Main

Relativistic laser plasmas have been shown to support the generation of bright beams of XUV radiation with attosecond duration9 and high spatial quality10 in reflection. Experimental observations5,10,11 in the spectral region above the maximum plasma frequency of the interaction12 (ωpmax) are consistent with a relativistic Doppler effect provided by a highly reflective critical density plasma surface collectively oscillating in the intense field of the incident laser pulse1,2,3,4. This periodic upshifting of the driving radiation into the specularly reflected direction results in harmonic spectra consistent with the relativistically oscillating mirror (ROM) mechanism characterized by I(n)ROMn−8/3scaling4,5, where n is the harmonic order. It should be noted that there is another mechanism that can dominate for frequencies below ωpmax of the target—coherent wake emission. Here we exclusively discuss harmonic frequencies above ωpmax for our interaction densities.

Studies into how laser energy couples to relativistic plasmas, however, have revealed a fundamentally different mechanism for coherent XUV/X-ray generation. Simulations show that dense nanobunches of electrons can be periodically formed and accelerated during each laser cycle at the vacuum–plasma interface for oblique incidence interactions13. Conditions have been identified (namely ultrashort plasma-density scale lengths) for which such nanobunches can emit bursts of CSE in specular reflection for few-cycle (<5) interactions7. CSE from relativistic laser plasma interactions is predicted to be characterized by a slowly varying, synchrotron-like harmonic spectrum scaling as I(n)CSEn−4/3 to n−6/5up to a rollover frequency ωrs that is intrinsically linked to δ, the spatial extent, and γmax the maximum relativistic Lorentz factor, of the nanobunch. Above ωrs the spectrum exhibits a very rapid exponential rollover7,8.

In this regime coherent XUV/X-ray emission can no longer be described by a relativistic Doppler upshift from a smooth critical-density-plasma surface oscillating in the laser field. Instead CSE relies on the formation and rapid acceleration of dense electron nanobunches at the relativistic plasma surface by the driving laser field for bright XUV/X-ray generation14.

Unfortunately, isolating the CSE mechanism in specular reflection during oblique incidence interactions is not straightforward from an experimental perspective. The requirement of high interaction intensity (1018 W cm−2) at present typically implies the use of many-cycle laser pulses (5), which in turn results in evolving plasma parameters, in particular the plasma density profile becoming comparable to λlaser, the laser wavelength. This evolution prevents the specific conditions7,8 required for CSE generation from being maintained (or even attained) over the entire pulse duration. On the contrary, the evolution of the plasma towards relatively longer density scale lengths favours the ROM mechanism to dominate14,15,16,17 over CSE during the interaction. Consequently, characteristic CSE spectra in reflection from relativistic laser plasma interactions have not been observed so far.

To overcome this problem we investigate an interaction geometry where the relativistic Doppler effect cannot play a role—normal incidence interactions with ultrathin foils where coherent XUV radiation is studied in transmission (Fig. 1a). In the transmitted direction it is not possible to observe emission due to ROM Doppler upshifting because this can occur only if there is a reflective surface moving towards the incident radiation. Previous work on the mechanisms of harmonic generation in transmission from foils has been predominantly examined for oblique incidence interactions14,18,19.

Figure 1: Mechanism for CSE in transmission during normal incidence interactions.
figure 1

a, A few-cycle super-Gaussian pulse, a0 = 20, in normal incidence on a 200-nm-thick solid-density (800 Nc) foil with a 100 nm linear pre-plasma ramp to vacuum is studied using the PICWIG 1D/3-P PIC code20. See Methods for the definition of a0 and Nc. b, The trajectories of those quasi-electrons that gained the longitudinal momentum px>5 during 1.5 laser cycles. c, The intensity of emission with respect to position and time from the same simulation parameters extracted from the nanobunch trajectories (blue implies stronger emission). d, A 2D PIC simulation (PSC code21) demonstrating dense electron nanobunch formation during normal incidence interactions. This simulation is performed for a 50 fs pulse with a0 = 20, target thickness 150 nm with a 100 nm linear ramp to vacuum on the front and rear surfaces, and density 40 Nc. The density profile is measured along the white dashed line (d) and the bunch width δ is measured at x. The CSE mechanism is discussed in greater detail in the Supplementary Information.

