High-order harmonic generation in a strongly overdriven regime

High-order harmonic generation (HHG) normally requires a careful adjustment of the driving laser intensity (typically ${10}^{14}–{10}^{15}$ W/${\mathrm{cm}}^2$) and gas medium parameters to obtain a microscopically and macroscopically optimized output. In contrast to conventional wisdom, we present experimental results indicating efficient HHG in all rare gases, using a high-density medium and a driving laser intensity of around ${10}^{16}$ W/${\mathrm{cm}}^2$. The experimental results are corroborated by theoretical simulations, which indicate that ionization-induced self-phase modulation and plasma defocusing self-regulate the driver laser intensity to a level that allows efficient HHG. A tenfold broadening of the driving near-infrared spectrum is observed, which results in the generation of continuous spectra from 18 to 140 eV in spite of using 50-fs-long driving pulses. The presented scheme represents a simple and versatile concept for the generation of extreme-ultraviolet and soft-x-ray continua, which could be used for transient absorption and reflection spectroscopy.

Figure 1

Schematic of the experimental setup. An NIR beam is focused into a dense atomic jet using a lens with a focal length of 1 m, resulting in an increase of the divergence and a spectral blueshift of the driving pulses. The generated XUV spectrum is analyzed using an XUV spectrometer.

Figure 2

Spectral broadening of the driving laser pulses for (a) Xe at $5\times {10}^{15}{\text{W/cm}}^2$, (b) Kr at $8\times {10}^{15}{\text{W/cm}}^2$, (c) Ar at $8\times {10}^{15}{\text{W/cm}}^2$, (d) Ne at $1.6\times {10}^{16}{\text{W/cm}}^2$, and (e) He at $1.6\times {10}^{16}{\text{W/cm}}^2$ using backing pressures from 2 to 10 bar. The spectra are normalized and the applied peak intensities are indicated. The black solid curve corresponds to the unperturbed NIR spectrum.

Figure 3

Normalized HHG spectra obtained from (a) Xe, (b) Kr, (c) Ar, (d) Ne, and (e) He. The blue solid curves represent spectra recorded at standard HHG conditions, i.e., moderate driving laser intensities and gas pressures, resulting in narrowband harmonics. The orange dotted curves represent HHG spectra obtained in the high-pressure jet ($2–10$ bar) at NIR driving laser intensities of $0.5\times {10}^{16}$ W/${\mathrm{cm}}^2$ (Xe), $0.8\times {10}^{16}$ W/${\mathrm{cm}}^2$ (Kr and Ar), and $1.6\times {10}^{16}$ W/${\mathrm{cm}}^2$ (Ne and He). In (e) narrowband lines are visible within the otherwise continuous HHG spectrum (orange dotted curve), which are attributed to NIR-induced free-induction decay [25] involving the $2p$ and higher excited states of ${\mathrm{He}}^{+}$ ions.

Figure 4

Spatially resolved HHG spectra for Ne using a backing pressure of (a) 2 bar and (b) 10 bar. The horizontal axis refers to the spectral coordinate and the vertical axis corresponds to the divergence.

Figure 5

Simulated properties of NIR pulses with an initial peak intensity of $8\times {10}^{15}$ W/${\mathrm{cm}}^2$ during and after propagation through a Ne jet using a peak pressure of 400 mbar. (a) Radially resolved NIR intensity distribution as a function of the propagation distance $z$ through the jet. The arrows mark specific $z$ values for which the on-axis temporal intensity distributions are shown in (b). (c) Driving laser spectral properties as a function of time. The black solid curve shows the cycle-averaged carrier frequency (normalized to the initial nominal central frequency) calculated from the temporal change of the refractive index, which is dominated by changes of the density of free electrons $n_e$ (red dashed curve).

Figure 6

Simulation results showing the spatial evolution of different microscopic and macroscopic quantities in HHG in the spectral region from 42 to 45 eV. (a) Polarizability shown in logarithmic scale for H27, (b) time-dependent coherence length calculated at $t=-12$ optical cycles (o.c.) of the driving laser (in logarithmic scale), and (c) macroscopic buildup of the harmonic signal for H27 intensity (in logarithmic scale). The black solid curve in (c) shows the parabolic pressure distribution which is peaked at 1.5 mm.

Figure 7

Simulated HHG properties in the strongly overdriven regime. (a) Spatially integrated HHG spectra at pressures of 133 mbar (red solid curve) and 400 mbar (blue dotted curve), showing the generation of a quasicontinuous XUV spectrum in the latter case. (b) Radially dependent HHG emission for harmonic orders 15–51 as a function of time. The data were analyzed at a distance of 70 cm from the jet and are shown on a logarithmic scale. The horizontal lines indicate that spatial filtering may result in the generation of short attosecond pulse trains.