Flattop focusing with full Poincaré beams under low numerical aperture illumination

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.

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.

High-resolution, wavefront-sensing, full-field polarimetry of arbitrary beams using phase retrieval

Recent advances in structured illumination are enabling a wide range of applications from imaging to metrology, which can benefit from advanced beam characterization techniques. Solving uniquely for the spatial distribution of polarization in a beam typically involves the use of two or more polarization optics, such as a polarizer and a waveplate, which is prohibitive for some wavelengths outside of the visible spectrum. We demonstrate a technique that circumvents the use of a waveplate by exploiting extended Gerchberg-Saxton phase retrieval to extract the phase. The technique enables high-resolution, wavefront-sensing, full-field polarimetry capable of solving for both simple and exotic polarization states, and moreover, is extensible to shorter wavelength light.

Polarimetric method of generating full Poincaré beams within a finite extent

A novel polarimetric method of generating a variety of Poincaré beams such as half Poincaré beams and full Poincaré beams using doubly inhomogeneous wave plates (d-plates) is proposed. In this method, every input state of polarization (SoP) through such a d-plate generates a unique Poincaré beam, thereby giving access to a potentially infinite number of them. Furthermore, the generation of full Poincaré beams is presented here as an instance of the geometrical problem of mapping the surface of a sphere onto a plane, and this insight allows one to design d-plates that convert the input SoP to every possible SoP, within a finite region of the beam. A gadget composed of three singly inhomogeneous wave plates for an equivalent realization of these d-plates is also presented.

Flexibly modulated Poincaré sphere vector optical field in input and focal planes

We theoretically design and experimentally generate the flexibly modulated Poincaré sphere vector optical field (PS-VOF), which can be constructed by flattening the Poincaré sphere surface. This new kind of PS-VOF provides additional degrees of freedom to modulate the spatial structure of polarization based on Poincaré sphere. The focal property of the PS-VOF is further studied, and we focus on studying the polarization coverage of the Poincaré sphere in the focal plane. In focusing process, the conversion and annihilation of spin angular momentum are presented. In addition, when the proportion of right-handed polarizations from the northern hemisphere of the Poincaré sphere satisfies Golden ratio (0.618) in the input plane, a full PS-VOF with high quality can be achieved in the focal plane. We hope this study of PS-VOF in both input and focal planes can enrich the family of VOFs, provide a new avenue in studying VOFs based on the Poincaré sphere, and can be potentially applied in the regions with sensitivity to polarizations.

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.

Unitary transformation for Poincaré beams on different parts of Poincaré sphere

We construct an experimental setup, consisting of conical refraction transformation in two biaxial cascade crystals and 4f-system, to realize Unitary transformation of light beam and the manipulation of Poincaré beams on the different parts of Poincaré sphere. The spatial structure of the polarization can be controlled by changing the polarization of the incident beam or rotating the angle between these two crystals. The beams with different SoPs covering the full-Poincaré sphere, part-Poincaré sphere and one point on the sphere are generated for the different angles between crystals. The Unitary transformation of light beam is proposed in the experiment with the invariant intensity distribution. Subsequently, the spin angular momentum is derived from the distribution of polarization measured in our experiment. Moreover, the conversion between orbital angular momentum and spin angular momentum of light beam is obtained by changing the angle between crystals. And the conversion progress can also be influenced by the polarization of incident beam. We realized the continuous control of the spatial structure of the angular momentum density, which has potential in the manipulation of optical trapping systems and polarization-multiplexed free-space optical communication.

Synthesis and characterization of non-uniformly totally polarized light beams: tutorial

Polarization of a light beam is traditionally studied under the hypothesis that the state of polarization is uniform across the transverse section of the beam. In such a case, if the paraxial approximation is also assumed, the propagation of the beam reduces to a scalar problem. Over the last few decades, light beams with spatially variant states of polarization have attracted great attention, due mainly to their potential use in applications such as optical trapping, laser machining, nanoscale imaging, polarimetry, etc. In this tutorial, an introductory treatment of non-uniformly totally polarized beams is given. Besides a brief review of some useful parameters for characterizing the polarization distribution of such beams across transverse planes, from both local and global points of view, several methods for generating them are described. It is expected that this tutorial will serve newcomers as a starting point for further studies on the subject.

