| Summary: | The adiabatic approximation has formed the basis for much of our understandings of the interaction of light and electrons. The classical nonrecoil approximation or quantum mechanical Wolkow states of free-electron waves have been routinely employed to interpret the outcomes of low-loss electron energy-loss spectroscopy (EELS) or electron holography. Despite the enormous success of semianalytical approximations, there are certainly ranges of electron–photon coupling strengths where more demanding self-consistent analyses are to be exploited to thoroughly grasp our experimental results. Slow-electron point-projection microscopes and many of the photoemission experiments are employed within such ranges. Here, we aim to classify those regimes and propose numerical solutions for an accurate simulation model. A survey of the works carried out within self-consistent Maxwell–Lorentz and Maxwell–Schrödinger frameworks are outlined. Several applications of the proposed frameworks are discussed, and an outlook for further investigations is also delivered. Abbreviations: CL: Cathodoluminescence CW: continuous – wave DLA: dielectric laser accelerator EDPHS: electron-driven photon source EEGS: electron energy-gain spectroscopy EELS: Electron energy-loss spectroscopy eV: electron-volt fs: femtosecond FDTD: finite-difference time-domain IR: infrared PIC: particle-in-cell PINEM: photon-induced near-field electron microscopy PLDOS: photonic local density of state PPM: point-projection electron microscopy SEM: scanning electron microscope SVA: slowly varying approximation TE: transverse electric TEM: transmission electron microscope THz: terahertz TM: transverse magnetic UV: ultraviolet
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