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Dielectric laser accelerators (DLAs) are fundamentally based on the interaction of photons with free electrons, where energy and momentum conservation are satisfied by mediation of a nanostructure. In this scheme, the photonic nanostructure induces near-fields which transfer energy from the photon to the electron, similar to the inverse-Smith–Purcell effect described in metallic gratings. This, in turn, may provide ground-breaking applications, as it is a technology promising to miniaturize particle accelerators down to the chip scale. This fundamental interaction can also be used to study and demonstrate quantum photon-electron phenomena. The spontaneous and stimulated Smith–Purcell effect and the photon-induced near-field electron-microscopy (PINEM) effect have evolved to be a fruitful ground for observing quantum effects. In particular, the energy spectrum of the free electron has been shown to have discrete energy peaks, spaced with the interacting photon energy. This energy spectrum is correlated to the photon statistics and number of photon exchanges that took place during the interaction. We give an overview of DLA and PINEM physics with a focus on electron phase-space manipulation. 

Abstract 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.