These singularities can be generated by diffractive or interference methods. In this paper, we show that a half-wave plate (HWP) can be used for polarization singularity index sign inversion. The result presented here is powerful, and it shows the importance of a HWP in the study of polarization singularities. The HWP affects the entire state of polarization (SOP) distribution in the index sign inversion process. The concomitant global change of the SOP distribution happens in an orderly fashion to change the polarity of the polarization singularity index. This method of changing the polarity of the polarization singularity index by a HWP holds good both for ellipse fields as well as for vector fields.