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.

The rule of thumb of tailored optical forces consists in the control of linear momentum exchange between light and matter. This may be done by appropriate selection of the interaction geometry, optical modes or environmental characteristics. Here we reveal that the interplay of the helicity of light and the chirality of matter turns the photon spin angular momentum into an efficient tool for selective trapping of chiral particles. This is demonstrated, both experimentally and theoretically, by exploring the three-dimensional optical trapping of chiral liquid crystal microspheres with circularly polarized Gaussian or Laguerre–Gaussian beams. These results suggest the development of novel optomechanical strategies that rely on the photon helicity towards selective trapping and manipulation of chiral objects by chiral light.

Molecular machines operated by light have been recently shown to be able to produce oriented motion at the molecular scale^1,2 as well as do macroscopic work when embedded in supramolecular structures^3,4,5. However, any supramolecular movement irremediably ceases as soon as the concentration of the interconverting molecular motors or switches reaches a photo-stationary state^6,7. To circumvent this limitation, researchers have typically relied on establishing oscillating illumination conditions—either by modulating the source intensity^8,9 or by using bespoke illumination arrangements^10,11,12,13. In contrast, here we report a supramolecular system in which the emergence of oscillating patterns is encoded at the molecular level. Our system comprises chiral liquid crystal structures that revolve continuously when illuminated, under the action of embedded light-driven molecular motors. The rotation at the supramolecular level is sustained by the diffusion of the motors away from a localized illumination area. Above a critical irradiation power, we observe a spontaneous symmetry breaking that dictates the directionality of the supramolecular rotation. The interplay between the twist of the supramolecular structure and the diffusion¹⁴ of the chiral molecular motors creates continuous, regular and unidirectional rotation of the liquid crystal structure under non-equilibrium conditions.

Topology is a universal concept that is encountered in daily life and is known to determine many static and dynamical properties of matter. Taming and controlling the topology of materials therefore constitutes a contemporary interdisciplinary challenge. Building on the controllable spatial properties of soft matter appears as a relevant strategy to address the challenge, in particular, because it may lead to paradigmatic model systems that allow checking theories experimentally. Here we report experimentally on a wealth of complex free-standing metastable topological architectures at the micron scale, in frustrated chiral nematic droplets. These results support recent works predicting the formation of free-standing knotted and linked disclination structures in confined chiral nematic fluids. We also demonstrate that various kinds of external fields (thermal, electrical and optical) can be used to achieve topological remote control. All this may foster the development of new devices based on topologically structured soft media.

We report on highly reflective spin-orbit geometric phase optical elements based on a helicity-preserving circular Bragg-reflection phenomenon. First, we present a dynamical geometric phase experiment using a flat chiral Bragg mirror. Then, we show that shaping such a geometric phase allows the efficient spin-orbit tailoring of light fields without the need to fulfill any condition on birefringent phase retardation, in contrast to the case of transmission spin-orbit optical elements. This is illustrated by optical vortex generation from chiral liquid crystal droplets in the Bragg regime that unveils spin-orbit consequences of the droplet’s curvature. Our results thus introduce a novel class of geometric phase elements—“Bragg-Berry” optical elements.