The fundamental mechanism for coherent XUV/X-ray generation in this geometry is studied using particle-in-cell (PIC) codes20,21 and is detailed in Fig. 1bd. Dense nanobunches of electrons are formed at the front surface of the target and accelerated into the transmitted direction owing to the relativistic ponderomotive force of the laser (Fig. 1b). This observation is in excellent agreement with previous work22. These nanobunches undergo rapid elliptical trajectories across the plasma–vacuum boundary before being emitted through the rear of the foil in the transmitted laser direction. Examining the temporal evolution of radiation emitted from a given trajectory reveals an intense, ultrafast (<0.1 laser cycle duration) XUV pulse emitted in the transmitted direction just as the bunch reverses its direction towards the target. This is shown by the blue regions in the XUV emission intensity mapped onto the bunch trajectories (Fig. 1c). The nanobunches are observed to have a spatial extent at the resolution limit of the simulation of δ10 nm and a density >0.4 Nmax (where Nmax is the maximum target density, Fig. 1d).

Figure 2 shows the spectrum and corresponding temporal structure generated in transmission during the rising edge of a 500 fs laser pulse in normal incidence on an ultrathin foil from PIC simulations. The spectrum is characterized by a low-frequency cutoff (corresponding to ωpmax of the parent foil) and an efficiency scaling slope closely following the n−4/3 predicted for CSE in specular reflection7,8. The n−8/3 ROM scaling is shown for comparison. In this geometry the high-density plasma acts as a high-pass frequency filter and permits the generation of an attosecond pulse train without the need for further spectral filtering. This is shown in Fig. 2b, which confirms the temporal coherence of the CSE mechanism. It is worth noting that simulations have also shown that the characteristic spectral shape of CSE can also lead to attosecond pulse production even in the absence of such filtering7,8.

Figure 2: PIC code simulations for CSE in transmission from normal incidence interactions.
figure 2

a,b, Spectrum (a) and corresponding pulse train (b) from the 1D simulation20 generated during the temporal interval −200 to −100 fs (cycles −60 to −30) on the rising edge of a 500 fs/150 cycle pulse centred on 0 fs (that is, −75 cycles (early) to +75 cycles (late)), with a0 = 20, in normal incidence on a 200 nm foil at maximum density Nmax = 800 Nc. See the Methods for the definition of a0 and Nc. To verify the scaling of the emission, the data have been normalized at nco = ωpmax/ωLaser = 8001/2 = 28, corresponding to a low-frequency cutoff harmonic order (where ωLaser is the laser frequency). The solid and dashed black lines correspond to I(n)CSEn−4/3 and I(n)ROMn−8/3 scalings, as labelled. The inset shows the relative absolute scaling for the CSE and ROM mechanics. For harmonic orders <nco emission is strongly suppressed owing to the opacity of the solid density plasma, which here corresponds to the maximum target density with nco = 28. It is important to note that the n−4/3 scaling shown here is a fit to the simulation. We have chosen this temporal window of the driving pulse as it most clearly shows the CSE mechanism. It is important to note that the observed spectral scaling from the simulation is due to a combination of both the CSE mechanism and the evolution of the spectrum over the entire interaction. The dashed red line in b is a guide to see the attosecond pulse structure. See Supplementary Information for a more general discussion on CSE and the dynamic evolution of the emitted spectral shape for 500 fs pulses and 50 fs pulses using both 1D and 2D simulations.