Nonlinear frequency conversion and manipulation of vector beams

Vector beams have been extensively investigated in recent years because of their fascinating vector character across the beam transverse section, which is demonstrated to be useful for optical micro-manipulation, optical micro-fabrication, optical communication, single molecule imaging, and so on. To date, it is still a challenge to realize nonlinear frequency conversion and manipulation of such vector beams because of the polarization sensitivity in most nonlinear processes. Here, for the first time, to the best of our knowledge, we generate second-harmonic vector beams by using three-wave mixing processes in our experiment, which occur in two orthogonally placed nonlinear crystals, and the vector property is recognized by using a Glan-Taylor polarizer. This nonlinear frequency conversion process enables vector beams to be obtained at new wavelengths, and opens up new possibilities for all-optical switching and manipulation of vector beams.

Classical and quantum analysis of propagation invariant vector flat-top beams

Laser beams with a near uniform intensity profile, such as flat-top and super-Gaussian beams, have found many applications, particularly in laser materials processing. Unfortunately such beams are not eigenmodes of free-space and, thus, alter their intensity profile during propagation. This may be overcome by creating vector flat-top beams. Here, we exploit the polarization dependent efficiency of spatial light modulators to create a vector flat-top beam that maintains its intensity profile and vector nature during propagation. We apply a holistic classical and quantum toolkit to analyze the dynamics of the vector state during propagation and demonstrate the versatility of these beams in an optical trapping and tweezing application. Our simple generation approach and holistic analysis toolbox will appeal to an audience who wish to employ these beams in a variety of applications.

Focus shaping and optical manipulation using highly focused second-order full Poincaré beam

Generation of vectorial optical fields with arbitrary polarization distribution is of great interest in plenty of applications. In this work, we propose and experimentally demonstrate the generation of a second-order full Poincaré (FP) beam and its application in two-dimensional (2D) flattop beam shaping with spatially variant polarization under a high numerical aperture focusing condition. In addition, the force mechanism of the focal field with 2D flattop beam profile is numerically studied, demonstrating the feasibility to trap a dielectric Rayleigh particle in three-dimensional space. The results show that the additional degree of freedom provided by the FP beam allows one to control the spatial structure of polarization, to engineer the focusing field, and to tailor the optical force exerted on a dielectric Rayleigh particle. The findings reported in the work may find useful applications in laser micromachining, optical trapping, and optical assembly.

Scattering of Poincaré beams: polarization speckles

Polarization speckle is a fine granular light pattern having spatially varying random polarization profile. We generate these speckle patterns by using the scattering of Poincaré beams, a special class of vector vortex beams, through a ground glass plate. Here, the Poincaré beams are generated using a polarization sensitive spatial light modulator displaying an on-axis hologram corresponding to an optical vortex phase profile. The different inhomogeneities of the rough surface experience different polarizations, which control the ability for scattered waves to interfere at the detection plane and causes a spatially varying polarization profile. We experimentally determined the spatial variation of local degree of polarization and orientation of the polarization ellipse for these speckle patterns from the Stokes analysis. We also determined the size of scalar speckles using the auto-correlation function of Stokes parameter S₀ and the size of polarization speckles using the sum of auto-correlation functions of remaining three Stokes parameters. We found that the change in scalar speckle size with the index of the vector beam is very small and of the order of 1 pixel size of the camera but the size of polarization speckles decreases with the increase in index of the vector beam.

Generation of vectorial optical fields with slot-antenna-based metasurface

A transmission-type metasurface composed of carefully designed rectangular slot antennas for the generation of vectorial optical fields is proposed and demonstrated. Acting as local linear polarizers, these slot antennas enable the spatial modulation of optical fields in amplitude, phase, and polarization for the cross-polarized component of the scattered field. As an illustration, a metasurface capable of forming a radially polarized scattered field with specific vectorial beam patterns with appropriate excitation at normal incidence is designed, fabricated, and tested. The radially polarized scattered field is designed to be further tightly focused by a high numerical aperture objective lens in order to obtain a uniform longitudinally polarized optical needle field along the propagation direction. Characterization experiments demonstrate that its overall extinction ratio satisfies the amplitude modulation requirement, and a corresponding π phase modulation is realized as proposed.

Experimental verification of significant reduction of turbulence-induced scintillation in a full Poincaré beam

It is theoretically predicted in [Opt. Lett.37, 1553 (2012)] that a full Poincaré (FP) beam can significantly reduce turbulence-induced scintillation. In this paper, we propose a method for synthesizing a FP beam for different beam orders and report experimental generation of the first-, second- and third-order FP beams. Furthermore, we carry out experimental measurement of the scintillation index of a FP beam passing through thermally induced turbulence. It is demonstrated that the FP beam indeed can significantly reduce the scintillation index compared to a Gaussian beam under certain conditions. Our results will be useful in long-distance free-space optical communications.

