Sub-laser-cycle control of relativistic plasma mirrors

We present measurements of high-order harmonics and relativistic electrons emitted into the vacuum from a plasma mirror driven by temporally shaped ultraintense laser wave forms, produced by collinearly combining the main laser field with its second harmonic. We experimentally show how these observables are influenced by the phase delay between these two frequencies at the attosecond timescale, and relate these observations to the underlying physics through an advanced analysis of 1D/2D particle-in-cell simulations. These results demonstrate that subcycle shaping of the driving laser field provides fine control on the properties of the relativistic electron bunches responsible for harmonic and particle emission from plasma mirrors.

Figure 1

(a) Experimental setup with the prepulse (red) and main pulse (purple) with adjustable relative delay $\tau$ as set by the two-part mirror M / ${\mathrm{M}}_{\mathrm{P}}$ and the three crystals ${\mathrm{C}}_1$, ${\mathrm{C}}_2$, WP for two-color wave form generation (see text). The inset shows wave forms obtained for ${\tau }_{\varphi ,h}=0$ (solid gray line) and ${\tau }_{\varphi ,e}=-T^{\prime }/4$ (dashed black line).

Figure 2

Angular emission pattern of accelerated electrons (left) and angularly resolved harmonic spectrum (right) obtained with the minimal gradient scale length $L_g\lesssim {\lambda }_L/50$ (a) and with a gradient scale length optimizing both ROM HHG and vacuum-laser-accelerated electron emission (b). The vertical black lines in the electron beam profiles mark the XUV spectrometer angular acceptance.

Figure 3

Angular emission pattern of accelerated electrons (left) and angularly resolved harmonic spectrum (right) obtained with a gradient scale length $L_g\lesssim {\lambda }_L/50$ and for phase delays maximizing either the electron emission ${\tau }_{\varphi ,e}$ (a) or the high-order harmonic emission ${\tau }_{\varphi ,h}$ (b). The vertical black lines in the electron beam profiles mark the XUV spectrometer angular acceptance.

Figure 4

Experimental harmonic spectrum ${\tilde{S}}_h$ (a) and accelerated electron beam profile ${\tilde{S}}_e$ (b) in the incidence plane as a function of the phase delay ${\tau }_{\varphi }$ (with an unknown experimental offset ${\tau }_0$). The total high-harmonic energy $W_h$ (blue circles) and electron charge $Q_e$ (red squares) obtained by integration over the vertical dimensions in the panels above are plotted in panel (c). The ejected electron charge and the harmonic energy similarly oscillate but with optima shifted by $\simeq 0.3T^{\prime }$. The experimental parameters are the same as in Fig. 3.

Figure 5

Ejected electron charge (red squares) and high-order harmonic energy (blue circles) as a function of the phase delay ${\tau }_{\varphi }$ obtained from 2D PIC simulations. Full blue and red lines show the normalized heuristic model predictions $S\left({\tau }_{\varphi }\right)$ and $P\left({\tau }_{\varphi }\right)$ for E-field steepness ($n=9$ here) and maximum pulling E field, respectively. The periodic modulations of these electronic and harmonic signals are shifted by $\simeq T^{\prime }/4$. The insets above show the driving fields for maximum electron (left) and high-harmonic (right) emission. A positive-valued electric field pulls electrons out of the plasma into vacuum.

Figure 6

Electron bunch properties during the pull phase as a function of the phase delay ${\tau }_{\varphi }$ extracted from 1D PIC simulations: Mean charge (a), mean velocity (b), and initial spatial width (c). Blue and red shadings mark the phase delay ranges maximizing harmonic and electron emissions, respectively, in the 2D simulations as shown in Fig. 5. The insets show the temporal evolution of the plasma electron density (grayscale color map in log scale) in each phase delay range, spatially resolved along the normal to the target surface. The emitted attosecond pulses are overlaid to this density map in purple. Note that the bunch charge (a) is not as that of the emitted VLA electron beam as displayed in Fig. 5.

Figure 7

Calculated relative group (left) and phase delays (right) between the 800-nm fundamental and the 400-nm second harmonic as a function of the incidence angle on the birefringent calcite crystal (${\mathrm{C}}_2$).

Figure 8

Angular emission pattern of accelerated electrons (left) and angularly resolved harmonic spectrum (right) obtained with the same two gradient scale lengths as in Fig. 2 ($L_{\mathrm{g}}\approx \lambda /50$ above and $L_{\mathrm{g}}\approx \lambda /16$ below). The phase delay of the two-color driving wave forms is set such that it optimizes low-divergence ROM HHG emission (a) or fast electron emission (b). The vertical black lines in the electron beam profiles mark the XUV spectrometer angular acceptance.

Figure 9

Angularly resolved harmonic spectra obtained with minimal plasma gradient scale length $L_{\mathrm{g}}\approx 0$ (a)-(c) and with $L_{\mathrm{g}}\approx 0.06\lambda$ (d). Two-color (${\omega }_{\mathrm{L}}+2{\omega }_{\mathrm{L}}$) driver with a phase delay ${\tau }_{\varphi }$ minimizing [(a) “2-color worst”] or maximizing [(b) “2-color best”] the low-divergence ROM HHG emission. Single-color (${\omega }_{\mathrm{L}}$) driver [(c) “1-color CWE;” (d) “1-color ROM”]. The linear color scale is the same in all panels such that the signals are quantitatively comparable. The red boxes in (a)–(d) mark the angular-spectral integration range for the efficiency comparison in the text.

Figure 10

Electron beam spatial profiles $S_{(}e)$ measured with minimal plasma gradient scale length $L_{\mathrm{g}}\approx 0$ (a)–(c), with $L_{\mathrm{g}}\approx 0.06\lambda$ (d)–(f), and with a single-color (${\omega }_{\mathrm{L}}$) laser driver (a),(d); a two-color (${\omega }_{\mathrm{L}}+2{\omega }_{\mathrm{L}}$) driver with a phase delay ${\tau }_{\varphi }$ maximizing (b),(e) or minimizing (c),(f) the electron signal.