Harmonic Generation from Relativistic Plasma Surfaces in Ultrasteep Plasma Density Gradients

Harmonic generation in the limit of ultrasteep density gradients is studied experimentally. Observations reveal that, while the efficient generation of high order harmonics from relativistic surfaces requires steep plasma density scale lengths ($L_p/\lambda <1$), the absolute efficiency of the harmonics declines for the steepest plasma density scale length $L_p\to 0$, thus demonstrating that near-steplike density gradients can be achieved for interactions using high-contrast high-intensity laser pulses. Absolute photon yields are obtained using a calibrated detection system. The efficiency of harmonics reflected from the laser driven plasma surface via the relativistic oscillating mirror was estimated to be in the range of ${10}^{-4}–{10}^{-6}$ of the laser pulse energy for photon energies ranging from 20–40 eV, with the best results being obtained for an intermediate density scale length.

Figure 1

Experimental setup: High-contrast laser pulses were focused with an $f/2$ off-axis parabolic mirror to up to $3\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2$ on a fused silica or plastic coated substrate at 45° $p$-pol. The XUV emission was recorded with two spectrometers separately (in the presented data only plastic coated targets are used). The flat-field spectrometer shown in configuration 1 allows a measurement of the beam divergence. The XUV spectrometer system in configuration 2 has a larger collection angle and was calibrated regarding the incident photon flux. The black line represents the centroid beam of the laser steering into the center of the XUV spectrometers.

Figure 2

(a) Surface field ${\mathbf{E}}_{\mathrm{crit}}$ at the critical density in units of the incident field ${\mathbf{E}}_0$, as estimated from the equation in Ref. 22 (black dashed line) and computed exactly by numerical integration for an exponential gradient (blue line). (b) Efficiency of ROM harmonics above the 14th order ${\eta }_{\mathrm{ROM}}={\int }_{14{\omega }_0}^{\infty }I(\omega )d\omega /P_0$ for $a_0=3.5$ at different plasma scale lengths from a set of 1D PIC simulations. Incidence was $p$-polarized, the plasma ramp is exponential up to a maximum density of $n_e=200n_c$.

Figure 3

Experimental efficiencies (circles) are compared to spectral densities from 1D PIC simulations (lines) for different plasma scale lengths (density $n_e=200n_c$, exponential density profile). The upper points and graphs (blue) correspond to $L_p=\lambda /5$ and the lower ones (red) to $L_p\le \lambda /10$. The experimental efficiencies have been normalized to a pulse energy of 250 mJ (energy that is focused to $a_0>1$). In the ultrarelativistic limit the efficiencies converge to the BGP power scaling $\eta \approx (\omega /{\omega }_0{)}^{-8/3}$ [7].