Direct Observation of Density-Gradient Effects in Harmonic Generation from Plasma Mirrors

High-order harmonics and attosecond pulses of light can be generated when ultraintense, ultrashort laser pulses reflect off a solid-density plasma with a sharp vacuum interface, i.e., a plasma mirror. We demonstrate experimentally the key influence of the steepness of the plasma-vacuum interface on the interaction, by measuring the spectral and spatial properties of harmonics generated on a plasma mirror whose initial density gradient scale length $L$ is continuously varied. Time-resolved interferometry is used to separately measure this scale length.

Figure 1

(a) Experimental scheme for density gradient control. Two mirrors $M_1$ and $M_2$ are used to separate the prepulse and main pulse in time, before the focusing parabola. Side and front views of the full laser beam are shown in red. (b) Resulting intensity distributions of the prepulse beam (gray scale) and main beam (bright central spot) at the focus. (c) Temporal evolution of the spatially resolved phase shift induced on the FDI probe pulse by the plasma expansion triggered by the prepulse. (d) Temporal evolution of the density gradient scale length $L$ at the center of the prepulse beam, as deduced from the measured phase shifts.

Figure 2

Effect of the initial gradient scale length $L$ at moderate laser intensity ($a_0\approx 0.7$). Upper row: measured angularly resolved harmonic spectra for three different values of $L$. The lower graphs show the evolution of the total emission $S^{\prime }(\omega )$ for three different harmonic orders, below (d) and above (f) the maximum plasma frequency ${\omega }_p^{\max }$ of fully ionized silica ($\approx 20{\omega }_L$). Each point corresponds to a single laser shot. Inset (e) shows a zoom on fringes observed in (b), right at the transition between CWE and ROM (see arrows), attributed to interferences between the harmonic signals associated with these two mechanisms.

Figure 3

Angularly resolved harmonic spectra obtained from 2D PIC simulations (CALDER code) for two different values of $L$, at the onset of the relativistic interaction regime ($a_0=0.9$). All physical parameters are comparable to those of the experiment of Fig. 2 except for the maximum plasma density, which is $n_e^{\max }=200n_c$ ($n_c$ critical plasma density for the laser), leading to a maximum plasma frequency (and hence a CWE cutoff) of $\sqrt{n_e^{\max }/n_c}\times {\omega }_L\approx 14{\omega }_L$.

Figure 4

Effect of the initial gradient scale length $L$ at maximum laser intensity ($I=5\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2$, $a_0\simeq 4.9$). (a),(b) Measured angularly resolved harmonic spectra for two different values of $L/\lambda$, 0 in (a) (no prepulse) and 0.06 in (b). Graph (c) shows the evolution of the total emission $S^{\prime }(\omega )$ for three different harmonic orders above the 20th harmonic. In (d), the divergence of the 24th harmonic is plotted as a function of $L$. For comparison, this graph also shows the divergences of two harmonics (gray region) in the moderate intensity regime of Fig. 2, for gradients where ROM dominates the signal. Each point corresponds to a single laser shot.