Real-time Stokes polarimetry using a polarization camera.

This Lab Note introduces the "Stokes Camera," a simple experimental arrangement for real-time measurement of spatial amplitude and polarization and thus spatially resolved Stokes parameters. It uses a polarization sensitive camera and a fixed quarter-wave plate, providing a one-shot, digital solution for polarization measurement that is only limited by the frame rate of the camera and the computation speed of the provided code. The note also provides background information on relevant polarization theory and vector vortex beams, which are used as a demonstration of the device.

Low-cost printed holography for the generation of structured light.

Recently, the study of structured light fields has attracted great interest, which includes their generation and characterization techniques, as well as their application. Most of these techniques rely on the use of expensive devices, such as liquid crystal spatial light modulators or digital micromirror devices that also require specialized knowledge and software. In this work, we present a scheme for producing low-cost amplitude holograms for the generation of structured light fields. We demonstrate the feasibility of this technique by creating a variety of paraxial modes, such as the well-known Laguerre-Gaussian and Hermite-Gaussian beams. We also demonstrate the potential of our technique in solving the phase retrieval problem to generate 2D and 3D holographic images of objects. Finally, we compare our proposal with the typical generation techniques using digital micromirror devices. Our proposal will pave the path for the generation of structured light beams in more affordable ways for the application in undergrad laboratories.

Helico-conical vector beams.

In this work, we propose and demonstrate experimentally a new family of vector beams, the helico-conical vector beams (HCVBs), whose spatial degree of freedom is encoded in the helico-conical optical beams. We use Stokes polarimetry to study their properties and find that upon propagation their transverse polarization distribution evolves from nonhomogeneous to quasihomogeneous, such that even though their global degree of nonseparability remains constant, locally it decreases to a minimum value as z → ∞. We corroborated this quantitatively using the Hellinger distance, a novel metric for vectorness that applies to spatially disjoint vector modes. To the best of our knowledge, HCVBs are the second family of vector beams featuring this behavior, paving the way for applications in optical tweezing or information encryption.

Tunable longitudinal spin-orbit separation of complex vector modes.

Complex vector modes are opening burgeoning opportunities for a wide variety of applications and therefore the flexible manipulation of their various properties has become a topic of late. As such, in this Letter, we demonstrate a longitudinal spin-orbit separation of complex vector modes propagating in free space. To achieve this, we employed the recently demonstrated circular Airy Gaussian vortex vector (CAGVV) modes, which feature a self-focusing property. More precisely, by properly manipulating the intrinsic parameters of CAGVV modes, the strong coupling between the two constituting orthogonal components can be engineered to undergo a spin-orbit separation along the propagation direction. In other words, while one polarization component focuses at one plane, the other focuses at a different plane. Such spin-orbit separation, which we demonstrated by numerical simulations and corroborated experimentally, can be adjusted on-demand by simply changing the initial parameters of the CAGVV mode. Our findings will be of great relevance in applications such as optical tweezers, to manipulate micro- or nano-particles at two different parallel planes.

Observation of Anomalous Orbital Angular Momentum Transfer in Parametric Nonlinearity.

Orbital angular momentum (OAM) conservation plays an important role in shaping and controlling structured light with nonlinear optics. The OAM of a beam originating from three-wave mixing should be the sum or difference of the other two inputs because no light-matter OAM exchange occurs in parametric nonlinear interactions. Here, we report anomalous OAM transfer in parametric upconversion, in which a Hermite-Gauss mode signal interacts with a specially engineered pump capable of astigmatic transformation, resulting in Laguerre-Gaussian mode sum-frequency generation (SFG). The anomaly here refers to the fact that the pump and signal both carry no net OAM, while their SFG does. We reveal experimentally that there is also an OAM inflow to the residual pump, having the same amount of that to the SFG but with the opposite sign, and thus holds system OAM conservation. This unexpected OAM selection rule improves our understanding of OAM transfer among interacting waves and may inspire new ideas for controlling OAM states via nonlinear optics.

Experimental generation of arbitrary abruptly autofusing Circular Airy Gaussian vortex vector beams.

