Electron-Light Interactions beyond the Adiabatic Approximation: Recoil Engineering and Spectral Interferometry

The adiabatic approximation has formed the basis for much of our understandings of the interaction of light and electrons. The classical non-recoil approximation or quantum mechanical Wolkow states of free electron waves have been routinely employed to interpret the outcomes of low-loss 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 Schrodinger frameworks are outlined. Several applications of the proposed frameworks are discussed, and an outlook for further investigations is also delivered.