Interaction of electron beams with optical nanostructures and metamaterials: From coherent photon sources towards shaping the wave function

Interaction of electron beams with optical nanostructures and metamaterials: From coherent photon sources towards shaping the wave function Nahid Talebi Stuttgart Center for Electron Microscopy, Max Planck Institute for Solid State Research,
Heisenbergstr. 1, 70569 Stuttgart

Abstract- Investigating the interaction of electron beams with materials and light has been a field of research since more than a century. The field was advanced theoretically by the raise of quantum mechanics and technically by the introduction of electron microscopes and accelerators. It is possible nowadays to uncover a multitude of information from electron-induced excitations in matter by means of advanced techniques like holography, tomography, and most recently photon-induced near-field electron microscopy. The question is whether the interaction can be controlled in an even more efficient way in order to unravel important questions like modal decomposition of the electron-induced polarization, by performing experiments with better spatial, temporal, and energy resolutions. This review discusses recent advances in controlling the electron and light interactions at the nanoscale. Theoretical and numerical aspects of the interaction of electrons with nanostructures and metamaterials will be discussed, with the aim to understand mechanisms of radiation in interaction of electrons with even more sophisticated structures. Based on these mechanisms of radiation, state-of-the art and novel electron- driven few-photon sources will be discussed. Applications of such sources to gain an understanding of quantum optical effects and also to perform spectral interferometry with electron microscopes will be covered. In an inverse approach, as in the case of the inverse Smith–Purcell effect, laser-induced excitations of nanostructures can cause the electron beams traveling in the near-field of such structures to get accelerated, provided a synchronization criterion is satisfied. This effect is the basis for linear dielectric and metallic electron accelerators. Moreover, acceleration goes along with bunching of the electrons. When single electrons are considered, an efficient design of nanostructures can lead to the shaping of the electron wave function travelling adjacent to them, for example to form attosecond electron pulses or chiral electron wave functions.
Keywords- Electron beam, Wave function, Radiation, Interference, Few-photon source, Acceleration, Beam shaping Outline-

1. Introduction
2. Mechanisms of radiation of the electron interacting with nanostructures and metamaterials 2.1. Plasmonics and metamaterials 2.2. Basic principles for electron – photon interactions 2.3. Cherenkov radiation 2.4. Transition radiation 2.5. Smith–Purcell effect
3. Electron-driven coherent radiation sources for the visible and UV range 2

3.1. Smith–Purcell photon sources 3.2. Metamaterial-based photon sources 3.3. Applications of electron-driven photon sources 3.3.1. Quantum optical experiments 3.3.2. Time-resolved spectroscopy 4. Mesoscopic metallic and dielectric laser accelerators 4.1. Plasmon- and metamaterial-based linear accelerators 4.2. Dielectric-based linear accelerators 5. Shaping the electron wave function
5.1. Shaping the transverse components of the wave function with thin masks 5.2. Shaping the longitudinal components of the wave function with nanostructures 6. Self-consistent methods to simulate the interaction of electrons with light and matter 6.1. Maxwell–Lorentz framework 6.2. Maxwell–Schrödinger framework 7. Conclusion and Outlook

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1. Introduction About one century after the introduction of the Schrödinger equation and the invention of the transmission electron microscope by Ernst Ruska, electron microscopy has entered nowadays the era of ultrahigh sub-Ångstrom spatial resolution [1]. However, microscopy of materials at high spatial resolution is not the only possible application of electron microscopes; indeed electron spectroscopy is almost playing the same important role for material characterization. Nanoscience is the science of understanding the dynamical physical and chemical processes which happen at the nanoscale, within the time–energy and momentum–space phase spaces. For this reason, electron probes offering enough brightness, emittance, and spatiotemporal coherence length are crucial for our understanding and manipulation of the nanoworld.
   Interestingly, similar to light, swift electrons can also undergo inelastic interaction with single electrons and by collective electron excitations within the sample, like plasmon and photon polaritons, as a result of which they will lose energy [2]. Within the classical formalism, the electron energy-loss (EEL) spectrum is theoretically rationalized by a simple but intuitive interpretation, which has a direct correspondence with the basic principles of quantum mechanics, demanding that all inelas

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