Ultrafast Transverse Modulation of Free Electrons by Interaction with Shaped Optical Fields

Abstract

Spatiotemporal electron-beam shaping is a bold frontier of electron microscopy. Over the past decade, shaping methods evolved from static phase plates to low-speed electrostatic and magnetostatic displays. Recently, a swift change of paradigm utilizing light to control free electrons has emerged. Here, we experimentally demonstrate arbitrary transverse modulation of electron beams without complicated electron-optics elements or material nanostructures, but rather using shaped light beams. On-demand spatial modulation of electron wavepackets is obtained via inelastic interaction with transversely shaped ultrafast light fields controlled by an external spatial light modulator. We illustrate this method for the cases of Hermite-Gaussian and Laguerre-Gaussian modulation and discuss their use in enhancing microscope sensitivity. Our approach dramatically widens the range of patterns that can be imprinted on the electron profile and greatly facilitates tailored electron-beam shaping.

Figure 1

Schematics of a photonic free-electron modulator (PELM). (a) An external spatial light modulator (SLM) is used to imprint an arbitrarily shaped amplitude and phase pattern on the optical field. The light beam is then focused on a thin Ag/Si₃N₄ film inside an ultrafast transmission electron microscope (UTEM). The SLM is placed in the conjugate plane with respect to the thin plate. Femtosecond electron pulses in the UTEM impinge on the Ag/Si₃N₄ film and interact with the modulated femtosecond light-pulse field at the Ag surface via stimulated inverse transition radiation. The inelastically scattered electrons are then imaged in space, time, and energy by means of electron energy-loss spectroscopy (EELS) performed in our EF-TEM setup. (b) Schematic picture of the optical modulation of a free electron wave by a shaped light wave with a Hermite-Gaussian transverse profile. (c) Sequence of measured EELS spectra (color map) plotted as a function of the delay time between the electron and light pulses. Sidebands at energies (in our case, ℏω = 1.57 eV) relative to the zero-loss peak (ZLP) are visible, where is the net number of exchanged photons. White solid line: selected EELS spectrum measured at t = 0, corresponding to the temporal and spatial coincidence between electron and light pulses.

Figure 2

Experimental demonstration of transverse optical modulation of free electrons via arbitrarily shaped ultrafast light fields. (a–c) Phase patterns implemented on the SLM used to modulate the light field: (a) homogeneous phase distribution, (b) π-phase shift along the horizontal direction, and (c) π-phase shift along the vertical direction. (d–f) Light transverse profiles measured for the corresponding SLM phase patterns in (a)–(c): a Gaussian profile in (d), a two-lobed horizontal Hermite-Gaussian profile (HG₁₀) in (e), and a two-lobed vertical Hermite-Gaussian profile (HG₀₁) in (f). (g–j) Inelastically scattered electron spatial maps measured under optical illumination with (g) Gaussian and (h–j) Hermite-Gaussian beams, obtained by the SLM modulation of the ultrafast light pulses shown in (a)–(c). All images are taken when the electron and light wavepackets have maximum temporal overlap.

Figure 3

Theoretical calculations of transverse optical modulation of free electrons via arbitrarily shaped ultrafast light fields. We present simulations corresponding to the same plots and labels as in Figure 2. The asymmetry in the electron beam profiles in (g)–(j) is due to the tilt angle of the incident light direction relative to the electron beam

Figure 4

Ultrafast vortex modulation of free electron pulses via an optical Laguerre-Gaussian (LG) beam. (a) Vortex phase pattern implemented on the SLM with azimuthal order equal to 1. (b) Optical beam profile at the conjugate plane where the Ag thin film resides showing the optical LG mode. (c) Energy-filtered electron image where we observe the optical vortex pattern directly imprinted on the electron transverse profile.

Figure 5

Theoretical calculations of topographical contrast enhancement of a weak-phase object using Hermite-Gaussian electron beams. (a, b) Simulated TEM images of an ordered array of Skyrmions (diameter of ∼50 nm, separation of 100 nm) obtained at the focus condition (zero defocus) with shaped electrons having (a) HG₁₀ and (b) HG₀₁ symmetries. The Hermite-Gaussian modulation of the electron wavepacket induced by the PELM is equivalent to the application of a Hilbert phase plate with the corresponding symmetry. (c) Quadratic average of the two images reported in panels (a) and (b), showing an enhanced local edge contrast of the array of Skyrmions. The field of view in all panels is 1.13 × 1.13 μm².