Single-Cycle Optical Control of Beam Electrons

We report the single-cycle optical control of a freely propagating electron beam with an isolated cycle of midinfrared light. In particular, we produce and characterize a modulated electron current with peak-cycle-specific subfemtosecond structure in time. The direct effects of the carrier-envelope phase, amplitude, and dispersion of the optical waveform on the temporal composition, pulse durations, and chirp of the free-space electron wave function demonstrate the subcycle nature of our control. These results and concept may create novel opportunities in free-electron lasers, laser-driven particle accelerators, ultrafast electron microscopy, and wherever else high-energy electrons are needed with the temporal structure of single-cycle light.

Figure 1

Concept of single-cycle electron-beam control. An electron beam (blue) is modulated by a single field cycle (red) of a phase-controlled waveform when passing through a freestanding metallic membrane (green). The temporally modulated electron current is directly characterized by real-space streaking induced by a second single-cycle field (red). The streaking by the isolated peak half-cycle spatially isolates a single attosecond peak of the modulated current.

Figure 2

Single-cycle control of subrelativistic beam electrons. (a) Experiment. A collimated 70-keV electron beam of $100\mu \mathrm{m}$ diameter ($2500\mathrm{electrons/s}$) is temporally modulated and analyzed by a single optical cycle of a midinfrared field (red). WP, wave plate; P, polarizer; AP, aperture. (b) Spectrum of the midinfrared pulses. (c) Electric field waveform of the midinfrared pulses. (d) Streaking signal of the temporally modulated electron pulses as a function of the modulation-streaking delay $\mathrm{\Delta }t$. Peak 0: electron’s peak current streaked by the isolated positive cycle. Peak $\pm 1$: peak current streaked by the negative field peaks. Peak $\pm 2$: side peak current streaked by the isolated cycle. (e) Streaking signal of the central feature (left) in comparison to a simulation (right) for an electron pulse duration of 1.0 fs (full width at half maximum). (f) Slice of the streaking pattern at an angle of 0.37 mrad. The observations (black circles) range between a simulation with an electron pule duration of 1.0 fs (blue solid curve) and 0.5 fs (blue dotted curve).

Figure 3

Electron pulse formation and carrier-envelope phase effects. (a) Waveform of the modulation field. (b) Electron current density in dependence of an increasing modulation strength. (c) Electron pulse durations (black squares) for the four peaks A–D [see (b)] as a function of the field strength of the central cycle. The shortest full width at half maximum durations are (A) $0.6\pm 0.6$, (B) $0.9\pm 0.8$, (C) $0.8\pm 0.6$, and (D) $3.1\pm 1.8\mathrm{fs}$. Dashed lines depict the result of quantum mechanical simulations. (d),(e) Carrier-envelope phase control. (d) Time-dependent intensity at highest streaking angle ($>0.35\mathrm{mrad}$) for a cosine field (upper) and for a minus-cosine field (lower). (e) Retrieved electron current density for the two control field shapes. The appearance of a single peak or double peaks is determined by the carrier-envelope phase. (f) Pulse durations (dots) of the peaks B–D as a function of the carrier-envelope phase. The transparent bands show the results of simulations with error margins. (g) Survey of the electron pulse durations so far obtained at different control wavelengths [4, 5, 14, 15, 16, 17, 18, 19, 20, 21, 41, 42, 43, 44]. Single-cycle electron control is applicable to any wavelength for which an octave-broad modulation element can be designed (see Supplemental Material [33]).

Figure 4

Free-electron control with multicycle midinfrared fields. (a) Experimental scheme for multicycle midinfrared control. (b) Measured streaking data. The oscillation period, and therefore the temporal separation of the electron pulses, is $\sim 21\mathrm{fs}$. (c) Train-averaged electron pulse duration (dots) as a function of the compression field strength in comparison to the results of quantum mechanical simulations (dashed line).