Spectral Interferometry with Electron Microscopes

Abstract

Interference patterns are not only a defining characteristic of waves, but also have several applications; characterization of coherent processes and holography. Spatial holography with electron waves, has paved the way towards space-resolved characterization of magnetic domains and electrostatic potentials with angstrom spatial resolution. Another impetus in electron microscopy has been introduced by ultrafast electron microscopy which uses pulses of sub-picosecond durations for probing a laser induced excitation of the sample. However, attosecond temporal resolution has not yet been reported, merely due to the statistical distribution of arrival times of electrons at the sample, with respect to the laser time reference. This is however, the very time resolution which will be needed for performing time-frequency analysis. These difficulties are addressed here by proposing a new methodology to improve the synchronization between electron and optical excitations through introducing an efficient electron-driven photon source. We use focused transition radiation of the electron as a pump for the sample. Due to the nature of transition radiation, the process is coherent. This technique allows us to perform spectral interferometry with electron microscopes, with applications in retrieving the phase of electron-induced polarizations and reconstructing dynamics of the induced vector potential.

Electron-beam spectroscopy for nanophotonics

“…140 An alternative proposal is to retrieve the sub-cycle dynamics of plasmons by using interference between the field of an specially designed plasmonic metamaterial lens excited by a fast electron and a plasmonic field of interest. 141,142 Recent developments with electron diffraction (without spatial resolution) have demonstrated sub-fs resolution in pulse trains, paving the way to sub-optical cycle temporal resolution in EELS/CL. 143 As a benchmark in this context, photoemission electron microscopy (PEEM) has been shown to render <10 nm spatial resolution through electron imaging, accompanied by ~10 fs resolution associated with pump/probe delay in two-photon photoemission (see below).…”

Electron-light interactions beyond the adiabatic approximation: recoil engineering and spectral interferometry

“…Instead of triggering the electron pulses with photon pulses using photoemission processes, an inverse approach has been outlined which is based on coherent electron-induced radiations like transition Figure 10. Basis of spectral interferometry with electron microscopes [35]. (a) An EDPHS interacts with an impinging electron and emits coherent radiation which is focused onto the sample.…”

“…radiation [35]. As discussed previously in section 2.2, two nanoantennas coupled to a waveguide can be used to manipulate the experienced recoil by the electron.…”

“…This structure offers several degrees of freedom for triggering the electron-induced emission toward the realization of a focused and directional radiation; attained by combining the photonic crystal structure with a multilayered hyperbolic material [123]. The radiation from this EDPHS structure is in the form of a transverse magnetic and ultrashort one cycle pulse [35] (refer Figure 10(b)). The second nanoantenna is then replaced by the sample, which the latter is positioned in the focal point of the EDPHS.…”

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

“…Moreover, by changing the distance, the relative phase of the electroninduced and photon-induced excitations in the sample can be further controlled, which causes interference patterns in the acquired EEL [155] or CL spectra ( figure 12(c)). The acquired EEL or CL energy-distance map allows one to extract the spectral phase of the electron-induced excitations relative to the photoninduced excitations [150].…”