Femtosecond X-ray diffraction addresses structural dynamics at atomic length and time scales and has led to ground-breaking new insight into basic physical as well as functional properties of materials [1,2]. To better exploit the strong scientific potential of this method, current developments of accelerator-based and laser-driven hard X-ray sources aim at ultrashort pulses at kilohertz repetition rates and a stable high average photon flux [3 –5]. In this way, subtle transient changes of diffraction patterns become amenable to experiment.

The generation of femtosecond hard X-ray pulses in laser-driven sources is based on the highly nonlinear nonperturbative interaction of a strong-field optical pulse with a metallic target in a three-step process. First, electrons are extracted from the target into vacuum by tunnel ionization, which is driven by the optical electric field component ${E_\perp}$ perpendicular to the target surface. Secondly, vacuum electrons are accelerated in the laser field for a period given by the optical cycle [6] and, thirdly, re-enter the target to generate X-rays. Inelastic collisions of electrons with target atoms lead to inner-shell ionization and emission of characteristic ${\rm K}\alpha$ pulses, while the electron deceleration results in broadband bremsstrahlung [7 –9]. The maximum kinetic energy, which the electrons acquire in the laser field scales with ${({E_{\rm{peak}}}\lambda)^2}\;{\propto}\;{I_{\rm{peak}}}{\lambda ^2}$, where ${E_{\rm{peak}}}$ and ${I_{\rm{peak}}}$ are the peak electric field and intensity of the optical pulse, and $\lambda $ is its center wavelength. The overall X-ray yield increases strongly with the electron kinetic energy as has been verified by experiment and theory [8,9].

Hard X-ray sources based on this concept have made use of intense femtosecond pulses from lasers with repetition rates below 100 Hz. While this approach has provided high X-ray photon numbers per pulse and reached some technical maturity [8,10 –13], X-ray sources working at much higher kilohertz repetition rates are indispensable for measuring subtle changes in transient X-ray diffraction patterns and deriving transient charge density maps from them [14 –17]. The latter technology has been optimized with respect to sensitivity and allows for measuring relative changes of diffracted intensity on the order of ${{10}^{- 3}}$ with a sub-100 fs time resolution [18]. To fully exploit the potential and improve the versatility of such laboratory-based experiments, a substantial enhancement of the available hard X-ray flux is required.

Here we present a novel femtosecond table-top hard X-ray source providing an X-ray photon flux of up to ${1.5} \times {{10}^{12}}\;{\rm photons}/{\rm s}$. An optical parametric chirped-pulse amplifier (OPCPA) system generating multi-millijoule femtosecond pulses at a center wavelength of 5 µm and a 1 kHz repetition rate [Fig. 1(a)] serves as the optical driver [19,20]. This system is described in detail in Supplement 1. The spectrum of the OPCPA idler output covers a wavelength range from 4 to 5.5 µm [Fig. 1(b)]. The recompressed idler pulses are linearly polarized, and have a duration of 80 fs [Fig. 1(c)], a temporal intensity contrast better than 1000, and an energy of up to 3.0 mJ, corresponding to an average power of 3.0 W with very low fluctuations of 1.2% rms. The beam profile [inset of Fig. 1(d)] is nearly diffraction-limited with an ${{\rm M}^{2}} \le {1.3}$ (${\rm M}$: beam quality factor).

 

Fig. 1. Experimental setup and characterization of the 5 µm driver: (a) schematic layout of the key parts of the 5 µm driver laser system and the setup for the generation and characterization of the hard X-ray pulses via diffraction on a GaAs wafer (SC, supercontinuum; CPA, chirped-pulse amplification; ZGP, ${{\rm ZnGeP}_2}$; OAPM, off-axis parabolic mirror). (b) Measured spectrum and (c) pulse shape retrieved via third-harmonic frequency-resolved optical gating (TH-FROG) of the 5 µm pulses. (d) Knife-edge measurements of the focal spot of the 5 µm beam (open blue circles, magenta line) and the X-ray source (black circles, red line). The inset shows a 2D profile of the 5 µm beam before expansion.

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For X-ray generation, the expanded 5 µm beam is focused with an off-axis parabolic mirror (focal length 100 mm) onto a 20 µm thick Cu tape target [red line/spools in Fig. 1(a)], placed in a vacuum chamber (pressure 0.1 mbar). The optical field has in-plane ($p$) polarization, and the optical spot size on the target is 19 µm [Fig. 1(d), blue symbols]. The tape target is moved by an electric drive at a velocity of several centimeters/second to provide a fresh target volume for each driving pulse. In parallel, there are two moving plastic tapes [blue lines/spools in Fig. 1(a)] which take up the Cu debris generated during optical pumping.

The characteristic ${\rm K}\alpha$ emission with a femtosecond time structure [2,9] fills the full solid angle of ${4}\pi$. For a quantitative analysis, part of the emission in forward direction passes a pinhole (diameter: 3 mm) directly after the exit of the vacuum chamber. The X-ray flux in this solid angle of ${5.2} \times {{10}^{- 3}}$ hits a GaAs single crystal wafer in (001) orientation, and the ${\rm K}{\alpha _1}$ and ${\rm K}{\alpha _2}$ components of the (002) Bragg reflection are recorded with a two-dimensional X-ray detector. The details of the setup and data analysis are given in Supplement 1.

