Cut-off scaling of high-harmonic generation driven by a femtosecond visible optical parametric amplifier

Coherent extreme ultraviolet (EUV) sources are of increasing importance in the scientific community because of their numerous scientific [1–5] and industrial [6] applications. Several types of laser-like sources have been developed in the EUV spectral range, such as plasma-based EUV sources [7], using both gas [8] and solid targets [9], and free electron lasers (FELs) [10]. FELs in particular are revolutionary light sources due to their very high photon flux allowing for pump-probe and imaging experiments. FELs typically operate by self-amplified spontaneous emission, which inevitably contributes to the poor coherence, pulse-to-pulse timing jitter and poor electric field reproducibility of the output pulses, limiting the time resolution in pump-probe experiments to around 100 fs [11]. In order to improve their coherence and stability, there has been much recent interest [12–17] in the direct seeding of high photon flux EUV sources with high-harmonic generation (HHG) in noble gases, due to their excellent temporal and spatial coherence. Pulse energies in the nJ range [18] are required to effectively seed FELs in the tens of eV photon energy range to overcome spontaneous emission and transfer the beneficial HHG coherence properties to the FEL output light. In addition, x-ray FELs can be seeded in the hard x-ray range by a coherent EUV source via cascade upconversion processes in undulators based on high-gain harmonic generation [19].

In recent years, the wavelength scaling of cut-off energy and conversion efficiency of HHG has been extensively studied with long-wavelength pulses in the infrared region [20–23], mainly because it is beneficial to extend the cut-off energy of the produced harmonics. However, the HHG efficiency dramatically decreases for longer driver wavelengths. The single-atom efficiency scales with the driver wavelengths as λ^−(5–6) [24–26], and the total efficiency that takes propagation and phase matching into account decreases even more rapidly as λ^−(8–10) [27] because phase matching becomes more difficult for longer driver wavelengths. Therefore, the long-wavelength IR drivers are not a good choice for HHG in the range of low photon energy, i.e. the EUV range (<∼100 eV), a spectral region of interest for many applications like photoelectron spectroscopy [28, 29] and lithography [30].

Visible drivers are better suited for the generation of high-flux EUV radiation because they guarantee higher conversion efficiencies than infrared drivers, the power spectrum is split among fewer harmonics orders and the cut-off energy falls within the optimum range for FEL seeding. In our previous studies, we used 800 nm pulses from a Ti:sapphire amplifier and its second harmonic at 400 nm to estimate the energy efficiency scaling of the HHG process, which was supported by a theoretical model that accurately predicted the wavelength scaling [31]. We predicted that by driving HHG with visible pulses, one should be able to obtain relatively high conversion efficiencies, between 10⁻⁶ and 10⁻⁴ in the spectral range below 100 eV in helium. Above this photon energy level, experimental studies in the infrared [32, 33] led to a λ^1.4–1.7 scaling law. However, a systematic scaling study in the visible range has not been previously reported, being of major importance for highly efficient HHG-based seeding schemes.

Besides the coherence and the high photon flux, spectral tunability is a crucial characteristic for a seed source. It is necessary to precisely match the seed wavelength to the central wavelength of the FEL for optimum performance. While Ti:sapphire chirped-pulse amplifiers (CPAs) are most widely used for femtosecond pulse amplification and HHG, their tunability is limited. In contrast, optical parametric amplifiers (OPAs) [34] are very useful to amplify pulses over a much broader wavelength range far beyond the 800 nm centre wavelength of Ti:sapphire lasers or its second harmonic.

In this paper, we present experimental results utilizing an OPA in the visible range, allowing for a broad tunability range from 470 to 640 nm. We then used the visible pulses from the OPA to drive HHG, obtained by focusing the driver pulses into Ar, Ne and He atoms, and experimentally studied the scaling laws for cut-off energy, extending the results from the IR to the visible wavelengths range. We also show full tunability of the generated EUV pulses, between 25 and 100 eV.

The paper is organized as follows. In section 2, we describe the experimental setup and the characteristics of the femtosecond visible OPA; in section 3, we describe the cut-off scaling study for HHG; in section 4, we demonstrate the full tunability of the EUV pulses produced through HHG; in section 5, we summarize the results.

The visible OPA [34–37] has been for many years a workhorse of ultrafast spectroscopy at femtosecond timescales, where µJ-level energies are needed. As for few-cycle pulse amplification in visible OPAs, compression down to 6 fs has been demonstrated in the low-energy regime by using chirped-mirror-based compressors [34]. Also, 4 fs pulses have been generated by using a more complex compression scheme based on adaptive methods [38]. In general, driving HHG requires hundreds of µJ of energy. To achieve high pulse energy, short pulse duration, high spatiotemporal quality and wavelength tunability in a visible light source, we designed an OPA in the manner described below, based on white light generation and an amplified Ti:sapphire laser. The design is similar to that of [40], but contains key differences based on our priorities of high spatiotemporal quality, crucial for HHG driving, and compatibility with a Ti:sapphire laser of 35 fs pulse duration.

