Abstract Structured light beams with engineered topological properties offer a powerful means to control spin angular momentum (SAM) and optical chirality, key quantities shaped by spin-orbit interaction (SOI) in light. Such effects are commonly associated with non-paraxial focusing or light-matter interfaces. Here, we demonstrate that higher-order Poincaré modes carrying a tunable Pancharatnam topological charge ℓ p enable deterministic control of SOI entirely in free space and within the paraxial regime. We show that modulation of ℓ p drives a measurable radial separation of circular polarization components - a free-space optical Hall effect arising from propagation-induced mechanisms alone. The effect originates from differential Gouy-phase evolution and radial divergence between the two circular components of an initially spin-balanced vector beam. This identifies ℓ p as a single, tunable parameter linking Pancharatnam topology to paraxial spin-orbit coupling, establishing a simple and material-independent route to generate and control optical chirality and SAM. This approach provides new opportunities for tunable optical manipulation, chiral sensing, and high-dimensional photonic information processing.

This feature issue of the Journal of the Optical Society of America A presents articles that explore spatiotemporal structured light: the tailoring of light's spatial, phase, polarization, and spatial and temporal degrees of freedom.

Laguerre-Gaussian (LG) modes are solutions of the paraxial Helmholtz equation in cylindrical coordinates and are associated with light fields carrying orbital angular momentum (OAM). It is customary to modulate such beams using phase-only vortex profiles, for example, when increasing (laddering up) or decreasing (laddering down) the OAM content of some given LG mode. However, the resulting beams have been shown to be hypergeometric-Gaussian modes, due to the changing radial amplitudes on propagation. In this work, we show that these beams in fact have the angular spectrum of elegant Laguerre-Gaussian (eLG) modes, and therefore map back to LG-type modes. Accordingly, the fields obtain new OAM and radial quantum numbers that depend on the initial OAM and additional OAM gained during modulation.

Modal decomposition of structured light allows its unraveling into a basis of spatial modes, the superposition of which can be used to infer any physical property of the field. This is conventionally achieved by a linear projective system operated in measurement mode. Here, we show how modal decomposition of arbitrary structured light fields can be achieved with nonlinear optics, unraveling an unknown beam in the infrared by spatially overlapping it with a modal set encoded sequentially onto an input visible beam. Next, we show how the decomposition can be done in a single step by a nonlinear version of off-axis digital holography, again for full field reconstruction of the unknown beam. We verify both approaches with topical structured light examples, including orbital angular momentum and Hermite-Gaussian beams. Our nonlinear approach to modal analysis will benefit those applications where the structured beam is at an inconvenient wavelength, and extends our perspective on nonlinear optics from frequency conversion to modal detection.

Symmetry breaking has been shown to reveal interesting phenomena in physical systems. A notable example is the fundamental work of Otto Stern and Walther Gerlach [Stern and Zerlach, Z. Physik 9, 349 (1922)10.1007/BF01326983] nearly 100 years ago demonstrating a spin angular momentum (SAM) deflection that differed from classical theory. Here we use non-separable states of SAM and orbital angular momentum (OAM), known as vector vortex modes, to demonstrate how a classical optics analogy can be used to reveal this non-separability, reminiscent of the work carried out by Stern and Gerlach. We show that by implementing a polarization insensitive device to measure the OAM, the SAM states can be deflected to spatially resolved positions.

JOSA A Editor-in-Chief Olga Korotkova, Deputy Editor Markus Testorf, and the members of the 2022 Emerging Researcher Best Paper Prize Committee announce the recipient of the 2022 prize for the best paper published by an emerging researcher in the Journal.

Remarkable strides have been made in the realm of efficiently sorting and analysing Orbital Angular Momentum (OAM) states of light through the application of geometric optical transformations employing mode sorters. In our study, we introduce a novel methodology that reconstructs OAM states of light through the demonstration of the reciprocity of light. This is achieved by operating a diffractive mode sorter in reverse, effecting an inverse geometric optical transformation that reverts simple lateral spots back to OAM modes of light. Our approach leveraged a digital micro-mirror device (DMD) to encode a hologram, producing an array of spots mimicking the output of a traditional mode sorter. Our system is not only limited solely to the generation of scalar OAM modes, with a simple manipulation of the polarisation of light we enhanced our system to encompass vector beam generation capabilities.

Structured light refers to the ability to tailor light in its many degrees of freedom, from the traditional control in time and space to more exotic multi-dimensional control for new forms of light, including vectorial light, toroidal excitations, spatio-temporal vortices, skyrmions, and optical mobius strips to name but a few. While the toolbox for the creation and detection of structured light has advanced tremendously, this has mostly been in the low power regime. More recently, structured light at high-power and high-intensities has emerged, fuelling new science and applications. In this progress report, we showcase the seminal work that has advanced this field, and indicate the open challenges and opportunities that remain.

Structured waves are ubiquitous for all areas of wave physics, both classical and quantum, where the wavefields are inhomogeneous and cannot be approximated by a single plane wave. Even the interference of two plane waves, or of a single inhomogeneous (evanescent) wave, provides a number of nontrivial phenomena and additional functionalities as compared to a single plane wave. Complex wavefields with inhomogeneities in the amplitude, phase, and polarization, including topological----- structures and singularities, underpin modern nanooptics and photonics, yet they are equally important, e.g. for quantum matter waves, acoustics, water waves, etc. Structured waves are crucial in optical and electron microscopy, wave propagation and scattering, imaging, communications, quantum optics, topological and non-Hermitian wave systems, quantum condensed-matter systems, optomechanics, plasmonics and metamaterials, optical and acoustic manipulation, and so forth. This Roadmap is written collectively by prominent researchers and aims to survey the role of structured waves in various areas of wave physics. Providing background, current research, and anticipating future developments, it will be of interest to a wide cross-disciplinary audience.