To investigate the generation of CSE in transmission from ultrathin foils we performed experiments using the Trident Laser Facility23 at the Los Alamos National Laboratory. Nanometre-scale thickness diamond-like carbon (DLC) foil targets were placed in the laser focus normal to the incident beam (Fig. 1a), resulting in peak interaction intensities of 4×1020 W cm−2. See Methods for laser pulse contrast considerations.

Figure 3 shows typical harmonic spectra obtained in transmission from 200 nm DLC targets using a Hitachi flatfield-grating-based XUV spectrometer and a backthinned Andor CCD (charge-coupled device) detector. The spectrum emitted in a cone along the laser axis is characterized by a very slow decay to high orders (Fig. 3a). The off-axis spectrum at larger angles around the laser axis exhibits a more rapid decay to high orders (Fig. 3b). These two spectra combined demonstrate XUV-emission cone narrowing with increasing harmonic order24. The spectrum also exhibits a low-frequency cutoff 25<nco<26. The presence of this low-frequency cutoff is a clear indication of the maintenance of a near-solid-density plasma at the time of CSE generation for 200 nm foils and confirms CSE from the front surface of the foil. This is in excellent agreement with hydrodynamic and PIC simulations for our exact pulse profile and interaction intensity. Spectra from 125 nm foils were also studied and exhibit no low-frequency cutoff in this spectral range, indicating a significantly reduced interaction density due to the lower target thickness.

Figure 3: Harmonic spectra in transmission from 200-nm DLC foils.
figure 3

a, A typical CCD image and spectrum obtained in transmission along the laser propagation axis from 200 nm foils (0 mrad to 52±8 mrad half-cone angle, spectral lines marked with asterisks) collected using an adjustable gold focusing optic. b, The spectrum obtained off the laser propagation axis (35±5 to 140±5 mrad halo). Strong suppression of lower-order harmonics (n<26) is observed, implying a maximum target density Nmax>252Nc = 625 Nc at the time of generation. See Supplementary Information for experimental set-ups.

Figure 4 shows harmonic spectra corrected for system transmission (normalized to n = 33) from normal-incidence interactions for 200 nm (red triangles) and 125 nm (open blue diamonds) DLC foils. The relative efficiency scaling for n<70 is significantly shallower than the n−8/3 expected for the ROM mechanism4,5 in both cases, and is consistent with CSE being the dominant emission mechanism. A very rapid rollover for n>70 is observed, again consistent with the CSE mechanism. The scaling of the absolute signal with foil thickness is shown in the inset of Fig. 4. No harmonic signal was observed for 50 nm DLC targets. The harmonic signal level increases by an average factor of 5.1±0.3 for an increase in target thickness from 125 to 200 nm. This marked signal increase is in good agreement with predictions for CSE signal variation with density scale length7,8.

Figure 4: Harmonic spectra from DLC foils normalized at n = 33.
figure 4

Harmonics from 200 nm (red triangles) and 125 nm (open blue diamonds) foils are spatially and spectrally integrated and corrected for system transmission giving best fits of n(−1.62,+0.12,−0.13) and n(−2.1,+0.15,−0.22), respectively, for n<70. The gap in the spectrum is due to spectrometer transmission. The bars represent uncertainty due to shot-to-shot fluctuations and propagation of errors from spectral deconvolution. The dashed (n−(1.49)) and dot–dashed (n−(2.25)) lines correspond to maxima (for 200 nm) and minima (for 125 nm) fits to the uncertainty for n<70, respectively, and essentially represent the extrema of the total uncertainty for this experiment. The curved solid black line serves as a guide to the spectral shape of the emission from the 200 nm foils. The inset shows the absolute count levels for 125 nm and 200 nm DLC targets and compares these with the relative signal strength expected from a corresponding ROM (n−8/3) source (that is, for equivalent signal level at n = 1). The observed absolute energy in a single harmonic can be estimated as 200±50 μJ at 20 nm (58th harmonic) for 200 nm DLC foils and can be considered a lower bound due to the limited detection aperture in our experiment. Further studies of the spatio-temporal evolution of the interaction will be required to optimize conversion efficiency. Simulations show that the scattered halo observed in the kiloelectronvolt beam is a direct result of using a 500 fs pulse. See Supplementary Information for a detailed discussion on this topic.