Complex vector modes represent a general state of light nonseparable in their spatial and polarization degrees of freedom, which have inspired a wide variety of novel applications and phenomena, such as their unexpected propagation behaviour. For example, they can propagate describing periodic polarization transitions, changing from one vector beam to another. Here, we put forward a novel class of vector modes with the capability to experience an abruptly autofocusing behaviour. To achieve such beams, we encode the spatial degree of freedom in the Circular Airy Gaussian vortex (CAGV) beams. We demonstrate the experimental generation of arbitrary CAGV vector beams and evince some of their properties, such as a rotation of intermodal phase. We anticipate that the fascinating properties of theses modes will prompt the development of novel applications associated to their autofocusing behaviour and polarization distribution.

Parametric upconversion of Ince-Gaussian modes.

The Ince-Gaussian (IG) mode, a recently discovered type of structured Gaussian beam, corresponds to eigenfunctions of the paraxial wave equation in elliptical coordinates. This propagation-invariant mode is of significance in various domains, in particular, its nonlinear transformation; however, there have been few relevant studies to date. In this Letter, we report the parametric upconversion of IG modes and associated full-field selection rule for the first time, to the best of our knowledge. We demonstrate that IG signals can be perfectly upconverted by a flattop-beam pump; in contrast, significant mode distortion occurred when using the most common Gaussian pump. Particular attention was given to the origin of the distortion, i.e., radial-mode degeneration induced by the sum-frequency generation excited by a Gaussian pump. This proof-of-principle demonstration has great significance in relevant areas, such as high-dimensional quantum frequency interfacing and upconversion imaging.

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.

All-digital Stokes polarimetry with a digital micromirror device.

Stokes polarimetry is widely used to extract the polarization structure of optical fields, typically from six measurements, although it can be extracted from only four. To measure the required intensities, most approaches are based on optical polarization components. In this work, we present an all-digital approach that enables a rapid measure of all four intensities without any moving components. Our method employs a polarization grating (PG) to simultaneously project the incoming mode into left- and right-circular polarized states, followed by a polarization-insensitive digital micromirror device (DMD), which digitally introduces a phase retardance for the acquisition of the remaining two polarization states. We demonstrate how this technique can be applied to measuring the SoP, vectorness, and intramodal phase of optical fields, without any moving components, and shows excellent agreement with theory, illustrating fast, real-time polarimetry.

Does the structure of light influence the speckle size?

It is well known that when a laser is reflected from a rough surface or transmitted through a diffusive medium, a speckle pattern will be formed at a given observation plane. An important parameter of speckle is its size, which for the case of homogeneous illumination, well-known relations for its computation have been derived. This is not the case for structured light beams of non-homogeneous intensity and phase distribution. Here, we propose and demonstrate, using Hermite- and Laguerre-Gaussian light modes, that the mean size of the speckle generated by these structured light beams can be measured assuming a homogeneous illumination. We further provide with mathematical expressions that relate the speckle size to the generalised definition of "spot size". To reinforce our assessment, we compare the mean speckle size generated by structured light modes with that generated by wave fronts of constant phase and amplitude and show that in both cases the mean speckle size is almost identical. Our findings reveal a fundamental property of speckle, which will be of great relevance in many speckle-based applications and will pave the way towards the development of novel applications.

Real-time Stokes polarimetry using a digital micromirror device.

Stokes polarimetry (SP) is a powerful technique that enables spatial reconstruction of the state of polarization (SoP) of a light beam using only intensity measurements. A given SoP is reconstructed from a set of four Stokes parameters, which are computed through four intensity measurements. Since all intensities must be performed on the same beam, it is common to record each intensity individually, one after the other, limiting its performance to light beams with static SoP. Here, we put forward a novel technique to extend SP to a broader set of light beams with dynamic SoP. This technique relies on the superposition principle, which enables the splitting of the input beam into identical copies, allowing the simultaneous measurement of all intensities. For this, the input beam is passed through a multiplexed digital hologram displayed on a polarization-insensitive Digital Micromirror Device (DMD) that grants independent and rapid (20 kHz) manipulation of each beam. We are able to reliably reconstruct the SoP with high fidelity and at speeds of up to 27 Hz, paving the way for real-time polarimetry of structured light.

In situ detection of a cooperative target's longitudinal and angular speed using structured light.

Laser remote sensing represents a powerful tool that enables the accurate measurement of the speed of moving targets. Crucially, most sensing techniques are two-dimensional (2D) and only enable direct determination of the speed along the line of sight. Here we put forward a novel three-dimensional technique that enables the direct and simultaneous measurement of both the longitudinal and angular speed of cooperative targets. This technique is based on the use of complex vector light beams, whose polarization and spatial degree of freedom are coupled in a non-separable way. We present evidence of our technique by performing a proof-of-principle experiment.