The key results characterizing the X-ray output of the laser-driven source are summarized in Fig. 2. Figure 2(a) displays the ${\rm K}{\alpha _1}$ and ${\rm K}{\alpha _2}$ (002) reflections on the X-ray detector. Their lateral separation is determined by the slightly different diffraction angles, while their length corresponds to the solid angle of emission as defined by the pinhole behind the target (see Supplement 1). In Fig. 2(b), the spatially integrated X-ray intensity [integration area marked by solid lines in Fig. 2(a)] minus the integrated background signal [area marked by dashed lines in Fig. 2(a)] is plotted as a function of the diffraction angle ${2}\Theta$. The ${\rm K}{\alpha _1}$ and ${\rm K}{\alpha _2}$ components are clearly discerned. The full spectrum of the X-ray emission [Fig. 2(e)] was measured with an energy resolving CdTe detector in the single-photon regime (energy resolution: 500 eV). The ${\rm K}\alpha$ and ${\rm K}\beta$ lines shown in the inset are complemented by the broad spectrum of bremsstrahlung. An exponential fit of the high-energy tail [solid line in Fig. 2(e)] yields a photon temperature of 29 keV, substantially higher than for shorter driver wavelengths.

 

Fig. 2. Characterization of the femtosecond hard X-ray source: (a) Debye–Scherrer ring sections of the (002) reflection from a GaAs wafer of the ${\rm Cu} - {\rm K}{\alpha _1}$ and ${\rm Cu} - {\rm K}{\alpha _2}$ emission recorded with a large area detector. (b) Spatially integrated X-ray flux as a function of the diffraction angle, as derived from the data in panel (a). (c) ${\rm K}\alpha$ photon number per pulse in the full solid angle as a function of the optical electric field ${E_\perp}$ perpendicular to the Cu surface. Data for the 5 µm OPCPA system (blue circles) are compared to the results for a Ti:sapphire driver laser (black circles). The solid lines are the results of theoretical calculations. The error bars indicate the uncertainty in pulse duration and focus diameter. (d) Normalized number of ${\rm Cu} - {\rm K}\alpha$ photons per shot as a function of the angle of incidence $\gamma$ of the optical beam on the target. (e) Full emission spectrum of the femtosecond X-ray source. Solid blue line: exponential fit of the bremsstrahlung with a photon temperature of 29 keV. The inset displays the ${\rm K}\alpha$ and ${\rm K}\beta$ emission lines.

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The total ${\rm K}\alpha$ flux from the source was studied in extensive measurements and depends strongly on the intensity and related peak field strength of the optical pulses. The total number $N$ of X-ray photons emitted per pulse into the full solid angle ${4}\pi$ was derived from the flux recorded by the area detector as described in Supplement 1. In Fig. 2(c), ${\rm N}$ is plotted as a function of the peak electric field ${E_\perp}$ of the 5 µm driving pulses perpendicular to the target surface (blue symbols). The field ${E_\perp} = {({2}{I_{\rm{peak}}}/{\rm c}{\varepsilon _0})^{1/2}}({1} + {{\rm R}^{1/2}})\;{\rm \sin}\gamma$ was calculated from the peak intensity ${I_{\rm{peak}}}$ of the optical pulses on the target, as estimated from the pulse energy, duration, and spot size [$c$, velocity of light; ${\varepsilon _0}$, permittivity of vacuum; ${\rm R}\; \approx \;{1}$, reflectivity of Cu at 5 µm; $\gamma$, angle of incidence on the target; see Fig. 1(a)]. The data were recorded at $\gamma = {65}^\circ$.

We observe a steep rise of the X-ray photon number over six orders of magnitude which is close to exponential for ${E_\perp}$ between 150 and 300 V/nm. The maximum X-ray photon number is ${\rm N} = {1.5} \times {{10}^9}$ per pulse, corresponding to an average X-ray flux of ${1.5} \times {{10}^{12}}$ photons per second and a conversion efficiency of ${6} \times {{10}^{- 4}}$. The solid magenta line in Fig. 2(c) is a result of theoretical calculations discussed below. The black symbols and the red line in Fig. 2(c) represent the results for 35 fs 0.8 µm driving pulses from an amplified Ti:sapphire laser system (incidence angle $\gamma = {42}^\circ$) [16,17], a standard source frequently used in current table-top diffraction experiments. Here the maximum X-ray photon number per pulse of ${5} \times {{10}^7}$ and the corresponding average flux are 30 times smaller than with the 5 µm driver laser. Moreover, there is a strong rescaling of the driving electric field between the two cases with much lower fields for the 5 µm pulses. This behavior is fully in line with a ${I_{\rm{peak}}}{\lambda ^2}$ scaling.