The on-axis cone angle of 1 keV emission (n = 1,000, see Methods) is observed to be 10±1 mrad at full-width at half-maximum. A key feature of this profile is the presence of a lower intensity wide-angle 120±10 rad scattered halo. This feature is also observed in two-dimensional (2D) simulations21 and is due to the reduction in the coherence of the generation mechanism during the later stages of the 500 fs pulse. See Supplementary Information for a description of this measurement and discussion on how foil evolution affects the absolute conversion efficiencies observed in this experiment.

A tantalizing prospect for a bright attosecond source25,26 such as the one presented here is the potential for increasing focused intensities significantly beyond those of the driving laser. Previous work on the ROM mechanism has shown that substantial increases in peak intensity can be obtained owing to the spatio-temporal compression of the incident electromagnetic radiation through the frequency upshifting process27. The significantly slower decay of CSE spectra (n−4/3) when compared with those produced by the ROM mechanism (n−8/3) indicates the potential for substantial increases in peak intensity, well beyond those predicted for ROM scaling under idealized conditions8.

Strongly beamed XUV/X-ray harmonic emission with scaling consistent with the CSE mechanism is observed in transmission from ultrathin solid foils. The ability to generate CSE extending to the X-ray regime in transmission is shown to be made possible by the unique electron dynamics driven by the intense laser field at the front surface of the relativistic plasma. These dynamics allow for dense nanobunches (that is, 109 m scale) to be formed and accelerated on ultrafast timescales (1015 s). The observation of harmonic spectra in transmission from ultrathin foils with characteristic CSE scaling is clear evidence that the unique dynamics provided during relativistic laser plasma interactions can produce and rapidly accelerate dense attosecond electron bunches suitable for the emission of bright, coherent XUV/X-ray radiation in a convenient, practical geometry (see Methods).

Methods

Laser-pulse contrast.

The Trident Laser Facility23 at Los Alamos National Laboratory is a Nd:glass (λL = 1,053 nm) system delivering laser pulses with an energy of EL = 80 J in 500 fs focused to a near-diffraction-limited focal spot using an F/3 off-axis parabolic mirror. With this system a laser peak to pre-pulse level contrast of 1:10−10 at 1 ns and 1:10−7 at 10 ps is achieved. The near-time (sub 10 ps) shot-to-shot variation in pulse contrast was measured using a single-shot third-order autocorrelator, showing typical values of 1:10−4 at 2 ps. It should be noted that contrast-enhancing plasma mirrors typical of relativistic laser–plasma-based harmonic generation were not required.

Simulations.

To study the CSE generation mechanism in normal incidence in transmission we have performed a parametric study using two simulations (1D, 3-P PICWIG (ref. 20) and 2D PSC (ref. 21) PIC codes) to identify the exact generation mechanism and anticipated spectral shape of the emission in transmission. In the manuscript, a0 is the normalized vector potential, where , and IL and λL are the focused intensity and wavelength of the driving laser. The critical density for the incident driving laser, Nc, is defined as Nc = (ε0meωL/e2)c and ωL is the laser frequency, which itself depends on the electron charge e and mass me.

Kiloelectronvolt beam footprint.

The CSE >1 keV was examined using an image plate detector and edge filter stack. The beam profile is determined by background subtraction and correction for multiple scans of the image plate. The image plate was placed behind a pair of magnets with an average B-field of 0.44 T to deflect charged particles and was filtered using 50 μm Al foil. To confirm the presence of kiloelectronvolt radiation a spectral step filter was used over the lower half of the image plate (100 μm CH). See Supplementary Information for the experimental set-up and further details.