Beam quality measure for vector beams

Generation of cylindrical vector modes via astigmatic mode conversion

In this work, we propose and demonstrate experimentally a compact technique for generating cylindrical vector beams based on a Michelson interferometer and a π-astigmatic mode converter. The latter is required to invert the topological charge of higher-order Laguerre-Gauss (LG) beams. Our proposed technique generalizes the use of astigmatic mode conversion, commonly associated only with scalar beams, to vector beams with a non-homogeneous polarization distribution. We anticipate that many applications based on Michelson interferometers will benefit from the unique properties of vector beams.

Multichannel focused higher-order Poincaré sphere beam generation based on a dielectric geometric metasurface

Focused vector beams (VBs) are important topic in the areas of light field manipulation. Geometric metasurfaces provide a convenient platform to facilitate the generation of focused VBs. In this study, we propose a dielectric geometric metasurface to generate multichannel focused higher-order Poincaré sphere (HOP) beams. With identical meta-atoms of half-wave plate, the metasurface comprises two sub-metasurfaces, and each of them includes two sets of rings related to Fresnel zones. For meta-atoms on each set of rings, the hyperbolic geometric phase profile is configured so that the mirror-symmetrical position-flip of the off-axis focal point is enabled under the chirality switch of the illuminating circular polarization. With the design of helical geometric phase profiles for the two sets of rings, a sub-metasurface generate two HOP beams at the symmetrical two focal points. The performance of the two sub-metasurfaces enables the metasurface with four sets of rings to generate the array of four HOP beams. The proposed method was validated by theoretical analyses, numerical simulation and experimental conduction. This research would be significant in miniaturizing and integrating optical systems involving applications of VB generations and applications.

Measuring the Optical Concurrence of Vector Beams with an Atomic-State Interferometer

We investigate the transmission of vector beams, correlated in their polarization and spatial degrees of freedom, through cold atoms in the presence of a transverse magnetic coupling field. The resulting phase-dependent dynamics allow us to imprint the spatially varying polarization of a vector beam onto atomic spin polarizations, thereby establishing a direct link between optical space-polarization correlations and atomic-state interference. We find that the resulting absorption profiles show interference fringes whose modulation strength is given by the squared concurrence of the vector beam, letting us identify optical concurrence from a single absorption image. We expect impact across a diverse range of applications, including spintronics, quantum memories, metrology, and clocks.

Quantum-inspired protocol for measuring the degree of similarity between spatial shapes

We put forward and demonstrate experimentally a quantum-inspired protocol that allows us to quantify the degree of similarity between two spatial shapes embedded in two optical beams without the need to measure the amplitude and phase across each beam. Instead the sought-after information can be retrieved by measuring the degree of polarization of the combined optical beam, a measurement that is much easier to implement experimentally. The protocol makes use of non-separable optical beams, whose main trait is that different degrees of freedom (polarization and spatial shape here) cannot be described independently. One important characteristic of the method described is that it allows us to compare two unknown spatial shapes.

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.

Vector beam bending via a polarization gradient

We propose, analyze and demonstrate experimentally an entirely new optical effect in which the centroid of a coherent optical beam can be designed to propagate along a curved trajectory in free space by tailoring the spatial distribution of linear polarization across the transverse beam profile. Specifically, a non-zero spatial gradient of second order or higher in the linear state of polarization is shown to cause the beam centroid to "accelerate" in the direction transverse to the direction of propagation. The effect is confirmed experimentally using spatial light modulation to create the distribution in linear polarization and then measuring the transverse location of the beam profile at varying propagation distances. The observed displacement of the beam centroid is shown to closely match the theory out to 34m propagation distance.

Tailoring ultra-broadband vector beams via programming the electric field vector of light

With spatially inhomogeneous polarization, vector beam (VB) has created substantial opportunities in both optics and photonics. However, the limited spectral bandwidth of VB generator hinders further advances for higher level of integration and functionality. Here, an innovative approach of programming the electric field vector of light is proposed to tailor arbitrary ultra-broadband VBs, in parallel among an unprecedented wavelength range over 1000 nm covering the visible and NIR band. We demonstrate the twisted nematic liquid crystals (TNLCs), specifically arranged in-situ by a dynamic programmable photopatterning, enable to directly manipulate the electric field vector of transmitted light into the VB as desired. Furthermore, the electrical responsiveness of TNLCs yields a dynamic multifunctionality between the VB and Gaussian beam. We anticipate this ultra-broadband VB generator would be promising for a variety of applications like optical manipulation, super-resolution imaging, and integrated optical communication system.

