Femtosecond Dynamics of Fast Electron Pulses in Relativistic Laser-Foil Interactions

We report the femtosecond time-resolved dynamics of relativistic electron pulses in ultraintense laser-foil interactions, by characterizing the terahertz self-radiation with single-shot ultrabroadband interferometry. Experimental measurements together with theoretical modeling reveal that the electron pulses inherit the duration of the driving laser pulse. We also visualize the electron recirculation dynamics, where electrons remain trapped inside the self-generated electrostatic potential well and rebound back and forth around the thin foil for hundreds of femtoseconds. Our results not only demonstrate an in situ, real-time metrology scheme for electron bursts, but also have important implications for understanding and manipulating the time-domain properties of laser-driven particle and radiation sources.

Figure 1

(a) Schematic illustrating intense laser-foil interactions and the generation of THz radiation by fast electrons traversing the foil’s rear surface. (b) Sketch of the noncollinear autocorrelator used for single-shot ultrabroadband THz detection. The collimated THz radiation is split into two replica beams (R1 and R2) with a beam splitter. After appropriate optical path delay, the two beams are focused and recombined noncollinearly at a cross angle of $\alpha$ onto the THz camera. (c) Schematic showing the noncollinear AC-based detection principle and a typical AC interferogram. The noncollinear geometry provides the space-to-time mapping between the spatial position, $\delta x$, in the THz spot and the relative time delay, $\delta t$, of the two replica beams as $\delta t=2\delta x·\sin (\alpha /2)/c$, where $c$ is the light velocity in vacuum.

Figure 2

Retrieval of fast-electron bunch durations. (a) A typical THz AC trace measured at the Cu-CH targets (where the Cu-layer thickness is $10\mathrm{\mu }\mathrm{m}$) impinged upon by 35-fs laser pulses, and fit with a Gaussian function (dashed red). (b) Experimentally measured (blue dots) and numerically calculated (red curve) THz duration as a function of the laser pulse duration. (c) Normalized THz CTR waveforms ($\theta =36°$) calculated for an electron bunch (${\tau }_{\mathrm{e}}=35\mathrm{fs}$, ${\sigma }_{\mathrm{e}}=11\mathrm{\mu }\mathrm{m}$, and $T_{\mathrm{e}}=0.8\mathrm{MeV}$) leaving perpendicularly (red, $\psi =0°$) or obliquely (blue, $\psi =16°$) to a metal-vacuum interface. The black dashed curve denotes the original Gaussian electron bunch waveform with a duration of 35 fs. (d) Experimentally retrieved electron bunch duration (blue squares) versus the laser pulse duration and the comparison with numerical calculations (red curve). The dashed diagonal in (b) and (d) represents the duration being equal to the laser duration, and the error bars are estimated based on the shot-to-shot fluctuation and the fitting uncertainty of the experimental AC traces.

Figure 3

Experimentally measured (blue dots) and numerically calculated (red curves) THz durations as a function of the Cu-layer thickness for (a) Cu foils and (b) Cu-CH targets. Recirculation is not considered in the calculations. The error bars are estimated based on the shot-to-shot fluctuation and the fitting uncertainty of the experimental AC traces. (c) THz AC traces (blue solid) measured at $5\text{−}\mathrm{\mu }\mathrm{m}$ and $10\text{−}\mathrm{\mu }\mathrm{m}$ Cu foils, and a comparison with numerical calculations taking recirculation into account (red dashed). (d) Spatiotemporal evolution of electrons illustrating the laser reacceleration of refluxing electrons, leading to the ejection of two electron pulses and accordingly the generation of dual-pulse THz radiation. The white curves represent the traces of electrons at different energies (solid, 1.6 MeV; dashed, 0.8 MeV; dash dotted, 0.4 MeV). See the Supplemental Material [29] for more details on the modeling of recirculation.

Figure 4

(a) Schematic illustrating the electron recirculation dynamics and resultant multicycle THz radiation induced at the target rear. (b) Calculated spatiotemporal evolution of electrons (color map) and the resultant THz field waveform (blue curve). The white curves in the color map represent the traces of electrons at different energies (solid, 1.6 MeV; dashed, 0.8 MeV; dash dotted, 0.4 MeV). The red dashed curve denotes the bipolar waveform of bTR induced at the first recirculation. (c)–(e) THz AC interferograms measured for different Cu foil thickness. The nonuniformity of interferograms along the vertical coordinate is due to the imperfect optical alignment or defective THz elements. In the high-contrast laser case, measurements showed that the electrons were ejected primarily around $\psi \sim 0°$, and $\theta$ was switched to $\sim 50°$ in order to collect more bTR. The white scale bars represent 200 fs. (f)–(h) Numerically calculated THz AC traces. See the Supplemental Material [29] for the calculation details. (i) Experimentally inferred sheath field strength and (j) recirculation duration. Red curves represent the theoretical projections at the indicated laser-to-electron conversion efficiency, $\eta$. The red shaded area shows the ion acceleration time evaluated by the empirical scaling law [33] in which the recirculation is not considered.