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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 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., Comment: 110 pages, many figures

Recent theoretical investigations [Belonoshko et al. Nature Geoscience 10, 312 (2017)] revealed occurrence of concerted migration of several atoms in bcc Fe at inner-core temperatures and pressures. Here, we combine first-principles and semi-empirical atomistic simulations to show that a diffusion mechanism analogous to the one predicted for bcc iron at extreme conditions is also operative and of relevance for the high-temperature bcc phase of pure Ti at ambient pressure. The mechanism entails a rapid collective movement of numerous (from two to dozens) neighbors along tangled closed-loop paths in defect-free crystal regions. We argue that this phenomenon closely resembles the diffusion behavior of superionics and liquid metals. Furthermore, we suggest that concerted migration is the atomistic manifestation of vanishingly small w-mode phonon frequencies previously detected via neutron scattering and the mechanism underlying anomalously large and markedly non-Arrhenius self-diffusivities characteristic of bcc Ti.

In this paper we give another proof of $p_c = \frac{\sqrt{q}}{1+\sqrt{q}}$ on $\mathbb{Z}^2$ with $q \in [1,4]$, based on the method of parafermionic observables., Comment: 29 pages, 6 figures

Laboratory optics, typically dealing with monochromatic light beams in a single reference frame, exhibits numerous spin-orbit interaction phenomena due to the coupling between the spin and orbital degrees of freedom of light. Similar phenomena appear for electrons and other spinning particles. Here we examine transformations of paraxial photon and relativistic-electron states carrying the spin and orbital angular momenta (AM) under the Lorentz boosts between different reference frames. We show that transverse boosts inevitably produce a rather nontrivial conversion from spin to orbital AM. The converted part is then separated between the intrinsic (vortex) and extrinsic (transverse shift or Hall effect) contributions. Although the spin, intrinsic-orbital, and extrinsic-orbital parts all point in different directions, such complex behavior is necessary for the proper Lorentz transformation of the total AM of the particle. Relativistic spin-orbit interactions can be important in scattering processes involving photons, electrons, and other relativistic spinning particles, as well as when studying light emitted by fast-moving bodies., Comment: 9 pages, 3 figures

A new class of phenomena stemming from topological states of quantum matter has recently found a variety of analogies in classical systems. Spin-locking and one-way propagation have been shown to drastically alter our view on scattering of electromagnetic waves, thus offering an unprecedented robustness to defects and disorder. Despite these successes, bringing these new ideas to practical grounds meets a number of serious limitations. In photonics, when it is crucial to implement topological photonic devices on a chip, two major challenges are associated with electromagnetic dissipation into heat and out-of-plane radiation into free space. Both these mechanisms may destroy the topological state and seriously affect the device performance. Here we experimentally demonstrate that the topological order for light can be implemented in all-dielectric on-chip prototype metasurfaces, which mitigate the effect of Ohmic losses by using exclusively dielectric materials, and reveal that coupling of the system to the radiative continuum does not affect the topological properties. Spin-Hall effect of light for spin-polarized topological edge states is revealed through near-field spectroscopy measurements., Comment: 12 pages, 5 figures