The experimental setup, whose schematic is shown in figure 1, is composed of a commercial Ti:sapphire system, a three-stage visible OPA and an HHG setup. The mode-locked Ti:sapphire oscillator (Octavius-85M, IdestaQE, Inc.) produces 25 fs, 1.2 nJ pulses at an 85 MHz repetition rate. The output pulses are amplified by a CPA system (Legend Elite Duo, Coherent, Inc.) producing 35 fs, 800 nm, 6 mJ pulses at a 1 kHz repetition rate. The use of a 35 fs pump laser allows compatibility with the most commonly used laser systems for strong-field physics. Because of the short pulse duration, the number of refractive optical elements needs to be minimized to avoid the material dispersion and self-phase modulation in the high-energy beam paths. To avoid those unwanted effects, it is important to use reflective optics also in the low-energy beam paths to approximately match the chirp of all branches. Failure to do so leads either to spatiotemporal degradation of the second harmonic generation (SHG), which provides the pump power for the system, or to instability of the white light continuum (WLC) generation, which is the seed. For the same reason, we used a relatively large number (3) of amplification stages. In this way, we could lower the gain per each stage (in particular, the second and the third), ensuring that the spatiotemporal properties of the beam are optimum.

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As shown in figure 1, we split the CPA output into three parts: 1% for seed generation, 9% for pumping the first stage, and 90% for pumping the second and the third stages. We focused the 1% beam, after a variable attenuator and a 10 nm band pass filter centred at 800 nm, into a 2 mm-thick sapphire plate. The process of WLC generation from a single filament in the sapphire plate produced low-energy (∼10 pJ per nm of bandwidth [34]) pulses in the visible range that we used to seed the first OPA stage. We used the band pass filter to increase the WLC stability by eliminating the spectral edges of the 800 nm pulses, thus making it less sensitive to fluctuations in the CPA compressor dispersion, and to dispersion variations in the other branches of the beam, induced by refractive optical elements. We frequency doubled the 9% beam in a 0.5 mm-thick BBO crystal for type-I phase matching. The output pump energy was 50 µJ at 400 nm for the first OPA stage (OPA 1). In this stage, we focused pump and seed in a 1 mm-thick type-I BBO crystal with an external noncollinear angle of ∼3.5° (2° internal) generating a visible signal output with pulse energies up to 5 µJ. The OPA gain was ∼5 × 10⁴ at the estimated pump intensity of ∼100 GW cm⁻². We compressed the output pulses by a pair of prisms at Brewster's angle (more details about the compressor characteristics are given later), and directed it to the second OPA stage.

We sent 90% of the main beam to a delay line for pump-seed synchronization and to a 150 µm-long type-I BBO crystal for SHG. We obtained 2 mJ output energy at 400 nm and used it to pump the second and third OPA stages. Before the amplification, we tilted the 400 nm beam front by ∼1° through a CaF₂ prism at Brewster's angle to match pump and signal wave fronts [40–43]. We did not use a larger angle for front tilting to reduce the spatial chirp of the beam at 400 nm. In the second OPA stage (OPA 2), the 2 mJ pump beam amplified the 3 µJ residual energy from the first stage up to 40 µJ in a 1 mm long type-I BBO crystal. We loosely focused the residual pump in the third stage (OPA 3) to further amplify the visible pulses to 200–550 µJ (depending on wavelength) in a BBO crystal of the same kind as in OPA 2. The pump-signal noncollinear angle for the second and third stages was also chosen as ∼2° internal. We chose this angle to obtain the desired bandwidth for supporting 30–40 fs pulse durations, similar to the pulse duration of the Ti:sapphire CPA output (35 fs), so we can directly compare the HHG results in the wavelength scaling studies. Figure 2(a) shows the calculated phase-matching angle for different noncollinear (pump-signal) internal angle α. The chosen 2° angle is far from the 3.7° that would guarantee signal-idler group velocity matching and thus the maximum possible bandwidth [34]. Figure 2(b) shows the corresponding calculated gain bands.

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We used two alternative schemes for pulse compression, both based on prism pairs. The first scheme follows the method described in [40]: one fused silica (FS) prism pair after the first stage (25 cm of apex-to-apex prism separation), and a second one at the output of the third stage (1 m prism separation). This scheme guarantees higher energies at the OPA output (up to 550 µJ), corresponding to a pump-signal conversion efficiency of >25%. A 30% fraction of the energy though is lost in the second compressor, mainly due to the multiple bounces on folding mirrors. The second scheme consists of only a single SF10 prism pair after the first stage (6.9 cm of prism separation), and no further compressor at the output. With the last scheme we produced less OPA output energy, but had no additional losses in the following beam path. As a result, the second scheme was overall more efficient, except for the shortest wavelength pulses.