A variation of the angle of incidence $\gamma$ of the pump beam on the Cu target changes the in-plane electric field component perpendicular to the target surface, the electric field relevant for X-ray generation [9]. In Fig. 2(d), the (normalized) X-ray flux per laser shot is plotted as a function of $\gamma$ and displays a maximum at $\gamma = {65}^\circ$, the angle at which the data in Fig. 2(c) were recorded. The diameter of the X-ray emitting target volume was determined with a knife-edge method detailed in Supplement 1. The result shown in Fig. 1(d) (black symbols) gives a source diameter of 34 µm.

The long-term stability and the pulse-to-pulse fluctuations of the generated hard X-ray flux are highly relevant for applications of the source in ultrafast experiments and limit the smallest measurable signals, e.g., intensity changes on particular Bragg peaks. Figure 3(a) shows the ${\rm Cu}-{\rm K}\alpha$ flux detected via the GaAs (002) reflection over a period of 1400 s. Each point was averaged over a time interval of 1 s or 1000 pulses. A variation of the average flux by about $\pm {10}\%$ around the mean value is observed over time scales larger than 100 s. This change is mainly caused by a slight displacement of the Cu target along the driver laser beam path away from the optimal focusing spot, due to a change of tension in the Cu tape target while spooling. As is evident from the X-ray flux data for different target positions shown in Supplement 1, a displacement as small as 50 µm from the optimal focus position is enough to explain such long-term drifts. During long-term optical pump/X-ray probe experiments, the position of the copper target is periodically corrected to the ideal position by employing an optimization feedback routine to ensure a stable and high ${\rm Cu} - {\rm K}\alpha$ flux.

 

Fig. 3. Stability of the generated X-ray flux: (a) long-term stability measurement of the ${\rm Cu} - {\rm K}\alpha$ flux emitted by the X-ray source. The two dips observed at ${t}\sim{180}$ and ${t}\sim{450}\;{\rm s}$ with a flux of zero are caused by a change in the direction of motion of the plastic tapes used for debris collection. (b) Power spectrum of the shot-to-shot ${\rm Cu} - {\rm K}\alpha$ flux. The inset shows a histogram of the number of photons detected per shot in comparison with a Poisson distribution for the same average flux.

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The Fourier spectrum of the shot-to-shot ${\rm Cu} - {\rm K}\alpha$ flux was determined to identify the major fluctuation frequencies. This spectrum is presented in Fig. 3(b). In the frequency range between 0.1 and 10 Hz, one finds a decrease by about two orders of magnitude in amplitude, roughly following an ${f^{- 1}}$ dependence on frequency $f$. Such behavior is typical for a photon source with the characteristics of pink noise. On top, the spooling mechanics of the Cu tape target and the plastic protection tapes driven by stepping motors introduce characteristic frequency components at $f\;\sim\;{0.5}$, 5, and 27 Hz. At higher frequencies (${\gt}{100}\;{\rm Hz}$), the experimental spectrum differs slightly from a Poisson distribution with the same average flux, as shown in the inset of Fig. 3(b). The shot-to-shot fluctuations are on the order of 40%. The overall behavior observed here is close to the earlier results for a source driven with femtosecond 0.8 µm pulses [18].

We now briefly discuss the different steps of X-ray generation with the 5 µm driver from a physics point of view, based on theoretical simulations with the model of Ref. [9]. Field-induced electron extraction from the target into vacuum, the first step, proceeds via tunnel ionization of Cu atoms. For the present experimental conditions, the simulations predict an extraction (tunneling) probability close to one, due to the strong distortion of the Cu electronic structure by the optical field perpendicular to the target surface. Acceleration of vacuum electrons in the strong optical field, the second step, becomes more efficient for a longer temporal period of the field as the overall acceleration time increases. The maximum kinetic energy of the electrons scales with ${I_{\rm{peak}}}{\lambda ^2}$, leading to the rescaling of the driving field. This behavior is nicely borne out by the 5 and 0.8 µm data sets in Fig. 2(c). The width of the spectrum of bremsstrahlung and the photon temperature [Fig. 2(e)] are proportional to the maximum kinetic energy of the electrons on the order of 100 keV. In line with the theoretical prediction, the photon temperature of 29 keV observed with the 5 µm driver is substantially higher than the values of 21 keV for a 3.9 µm driver [8] and 19 keV for 0.8 µm excitation [17].

The accelerated electrons reentering the target undergo inelastic collisions with Cu atoms, leading to K-shell ionization and emission of characteristic unpolarized X-rays (third step). The collision cross section shows a minor variation for electron energies between 20 and 100 keV [9]. As a result, the number of successful ionization events induced by an electron and the number of generated ${\rm K}\alpha$ photons increase strongly with its kinetic energy. This mechanism is behind the much higher X-ray photon flux generated with the 5 µm compared to the 0.8 µm driver. It is important to note that the theoretical calculations [solid lines in Fig. 2(c)] reproduce the experimental results in a quantitative way. The calculations predict a duration of the ${\rm K}\alpha$ X-ray pulses of 120 fs.

In conclusion, we presented a novel femtosecond hard X-ray source providing an unprecedented flux of ${1.5} \times {{10}^{12\;}}{\rm Cu} - {\rm K}\alpha$ photons per second. We envisage a broad range of applications in condensed matter research, allowing for new insight into the dynamics of atomic arrangements and electronic structure.