Super-Gaussian conical refraction beam

We demonstrate the transformation of Gaussian input beams into super-Gaussian beams with a quasi flat-top transverse profile by means of the conical refraction phenomenon by adjusting the ratio between the ring radius and the waist radius of the input beam to 0.445. We discuss the beam propagation of the super-Gaussian beam and show that it has a confocal parameter three times larger than the one that would be obtained from a Gaussian beam. The experiments performed with a KGd(WO₄)₂ biaxial crystal are in good agreement with the theoretical predictions.

Orbital angular momentum of optical vortices from power measurements and the cross-correlation function

We show that the complex-amplitude cross-correlation function between two beams can be obtained by the global Stokes parameters. We apply this approach to determine the topological charge of a Laguerre-Gaussian (LG) beam by performing power measurements only. Additionally, we study the connection of the cross-correlation function with the degree of polarization for nonuniformly polarized beams, and we obtain closed-form expressions of the cross correlation for LG vector modes and the generalized full Poincaré beams.

Demonstration of flat-top focusing under radial polarization illumination

We experimentally demonstrate the generation of a flat-top intensity distribution using a radially polarized vector beam. Our approach uses higher numerical aperture focusing than what has been previously reported for a single, fixed, vector beam. In addition, the flat-top focus generated in our scheme exhibits a polarization gradient along the radial coordinate in the focal volume, with an on-axis longitudinal field component that persists over 2λ, which is a stark difference from conventional flat-top fields, which exhibit intensity profiles that are uniformly polarized. Our experimental results are found to be in good agreement with the theoretical prediction.

Vectorial optical field generator for the creation of arbitrarily complex fields

Generation of vectorial optical fields with complex spatial distribution in the cross section is of great interest in areas where exotic optical fields are desired, including particle manipulation, optical nanofabrication, beam shaping and optical imaging. In this work, a vectorial optical field generator capable of creating arbitrarily complex beam cross section is designed, built and tested. Based on two reflective phase-only liquid crystal spatial light modulators, this generator is capable of controlling all the parameters of the spatial distributions of an optical field, including the phase, amplitude and polarization (ellipticity and orientation) on a pixel-by-pixel basis. Various optical fields containing phase, amplitude and/or polarization modulations are successfully generated and tested using Stokes parameter measurement to demonstrate the capability and versatility of this optical field generator.

Generating and measuring nondiffracting vector Bessel beams

Nondiffracting vector Bessel beams are of considerable interest due to their nondiffracting nature and unique high-numerical-aperture focusing properties. Here we demonstrate their creation by a simple procedure requiring only a spatial light modulator and an azimuthally varying birefringent plate, known as a q-plate. We extend our control of both the geometric and dynamic phases to perform a polarization and modal decomposition on the vector field. We study both single-charged Bessel beams as well as superpositions and find good agreement with theory. Since we are able to encode nondiffracting modes with circular polarizations possessing different orbital angular momenta, we suggest these modes will be of interest in optical trapping, microscopy, and optical communication.

Compact flattop laser beam shaper using vectorial vortex

In this paper, we demonstrate a compact flattop beam shaper to realize two-dimensional flattop focus through generating a second order full Poincaré beam. Liquid crystal material is used in the device as the voltage-dependent birefringent material to provide appropriate phase retardation modulation. The beam shaper is fabricated and tested. Experimental results show that high quality flattop profiles can be obtained with steep edge roll-off. The tolerance of different input beam sizes of the beam shaper is also verified in the experimental demonstration.

Optical forces on submicron particles induced by full Poincaré beams

In this paper, we have considered the optical forces acting on submicron particles induced by arbitrary-order full Poincaré (FP) beams. Different from the traditional scalar beams, the optical forces of the FP beams include three contributions: the scattering, gradient, and curl forces. The last contribution is due to both the vectorial properties of the FP beams' polarization and the rotating phase structure of the FP beams. We analytically derive all components of the optical forces of the FP beams acting on Rayleigh particles. The numerical results show that the optical curl force is very significant to the absorbing Rayleigh particles, and it has the same order with the scattering force. The total vortex force fields and their trapping effects of different order FP beams on the absorbing dielectric and metallic Rayleigh particles are discussed in detail. Our results may stimulate further investigations on the trapping effect of various vector-vortex beams on submicron or nanometer sized objects.

Full Poincaré beams II: partial polarization

Optical fields whose coherence and/or polarization properties appear to change under propagation have intrigued researchers for many years. We describe and experimentally demonstrate a class of optical fields whose polarization content at any transverse plane spans a disk-like region within the Poincaré sphere. When examined through a paraxial focal region, the disk rotates under propagation, spanning all possible states of polarization. We map the change in Stokes parameters through focus for each case, comparing experiment with the theoretical predictions.