## 2 Experimental Setup  
The experiment was performed at the short-focal area of the Apollon laser facility (Saclay, France), using its F2 secondary beam [44]. This beam utilizes a Ti:Sapphire laser, delivering pulses with a full-width-at-half-maximum (FWHM) duration of 24 fs, a mean on-target energy of 11 J, and a central laser wavelength of 815 nm. Two configurations were tested: direct shots (without a DPM) and shots with a DPM [34], in which case the on-target laser energy was reduced to 5.7 J, due to a measured DPM reflectivity of \(\sim\)52% reflectivity. The experimental setup is sketched in Figure 1. The DPM was placed inside the interaction chamber, between the \(f/3\) off-axis parabola (OAP) and the target. The laser focusing used here results from a well-known trade-off: focusing the laser beam too tightly can be detrimental because the energetic electrons escape the laser-heated zone too quickly [45]. Conversely, increasing the focal spot size is generally beneficial for electron heating [46] and ion acceleration [47]. However, for a given laser energy, high intensity from a not-too-tight laser spot is preferable [3], hence our common choice of \(f/3\) focusing. The beam was focused onto the target with a 45\({}^{\circ}\) incidence angle. A camera recorded the image of the reflected laser beam on a Spectralon scatter plate positioned along the specular reflection axis (Labsphere, Inc., North Sutton, NH, USA). The transmitted light was monitored by another Spectralon plate placed along the laser transmission axis. Aluminum foils of 0.8-2 \(\upmu\)m thicknesses were used on direct shots, while thinner silicon foils, ranging from 10 nm to 300 nm (with, facing the incident laser, an additional coating of 50 nm of Al for some of them, in order to improve the laser absorption and the proton generation [48]), were used with the DPM. The proton spectra were measured using stacks of EBT3 Gafchromic radiochromic films (RCFs) (Ashland Advanced Materials, Bridgewater, NJ, USA) interlaced with aluminum filters, placed at 25 mm from the target. Figure 1: Experimental setup. The DPM was positioned between the \(f/3\) off-axis parabola (OAP) and the target. The laser beam hit the target at 45\({}^{\circ}\) relative to the target normal. Cameras outside the chamber captured images of the reflected and transmitted laser beams on Spectralon plates. A stack of RCFs (with aluminum filters) was used to measure the proton energy spectrum and spatial profile. Figure 2 provides information on the focusing of the 140-mm-diameter, near-field laser beam. The focal spot was measured to be elliptical with \(2.8\,\upmu\mathrm{m}\times 3.7\,\upmu\mathrm{m}\) FWHM dimensions (see Figure 2a). It contained \(\sim\)47% of the on-target laser energy, resulting in a peak intensity of \(\sim\)\(1.5\times 10^{21}\,\mathrm{W}\,\mathrm{cm}^{-2}\). This peak intensity is evaluated directly from the focal spot image shown in Figure 2a (see caption). These values are very close to those obtained on direct shots during the commissioning of the F2 beam [44], demonstrating that the DPM did not deteriorate the laser focal spot. Figure 2b details the laser energy distribution within the laser spot. The graph plots the fraction of the laser energy within an encircled region as a function of the circle radius from the focal spot center. The temporal intensity profile of the laser beam (measured without a DPM) is shown in Figure 3a. One can see that before the intensity peak (at time zero), there exists a 750 fs long plateau with a mean intensity of \(\sim\)\(10^{18}\,\mathrm{W}\,\mathrm{cm}^{-2}\). This mildly relativistic intensity level is sufficient to destroy Al targets with thickness below \(1\,\upmu\mathrm{m}\)[44]. Figure 3: (**a**) Laser contrast measurement during direct (DPM-free) shots. (**b**) Images of the specularly reflected laser beam collected on a Spectralon plate during a direct shot on a \(1.5\,\upmu\mathrm{m}\) thick Al target and (**b1**) a DPM shot on a 150 nm (100 nm Si + 50 nm Al) thick target (**b2**).