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.

Complex vector light modes, classically entangled in their spatial and polarization degrees of freedom (DoF), have become ubiquitous in a vast diversity of research fields. Crucially, while polarization is limited to a bi-dimensional space, the spatial mode is unbounded, and it can be specified by any of the sets of solutions the wave equation can support in different coordinate systems. Here, we report on a class of vector beams with elliptical symmetry where the spatial DoF is encoded in the Ince–Gaussian modes of the cylindrical elliptical coordinates. We outline their geometric representation on the higher-order Poincaré sphere, demonstrate their experimental generation, and analyze the quality of the generated modes via Stokes polarimetry. We anticipate that such vector modes will be of great relevance in applications, such as optical manipulations, laser material processing, and optical communications among others.

Complex vector light modes with a spatial variant polarization distribution have become topical of late, enabling the development of novel applications in numerous research fields. Key to this is the remarkable similarities they hold with quantum entangled states, which arises from the non-separability between the spatial and polarisation degrees of freedom (DoF). As such, the demand for diversification of generation methods and characterization techniques have increased dramatically. Here we put forward a comprehensive tutorial about the use of digital micromirrors devices (DMDs) in the generation and characterization of vector modes, providing details on the implementation of techniques that fully exploits the unsurpassed advantage of DMDs, such as their high refresh rates and polarisation independence. We start by briefly describing the operating principles of DMD and follow with a thorough explanation of some of the methods to shape arbitrary vector modes. Finally, we describe some techniques aiming at the real-time characterization of vector beams. This tutorial highlights the value of DMDs as an alternative tool for the generation and characterization of complex vector light fields, of great relevance in a wide variety of applications.

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.

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.

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.