Figure 1

(a, b) Brunel electron trajectories for $a_0=0.4$, for electrons crossing at a given depth $x_{8{\omega }_L}$ in the plasma, such that ${\omega }_p\left(x_{8{\omega }_L}\right)=8{\omega }_L$, for two density gradients, (a) $\delta ={\lambda }_L/100$ and (b) $\delta ={\lambda }_L/200$. The shaded (red) area corresponds to the overdense part of the plasma ($N>N_c{\cos }^2\theta$). Red lines are the trajectories around the maximum of the laser pulse envelope, and green lines in its edges, at a time when the laser amplitude is halved. (c) Typical unevenly spaced CWE attosecond pulse train. (d) Corresponding harmonic spectrum from $7{\omega }_L$ to $14{\omega }_L$. (e) Harmonic spectral width as a function of harmonic order for $a_0=0.2$, from experiment [filled (blue) circles] and from the analytical model for different plasma density gradients [(red) lines].Reuse & Permissions

Figure 2

(a) Intensity of the ninth harmonic signal [filled (blue) circles] for laser intensities ranging from ${10}^{16}$ to ${10}^{17}$ W cm${}^{-2}$, together with a power-law fit of exponent 2.6 [dashed (green) line]. (b) Width of the ninth harmonic as a function of the laser intensity, from experiment [filled (blue) circles] and from the model [(red) lines] for different plasma gradient lengths.Reuse & Permissions

Figure 3

Chirp dependence of the experimental harmonic spectrum for (a) $\xi =-1$, (b) $\xi =0$, and (c) $\xi =1$, where $\xi$ is the normalized quadratic spectral phase, $\xi {\tau }^2={({\partial }^2{\varphi }_{\omega }/\partial {\omega }^2)}_{{\omega }_0}$, with ${\varphi }_{\omega }$ the laser spectral phase. Dotted (red) lines show spectra obtained from the model. (d) Spectral width of the eighth harmonic as a function of the laser chirp from experiment (blue symbols) and model (red symbols) for different plasma gradient lengths: $\delta ={\lambda }_L/200$ (solid line); $\delta ={\lambda }_L/150$ and $\delta ={\lambda }_L/250$ (dashed lines).Reuse & Permissions

Figure 4

Spectral width of the eighth harmonic as a function of the delay $\Delta t$ between the prepulse at ${10}^{15}$ W cm${}^{-2}$ and the probe at $9\times {10}^{16}$ W cm${}^{-2}$ ($a_0=0.2$). The experimental results [filled (blue) circles] are fitted by the model [solid (red) lines], using an intensity dependence exponent $b=2.6$ and a linear expansion of the plasma with $c_s=20$ nm/ps. The upper $x$ axis shows the values of $\delta \left(t\right)=c_{s}t$ used in the model for the fit.Reuse & Permissions