Single-shot characterization of vector beams by generalized measurements

Vector vortex beams, featuring independent spatial modes in orthogonal polarization components, offer an increase in information density for emerging applications in both classical and quantum communication technology. Recent advances in optical instrumentation have led to the ability of generating and manipulating such beams. Their tomography is generally accomplished by projection measurements to identify polarization as well as spatial modes. In this paper we demonstrate spatially resolved generalized measurements of arbitrary vector vortex beams. We perform positive operator valued measurements (POVMs) in an interferometric setup that characterizes the vector light mode in a single-shot. This offers superior data acquisition speed compared to conventional Stokes tomography techniques, with potential benefits for communication protocols as well as dynamic polarization microscopy of materials.

Modal description of paraxial structured light propagation: tutorial

Here we outline a description of paraxial light propagation from a modal perspective. By decomposing the initial transverse field into a spatial basis whose elements have known and analytical propagation characteristics, we are able to analytically propagate any desired field, making the calculation fast and easy. By selecting a basis other than that of planes waves, we overcome the problem of numerical artifacts in the angular spectrum approach and at the same time are able to offer an intuitive understanding for why certain classes of fields propagate as they do. We outline the concept theoretically, compare it to the numerical angular spectrum approach, and confirm its veracity experimentally using a range of instructive examples. We believe that this modal approach to propagating light will be a useful addition to the toolbox for propagating optical fields.

Laser-Material Interactions of High-Quality Ultrashort Pulsed Vector Vortex Beams

Diffractive multi-beams based on 1 × 5 and 2 × 2 binary Dammann gratings applied to a spatial light modulator (SLM) combined with a nanostructured S-wave plate have been used to generate uniform multiple cylindrical vector beams with radial and azimuthal polarizations. The vector quality factor (concurrence) of the single vector vortex beam was found to be C = 0.95 ± 0.02, hence showing a high degree of vector purity. The multi-beams have been used to ablate polished metal samples (Ti-6Al-4V) with laser-induced periodic surface structures (LIPSS), which confirm the polarization states unambiguously. The measured ablation thresholds of the ring mode radial and azimuthal polarizations are close to those of a Gaussian mode when allowance is made for the expected absolute intensity distribution of a ring beam generated from a Gaussian. In addition, ring mode vortex beams with varying orbital angular momentum (OAM) exhibit the same ablation threshold on titanium alloy. Beam scanning with ring modes for surface LIPSS formation can increase micro-structuring throughput by optimizing fluence over a larger effective beam diameter. The comparison of each machined spot was analysed with a machine learning method—cosine similarity—which confirmed the degree of spatial uniformity achieved, reaching cosθ > 0.96 and 0.92 for the 1 × 5 and 2 × 2 arrays, respectively. Scanning electron microscopy (SEM), optical microscopy and white light surface profiling were used to characterize and quantify the effects of surface modification.

Digital Stokes polarimetry and its application to structured light: tutorial

Stokes polarimetry is a mature topic in optics, most commonly performed to extract the polarization structure of optical fields for a range of diverse applications. For historical reasons, most Stokes polarimetry approaches are based on static optical polarization components that must be manually adjusted, prohibiting automated, real-time analysis of fast changing fields. Here we provide a tutorial on performing Stokes polarimetry in an all-digital approach, exploiting a modern optical toolkit based on liquid-crystal-on-silicon spatial light modulators and digital micromirror devices. We explain in a tutorial fashion how to implement two digital approaches, based on these two devices, for extracting Stokes parameters in a fast, cheap, and dynamic manner. After outlining the core concepts, we demonstrate their applicability to the modern topic of structured light, and highlight some common experimental issues. In particular, we illustrate how digital Stokes polarimetry can be used to measure key optical parameters such as the state of polarization, degree of vectorness, and intra-modal phase of complex light fields.

Modal analysis of structured light with spatial light modulators: a practical tutorial

A quantitative analysis of optical fields is essential, particularly when the light is structured in some desired manner, or when there is perhaps an undesired structure that must be corrected for. A ubiquitous procedure in the optical community is that of optical mode projections-a modal analysis of light-for the unveiling of amplitude and phase information of a light field. When correctly performed, all the salient features of the field can be deduced with high fidelity, including its orbital angular momentum, vectorial properties, wavefront, and Poynting vector. Here, we present a practical tutorial on how to perform an efficient and effective optical modal decomposition, with emphasis on holographic approaches using spatial light modulators, highlighting the care required at each step of the process.