Increasing the information capacity of communication channels is a pressing need, driven by growing data demands and the consequent impending data crunch with existing modulation schemes. In this regard, mode division multiplexing (MDM), where the spatial modes of light form the encoding basis, has enormous potential and appeal, but is impeded by modal noise due to imperfect channels. Here we overcome this challenge by breaking the existing MDM paradigm of using the modes themselves as a discrete basis, instead exploiting the polarization inhomogeneity (vectorness) of vectorial light as our information carrier. We show that this encoding basis can be partitioned and detected almost at will, and measured in a channel independent fashion, a fact we confirm experimentally using atmospheric turbulence as a highly perturbing channel example. Our approach replaces conventional amplitude modulation with a novel modal alternative for potentially orders of magnitude channel information enhancement, yet is robust to fading even through noisy channels, offering a new paradigm to exploiting the spatial mode basis for optical communication.

Skyrmions are topologically stable fields that cannot be smoothly deformed into any other field configuration that differs topologically, that is, one that possesses a different integer topological invariant called the Skyrme number. They have been studied as 3-dimensional and 2-dimensional skyrmions in both magnetic and, more recently, optical systems. Here, we introduce an optical analogy to magnetic skyrmions and demonstrate their dynamics within a magnetic field. Our optical skyrmions and synthetic magnetic field are both engineered using superpositions of Bessel-Gaussian beams, with time dynamics observed over the propagation distance. We show that the skyrmionic form changes during propagation, exhibiting controllable periodic precession over a well defined range, analogous to time varying spin precession in homogeneous magnetic fields. This local precession manifests as the global beating between skyrmion types, while still maintaining the invariance of the Skyrme number, which we monitor through a full Stokes analysis of the optical field. Finally, we outline, through numerical simulation, how this approach could be extended to create time varying magnetic fields, offering free-space optical control as a powerful analogue to solid state systems.

Measuring and correcting wavefront aberrations is an important process in a wide variety of disciplines, from ophthalmology, laser cutting, and astronomy to free-space communication and microscopy, and always relies on measuring intensities to infer phase. One approach is to use the transport-of-intensity as a means for phase retrieval, exploiting the connection between observed energy flow in optical fields and their wavefronts. Here we present a simple scheme, using a digital micro-mirror device (DMD), to perform angular spectrum propagation and extract the wavefront of optical fields at various wavelengths, dynamically, with high resolution and tuneable sensitivity. We verify the capability of our approach by extracting common Zernike aberrations, turbulent phase screens, and lens phases under static and dynamic conditions at multiple wavelengths and polarizations. We use this setup for adaptive optics, correcting distortion using a second DMD to apply conjugate phase modulation. We observed effective wavefront recovery under a variety of conditions which allowed for convenient real-time adaptive correction in a compact arrangement. Our approach provides an all-digital system that is versatile, cheap, fast, accurate, broadband and polarization invariant.

The number of mirror segments, mirror geometry and orientation are essential parameters when assessing the beam-shaping capabilities of deformable mirrors. Here, we use a Liquid Crystal on Silicon Spatial Light Modulator (LCoS-SLM) to mimic the mechanical design of a deformable mirror and quantitatively analyse the effect of the number of mirror segments and their geometrical structure on resulting structured modes. Our approach can be used as a test bed prior to designing a deformable mirror for high power beam shaping.

In this work, we will present two techniques for extracting the wavefront and polarization structure of optical fields. The first being a digital analogy to Stokes polarimetry involving only four measurements, as opposed to the usual six. Here, we implement static polarisation optics, such as a Polarization Grating (PG) to project a mode into left- and right-circular states, which are subsequently directed to a Digital Micro-mirror Device (DMD) to impart a phase retardance for full phase and polarisation reconstruction. The second approach uses the transport-of-intensity which harnesses the connection between observed energy flow in optical fields and their wavefronts. We present a simple scheme using a DMD to perform angular spectrum propagation and extract the wavefront of optical fields. Finally, we demonstrate these approaches by spatially resolving complex polarization structures such as metasurfaces, liquid crystal devices and chiral materials.

Digital micromirror devices (DMDs) are wavelength and polarization independent, have a faster response rate and are affordable- making it a prime beam shaping tool for the commercial world. However, due to its micro-mirror structure and encoded grating, DMDs diffract and disperse broadband light. Although this dispersion problem has been addressed before, the solutions presented require expensive optics and or precise alignment, making it costly and impractical for commercial use. In this work we propose a simple and easily implementable solution that requires a single lens. We then demonstrate this experimentally by generating broadband modes in the image plane.

Diffractive optical elements are advantageous due to high power thresholds, but are expensive with the increasing modulation steps. We use SLMs as a guide to experimentally evaluate the steps needed for different structured modes.

Structured light has become topical of late, allowing custom optical fields to be tailored in all degrees of freedom, and finding applications that include optical trapping and tweezing, microscopy, communications and even quantum protocols. Commonly, the light is tailored in its spatial degrees of freedom for arbitrary polarization, amplitude and phase control, executed on spatial light modulators. This invited talk will outline the role of digital micro-mirror devices (DMDs) in the creation, control and detection of structured light fields, covering fundamentals for “getting started” to the state-of-the-art in real-time control with high speed and fidelity. The talk will cover topics ranging from lasers to single photons, highlighting the versatility of the DMD toolkit.