## 2 Experimental Results  
The experiment was performed using the Gemini laser at the Rutherford Appleton Laboratory, which delivers pulses of duration \(\tau_{L}\sim 40\) fs (full width at half maximum, FWHM) at \(\sim\)810 nm central wavelength, \(\lambda_{L}\). The inherent intensity contrast ratio of the laser beam was enhanced by using a double plasma mirror system [28], to achieve measured values of \(\sim\)10\({}^{9}\) at 5 ps and \(\sim\)10\({}^{11}\) at 1 ns prior to the peak of the pulse. The pulse was also reflected from an adaptive optic mirror in order to minimise aberrations of the laser wavefront and therefore produce a high quality focal spot. A \(\lambda_{L}/4\) wave plate was positioned in the beam to produce circularly polarized light. The beam was focused using a F/2 off-axis parabolic mirror to a spot with diameter equal to 3 \(\upmu\)m (FWHM). An energy of \(\sim\)2 J was measured within the focal spot FWHM, resulting in a calculated peak intensity of 6 \(\times\) 10\({}^{20}\) Wcm\({}^{-2}\). Planar aluminium target foils with thickness, \(l\), equal to 10, 20, 40, 50, 100 and 200 nm were employed, with the target irradiated at normal incidence. Harmonic radiation produced at the PCDS is collected by same parabolic mirror, reflected back down the beam path and transmitted through a dielectric turning mirror, where it is measured using an optical spectrometer (detailed below), as shown in Figure 1a. Figure 1b shows a reference spectrum of the incident laser pulse. Early in the interaction with the laser pulse, plasma electrons are heated, driving expansion of the target and thus the PCDS moves against the laser pulse propagation direction, resulting in it being blue-shifted with respect to a stationary detector, due to the relativistic Doppler effect. As the laser intensity increases, a point is achieved in which the radiation pressure exceeds the plasma thermal pressure and thus the PCDS is driven inward and the laser undergoes hole-boring, giving rise to red-shifting of the reflected light. Both the fundamental wavelength and harmonics produced at the PCDS are shifted by an amount defined by the PCDS velocity, as follows:  
\[\beta_{0}=\frac{v}{c}=\frac{1/\lambda_{0}^{2}-1/\lambda^{2}}{1/\lambda_{0}^{2 }+1/\lambda^{2}} \tag{6}\]  
where \(\lambda_{0}\) is the nominal wavelength of the second harmonic (i.e., \(\lambda_{0}=\lambda_{L}/2\)) and \(\lambda\) is the shifted wavelength. Measuring the wavelength shift of the reflected light thus enables the velocity of the PCDS to be determined. The second harmonic is used, in preference to the fundamental wavelength, because it is produced in the intense region of the focal spot (resulting in less spatial averaging), in a smaller temporal window near the peak of the pulse (less temporal averaging) and is subject to significantly less nonlinear effects, such as self-phase modulation, which contribute to spectral broadening (or narrowing). Those processes can mask wavelength shifts arising from the PCDS dynamics. The spectrum of light in the back reflected path was measured using an optical spectrometer (Andor Shamrock model 303i). Figure 1: (**a**) Schematic of the experimental set-up. Key: FP—focusing parabola; DPM—double plasma mirror; CP—collimating parabola; M—mirror; OS—optical spectrometer; AO—adaptive optic; \(\lambda\)/4—quarter waveplate; F/2—off-axis parabolic mirror with F/2 focusing; T—target foil; PTFE—PTFE scatter screen for imaging the transmitted laser light; (**b**) Example measurement of the spectrum of the laser light before interaction, as made with an optical spectrometer. This spectrometer enables 1D spatially resolved measurements (the other detector dimension corresponds to spectral spread) via the incorporation of a narrow slit (50 \(\upmu\)m width) in the signal input. In addition to the measurements of reflected light, the laser energy transmitted through the target foil was also diagnosed by measuring the light on a PTFE scatter screen positioned 30 cm behind it (see Figure 1a).