Polarisation-insensitive generation of complex vector modes from a digital micromirror device

In recent time there has been an increasing amount of interest in developing novel techniques for the generation of complex vector light beams. Amongst these, digital holography stands out as one of the most flexible and versatile with almost unlimited freedom in the generation of scalar and complex vector light fields featuring arbitrary polarisation distributions and spatial profiles. In this manuscript we put forward a novel technique, which relies on the polarisation-insensitive attribute of Digital Micromirror Devices (DMDs). In a prior work where we outlined a new detection scheme based on Stokes projections we alluded to this technique. Here we outline the creation process in full, providing all the details for its experimental implementation. In addition, we fully characterise the performance of such technique, providing a quantitative analysis of the generated modes. To this end, we experimentally reconstruct the transverse polarisation distribution of arbitrary vector modes and compare the ellipticity and flatness of the polarisation ellipses with theoretical predictions. Further, we also generate vector modes with arbitrary degrees of non-separability and determine their degree of concurrence comparing this to theoretical predictions.

Gaussian spatial-polarization entanglement in a folded Mach-Zehnder interferometer

Gaussian spatial-polarization entanglement in a coherent vectorial paraxial light field is studied. Detection of spatial-polarization entanglement through fringe movement on rotation of a linear polarizer, with the light field passing through the polarizer, is outlined. The fringe movement is shown to be a sufficient condition for the detection of spatial-polarization entanglement in coherent paraxial vector light fields. Two Gaussian light fields with a small relative tilt but with significant spatial overlap and with orthogonal polarizations are shown to possess close to 1 ebit of spatial-polarization entanglement. Tunable Gaussian spatial-polarization entanglement is experimentally demonstrated in a folded Mach-Zehnder interferometer.

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.

Comparison of aplanatic and real lens focused spots in the framework of the local plane interface approximation

Tight focusing of various beams is widely used for microscopy, optical tweezers, lithography, optical storage, etc. In literature, the investigation of the tightly focused spot is very often based on an ideal lens, which is aplanatic, by the Debye-Wolf integral. In this work, we formulate the aplanatic lens by interpreting the Gaussian reference sphere as a fictitious surface. In this manner, the formulation of an ideal lens is analogous to the one of a real lens by local plane interface approximation, which is well known. It is straightforward to interpret. And furthermore, we compare the tight focusing of differently polarized beams via ideal and real lenses with circular and annular apertures. We find the focal spot by a well-designed real lens is in good agreement with that of the ideal lens in the case of perfect alignment. But the appearance of misalignment distorts the focal spot. The deformed focal spot is more sensitive in the case of the annular aperture compared with the circular aperture. It is in good agreement with the experimental results in literature. An investigation of the tolerance of misalignment of a specific lens system is also performed.

Beyond the display: phase-only liquid crystal on Silicon devices and their applications in photonics [Invited]

Existing for almost four decades, liquid crystal on Silicon (LCOS) technology is rapidly growing into photonic applications. We review the basics of the technology, from the wafer to the driving solutions, the progress over the last decade and the future outlook. Furthermore we review the most exciting industrial and scientific applications of the LCOS technology.

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

DD-OFDM transmission over few-mode fiber based on direct vector mode multiplexing

The fiber vector eigenmode based mode division multiplexing (VMDM) transmission over few-mode fiber (FMF) with the 1st-order cylinder vector beams (CVBs) has been demonstrated. The performances of generated CVB using q-plate (QP) have been characterized before and after transmission over the FMF respectively based on the high-order Poincaré sphere model and polarization grating (PG). The measured minimum mode isolations between the two CVBs (TM₀₁ and TE₀₁ modes) of the used 4-mode FMF are about 16.8 dB after transmitting over 5 m and 12.5 dB over 100 m respectively. Then the dual-vector-mode-multiplexed transmissions over FMF of 96 Gb/s with length of 5m and 48 Gb/s of 100 m have been realized in combination with the modulation of direct-detection (DD) orthogonal-frequency-division-multiplexing (OFDM) without using multiple-input multiple-output (MIMO) digital signal processing (DSP). The experimental results indicate that the CVB-based technology could find the potential in large-capacity short-reach optical interconnects.

