Generation and control of Doppler harmonics approaching $10^{22}\textrm{W/cm}^2$ on plasma mirrors

Abstract

In this letter, we report Doppler harmonic generation with a relativistic plasma mirror at unprecedented intensities $>10^{21} ~\textrm{W/cm}^2$ using a PetaWatt-class laser. We show that beyond a few $10^{21} ~\textrm{W/cm}^2$ a precise control of the laser contrast at the sub-picosecond time scale becomes essential to drive the efficient generation of high-order harmonics. Such control is paramount for deploying plasma mirrors in high-field applications at PetaWatt-class laser facilities, including, for instance, their use as intensity boosters in the pursuit of the strong-field regime of quantum electrodynamics.

Figures (4)

• Figure 1: (a) Laser temporal profile measured with a Sequoia cross-correlator: -150ps window / 0.9ps resolution in black, $\pm 5$ps window / 0.1ps resolution in red. Inset: sub-300fs Wizzler measurement before the DPM. (b) DPM transmission as a function of the maximum intensity and fluence incident on the first PM surface (orange markers). The deduced transmissions of each plasma mirror (red and blue circles) are shown as a function of the intensity on each PM surface (black and purple lines), obtained from a power-law fit (see Sup. Mat. SuppMat)
• Figure 2: (a) Experimental scheme: the laser is focused onto the pre-ionized target and the XUV spectrum is measured using a $2$-mm entrance slit and a curved XUV grating imaging the HHG source (in the dispersive direction) onto a micro-channel-plate detector coupled to a phosphor screen imaged by a camera. (b-j) Angularly resolved XUV spectra for different on-target laser intensities: $1.3 \times 10^{21} ~ \textrm{W/cm}^2$ (b–d), $2.4 \times 10^{21}~ \textrm{W/cm}^2$ (e–g), and $6.6 \times 10^{21} ~ \textrm{W/cm}^2$ (h–j), and for different gradient scale lengths: short ($L=0$, first column), intermediate ($L\approx \lambda/11$, second column), and long ($L > \lambda/5$, third column). All spectra are normalized to the maximum value across the entire dataset. (k-l) Relative efficiency of the $\textrm{11}^{th}$ (k) and $\textrm{30}^{th}$ (l) harmonics as a function of the plasma gradient length, calculated as the sum of the signal within a 6mrad x 85mrad angular window. For each harmonic order, the efficiencies are normalized to the maximum value across the entire dataset. Data points corresponding to panels (b–j) are marked with a black contour.
• Figure 3: High-resolution PIC simulations corresponding to the experimental cases. (a–f) For an initial plasma gradient length of $\lambda/10$: target ion density at the peak of the laser pulse for intensities of $1.3 \times 10^{21} ~ \textrm{W/cm}^2$ (a–b), $2.4 \times 10^{21} ~ \textrm{W/cm}^2$ (c–d), and $6.6 \times 10^{21} ~ \textrm{W/cm}^2$ (e–f). First column (a,c,e): idealized 37 fs FWHM Gaussian laser pulse (no pedestal); second column (b,d,f): realistic laser temporal profile (with pedestal). In each panel, the black dashed line delimits the initial boundary between the plasma gradient and the bulk region. (g-l) Harmonic generation efficiency for the $\textrm{11}^{th}$ (first row) and $\textrm{30}^{th}$ (second row) orders as a function of plasma scale length, calculated as the sum of the harmonic signal collected by the detector (or within the same 85 mrad angular window for numerical data), for the three intensities on target: 1.3 (red lines), 2.4 (blue), and 6.6 $\times 10^{21} ~ \textrm{W/cm}^2$ (green). Harmonic efficiency from PIC simulations without pedestal, first column (g-h), with realistic laser temporal profile, second column (i-j), compared with the experimental harmonic efficiencies from Fig. \ref{['fig:exp_results']}, last column (k-l). For each panel, the efficiencies are normalized with respect to the maximum value.
• Figure 4: PIC simulations to investigate the impact of sub-ps contrast on HHG efficiency of the $\textrm{11}^{th}$ order for a plasma scale length of $\lambda/10$ (optimizing HHG in the absence of pedestal, see Fig.\ref{['fig:exp_vs_num_res']}(g)). For a more general study of HHG efficiency, no angular filtering corresponding to a specific detector window is applied here. (a,b) HHG efficiency, panel (b), for the three experimental main pulse intensities as a function of the average sub-220 fs temporal contrast, panel (a), using a realistic temporal profile (the one of the laser before the DPM), solid lines, and a simplified 220 fs super-Gaussian profile (order 60), dashed lines. (c–f) HHG efficiency versus sub-350fs pedestal intensity and main pulse intensity for a super-Gaussian pedestal whose duration is 75 fs (c), 167 fs (d), 258 fs (e), and 350 fs (f). Black dashed lines indicate the pedestal intensity cutoff, defined as where the HHG efficiency drops below $70\%$ of the pedestal-free case. (g) Deduced cutoff contrasts for controlled laser–plasma interaction as a function of pedestal duration and on-target main pulse intensity. Colored crosses mark the three probed experimental conditions.