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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.

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.

One of the most prominent features of quantum entanglement is its invariability under local unitary transformations, which implies that the degree of entanglement or nonseparability remains constant during free-space propagation, true for both quantum and classically entangled modes. Here we demonstrate an exception to this rule using a carefully engineered vectorial light field, and we study its nonseparability dynamics upon free-space propagation. We show that the local nonseparability between the spatial and polarization degrees of freedom dramatically decays to zero while preserving the purity of the state and hence the global nonseparability. We show this by numerical simulations and corroborate it experimentally. Our results evince novel properties of classically entangled modes and point to the need for new measures of nonseparability for such vectorial fields, while paving the way for novel applications for customized structured light.

Vector modes represent the most general state of light in which the spatial and polarisation degrees of freedom are coupled in a non-separable way. Crucially, while polarisation is limited to a bi-dimensional space, the spatial degree of freedom can take any spatial profile. However, most generation and application techniques are mainly limited to spatial modes with polar cylindrical symmetry, such as Laguerre– and Bessel–Gauss modes. In this paper we put forward a novel class of vector modes whose spatial degree of freedom is encoded in the helical Mathieu–Gauss beams of the elliptical cylindrical coordinates. We first introduce these modes theoretically and outline their geometric representation on the higher-order Poincaré sphere. Later on, we demonstrate their experimental generation using a polarisation-insensitive technique comprising the use of a digital micromirror device. Finally, we provide a qualitative and a quantitative characterisation of the same using modern approaches based on quantum mechanics tools. It is worth mentioning that non-polar vector beams are highly desirable in various applications, such as optical trapping and optical communications.

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The non-separability between the spatial and polarization Degrees of Freedom (DoF) of complex vector light fields has drawn significant attention in recent times. Key to this is its remarkable similarities with quantum entanglement, with quantum-like effects observed at the classical level. Crucially, this parallelism enables the use of quantum tools to quantify the coupling between the spatial and polarization DoFs, usually implemented with polarization-dependent spatial light modulators, which requires the splitting of the vector mode into two orthogonal polarization components. Here, we put forward an alternative approach that relies on the use of Digital Micromirror Devices (DMDs) for a fast, cheap, and robust measurement, while the polarization-independent nature of DMDs enables a reduction in the number of required measurements by 25%. We tested our approach experimentally on cylindrical vector modes with arbitrary degrees of non-separability, of great relevance in a wide variety of applications. Our technique provides a reliable way to measure in real time the purity of vector modes, paving the way for a wide variety of applications where the degree of non-separability can be used as an optical sensor.

Perfect (optical) vortex (PV) beams are fields which are mooted to be independent of the orbital angular momentum (OAM) they carry. To date, the best experimental approximation of these modes is obtained from passing Bessel-Gaussian beams through a Fourier lens. However, the OAMdependent width of these quasi-PVs is not precisely known and is often understated. We address this here by deriving and experimentally confirming an explicit analytic expression for the second moment width of quasi-PVs. We show that the width scales in proportion to √ in the best case, the same as most "regular" vortex modes albeit with a much smaller proportionality constant. Our work will be of interest to the large community who seek to use such structured light fields in various applications, including optical trapping, tweezing and communications.