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.

Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters

Spatial modes have received substantial attention over the last decades and are used in optical communication applications. In fiber-optic communications, the employed linearly polarized modes and phase vortex modes carrying orbital angular momentum can be synthesized by fiber vector eigenmodes. To improve the transmission capacity and miniaturize the communication system, straightforward fiber vector eigenmode multiplexing and generation of fiber-eigenmode-like polarization vortices (vector vortex modes) using photonic integrated devices are of substantial interest. Here, we propose and demonstrate direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters. By exploiting vector vortex modes (radially and azimuthally polarized beams) generated from silicon microring resonators etched with angular gratings, we report data-carrying fiber vector eigenmode multiplexing transmission through a 2-km large-core fiber, showing low-level mode crosstalk and favorable link performance. These demonstrations may open up added capacity scaling opportunities by directly accessing multiple vector eigenmodes in the fiber and provide compact solutions to replace bulky diffractive optical elements for generating various optical vector beams.

Entanglement beating in free space through spin-orbit coupling

It is well known that the entanglement of a quantum state is invariant under local unitary transformations. This rule dictates, for example, that the entanglement of internal degrees of freedom of a photon remains invariant during free-space propagation. Here, we outline a scenario in which this paradigm does not hold. Using local Bell states engineered from classical vector vortex beams with non-separable degrees of freedom, the so-called classically entangled states, we demonstrate that the entanglement evolves during propagation, oscillating between maximally entangled (purely vector) and product states (purely scalar). We outline the spin-orbit interaction behind these novel propagation dynamics and confirm the results experimentally, demonstrating spin-orbit coupling in paraxial beams. This demonstration highlights a hitherto unnoticed property of classical entanglement and simultaneously offers a device for the on-demand delivery of vector states to targets, for example, for dynamic laser materials processing, switchable resolution within stimulated emission depletion (STED) systems, and a tractor beam for entanglement.

Simultaneous generation of multiple vector beams on a single SLM

Complex vector light fields, classically entangled in polarization and phase, have become ubiquitous in a wide variety of research fields. This has triggered the demonstration of a wide variety of generation techniques. Of particular relevance are those based on computer-controlled devices due to their great flexibility. In particular, spatial light modulators have demonstrated their high capabilities to generate any vector beam, with various spatial profiles and polarization distributions. Here, we put forward a novel technique that exploits the superposition principle in optics to enable the simultaneous generation of many vector beams using a single digital hologram. As proof-of-principle, we demonstrated the simultaneous generation of sixteen vector vortex beams with various polarization distributions and spatial shapes on a single SLM, each with their own spatial shape and polarization distribution.

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.

Vector Beam Polarization State Spectrum Analyzer

We present a proof of concept for a vector beam polarization state spectrum analyzer based on the combination of a polarization diffraction grating (PDG) and an encoded harmonic q-plate grating (QPG). As a result, a two-dimensional polarization diffraction grating is formed that generates six different q-plate channels with topological charges from -3 to +3 in the horizontal direction, and each is split in the vertical direction into the six polarization channels at the cardinal points of the corresponding higher-order Poincaré sphere. Consequently, 36 different channels are generated in parallel. This special polarization diffractive element is experimentally demonstrated using a single phase-only spatial light modulator in a reflective optical architecture. Finally, we show that this system can be used as a vector beam polarization state spectrum analyzer, where both the topological charge and the state of polarization of an input vector beam can be simultaneously determined in a single experiment. We expect that these results would be useful for applications in optical communications.

Linearly polarized orbital angular momentum mode purity measurement in optical fibers

We presented a simple method for measuring the mode purity of linearly polarized orbital angular momentum (OAM) modes in optical fibers. The method is based on the analysis of OAM beam projections filtered by a polarizer. The amplitude spectrum and phase spectrum of a data ring derived from the beam pattern are obtained by Fourier transform. Then the coefficients of the mixed electric field expression can be determined and the mode purity can be obtained. The proposed method is validated and it is experimentally demonstrated in a two-mode fiber.

Arithmetic with q-plates

In this work we show the capability to form various q-plate equivalent systems using combinations of commercially available q-plates. We show operations like changing the sign of the q-value, or the addition and subtraction of q-plates. These operations only require simple combinations of q-plates and half-wave plates. Experimental results are presented in all cases. Following this procedure, experimental testing of higher and negative q-valued devices can be carried out using commonly available q-valued devices.