A vector holographic optical trap.

The invention of optical tweezers almost forty years ago has triggered applications spanning multiple disciplines and has also found its way into commercial products. A major breakthrough came with the invention of holographic optical tweezers (HOTs), allowing simultaneous manipulation of many particles, traditionally done with arrays of scalar beams. Here we demonstrate a vector HOT with arrays of digitally controlled Higher-Order Poincaré Sphere (HOPS) beams. We employ a simple set-up using a spatial light modulator and show that each beam in the array can be manipulated independently and set to an arbitrary HOPS state, including replicating traditional scalar beam HOTs. We demonstrate trapping and tweezing with customized arrays of HOPS beams comprising scalar orbital angular momentum and cylindrical vector beams, including radially and azimuthally polarized beams simultaneously in the same trap. Our approach is general enough to be easily extended to arbitrary vector beams, could be implemented with fast refresh rates and will be of interest to the structured light and optical manipulation communities alike.

Self-healing high-dimensional quantum key distribution using hybrid spin-orbit Bessel states.

Using spatial modes for quantum key distribution (QKD) has become highly topical due to their infinite dimensionality, promising high information capacity per photon. However, spatial distortions reduce the feasible secret key rates and compromise the security of a quantum channel. In an extreme form such a distortion might be a physical obstacle, impeding line-of-sight for free-space channels. Here, by controlling the radial degree of freedom of a photon's spatial mode, we are able to demonstrate hybrid high-dimensional QKD through obstacles with self-reconstructing single photons. We construct high-dimensional mutually unbiased bases using spin-orbit hybrid states that are radially modulated with a non-diffracting Bessel-Gaussian (BG) profile, and show secure transmission through partially obstructed quantum links. Using a prepare-measure protocol we report higher quantum state self-reconstruction and information retention for the non-diffracting BG modes as compared to Laguerre-Gaussian modes, obtaining a quantum bit error rate (QBER) that is up to 3× lower. This work highlights the importance of controlling the radial mode of single photons in quantum information processing and communication as well as the advantages of QKD with hybrid states.

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.

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.

Radially dependent angular acceleration of twisted light.

While photons travel in a straight line at constant velocity in free space, the intensity profile of structured light may be tailored for acceleration in any degree of freedom. Here we propose a simple approach to control the angular acceleration of light. Using Laguerre-Gaussian modes as our twisted beams carrying orbital angular momentum, we show that superpositions of opposite handedness result in a radially dependent angular acceleration as they pass through a focus (waist plane). Due to conservation of orbital angular momentum, we find that propagation dynamics are complex despite the free-space medium: the outer part of the beam (rings) rotates in an opposite direction to the inner part (petals), and while the outer part accelerates, the inner part decelerates. We outline the concepts theoretically and confirm them experimentally. Such exotic structured light beams are topical due to their many applications, for instance in optical trapping and tweezing, metrology, and fundamental studies in optics.

On the resilience of scalar and vector vortex modes in turbulence.

Free-space optical communication with spatial modes of light has become topical due to the possibility of dramatically increasing communication bandwidth via Mode Division Multiplexing (MDM). While both scalar and vector vortex modes have been used as transmission bases, it has been suggested that the latter is more robust in turbulence. Using orbital angular momentum as an example, we demonstrate theoretically and experimentally that the crosstalk due to turbulence is the same in the scalar and vector basis sets of such modes. This work brings new insights about the behaviour of vector and scalar modes in turbulence, but more importantly it demonstrates that when considering optimal modes for MDM, the choice should not necessarily be based on their vectorial nature.

Beam quality measure for vector beams.

Vector beams have found a myriad of applications, from laser materials processing to microscopy, and are now easily produced in the laboratory. They are usually differentiated from scalar beams by qualitative measures, for example, visual inspection of beam profiles after a rotating polarizer. Here we introduce a quantitative beam quality measure for vector beams and demonstrate it on cylindrical vector vortex beams. We show how a single measure can be defined for the vector quality, from 0 (purely scalar) to 1 (purely vector). Our measure is derived from a quantum toolkit, which we show applies to classical vector beams.