The OPA output spectra for the two aforementioned cases are shown in figure 3 (panel (a): S1–S4 for FS compressor, panel (b): S5–S9 for SF10 compressor) together with the final energies after compression, and the measured and transform-limited pulse durations. We also show the normalized WLC spectrum as a dashed line.

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SF10, the prism material used in the compressor scheme 2 (S5–S9), has higher third-order dispersion (TOD) compared to the FS used in the compressor scheme 1 based on two prism pairs (S1–S4). For pulse durations of >30 fs TOD does not play an important role.

We measured the pulse duration with a background free autocorrelator based on self-diffraction using a 150 µm-long BBO crystal [44]. When we employed two compressors (compressor scheme 1, FS, with spectra in figure 3(a)), we had large variations in the pulse duration between 26 and 71 fs due to difficulties in the compressor alignment. For the compression scheme 2 based on one SF10 prism pair, we were more successful in keeping a constant duration between 34 and 46 fs. In most cases, we were able to compress the pulses close to their transform limit. Figure 4 shows an autocorrelation trace (dots: experimental points, line: Gaussian fit) of the pulse at 470 nm using the compression scheme 1 (FS) and another at 590 nm using compression scheme 2 (SF10). The corresponding spectra from figure 3 are shown in the two insets, and the corresponding pulse durations are indicated in full-width at half-maximum (FWHM). Note that the decorrelation factor for a self-diffraction autocorrelation is 1.22 because of the third-order nonlinear process involved.

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By blocking the WLC seed, the OPA signal energy drops to 1% of its seeded value, showing excellent superfluorescence suppression. This measurement gives the upper limit of the superfluorescence power. The rms fluctuations of the OPA signal energy are less than 2.5% measured over 9 min. The quality of the beam is also good, as shown in figure 5, where we measured an M² parameter of 1.9. Good beam quality is mandatory to reach a laser intensity necessary for HHG experiments. We did not observe a significant angular chirp in the beam, which would be deleterious for the HHG experiments.

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The visible OPA described in section 2 allowed studying the impact of drive wavelength on the cut-off energy extension of HHG. This study is necessary for building an optimized seed source for FELs. As previously discussed, driving HHG with visible pulses is beneficial to the conversion efficiency at the expense of the cut-off energy extension. The cut-off scaling law in the visible range was never explored experimentally, as we pursue in this work.

In the HHG experiments, we focused the OPA beam into gas jets of different gases (Ar, Ne and He), and measured the total HHG output signal and its spectrum. Figure 6 shows the photographs of the HHG setup illuminated by each colour from the tunable visible OPA system. The schematic of the setup is shown in figure 1.

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We measured the HHG signal and efficiency with a highly sensitive Al-coated EUV calibrated photodiode (AXUV100, IRD, Inc.). We used different EUV filters to separate the driver pulse from the harmonics: a 500 nm-thick Al filter allowing ∼20% transmission over the Al transmission window (20–70 eV), or a 500 nm-thick Be filter allowing ∼20% transmission between 50 and 110 eV. We magnified the photodiode signal with a low-noise amplifier to significantly improve the detection sensitivity. To acquire the HHG spectra, we collected the high-harmonic beam with a toroidal mirror, and imaged it onto the slit of the EUV spectrometer [23]. We recorded the spectra with a microchannel plate backed by a phosphor screen followed by a thermo-electrically cooled visible charge-coupled device (CCD).

For the experimental study on the cut-off energy, we changed the central wavelength of the OPA while keeping other characteristics as constant as possible, and measured the cut-off energy versus driver wavelength. We kept roughly constant energies, intensities and spot sizes (measured with the knife edge method at the gas jet position) for all four drivers. We focused the study on helium gas because its high ionization potential allows the highest cut-off energy among all gases. We drove HHG with the OPA tuned at three different central wavelengths, obtained with the SF10-based compression scheme (figure 3(b)), and drove HHG also with the light at 400 nm from the second harmonic of the Ti:sapphire laser. We controlled the spot size with an iris at fixed aperture before the vacuum chamber and focused the pulses into the gas jet (gas pressure: 50 mbar, backing pressure: 3 bar), with the parameters summarized in table 1.

Figure 7 shows the experimental data as green squares, while the blue dashed line showing the linear fitting curve in logarithmic scale (λ^{1.7 ± 0.2}), which stays within the range of the phase-matched cut-off relation (λ^1.4–1.7) observed in the infrared region [33]. The absolute value of the cut-off energy is not optimized due to the low energy of the OPA driver pulses. The pulse energy available at the gas jet was about 120 µJ, and we needed to focus the OPA pulses tightly (f = 100 mm) to reach an intensity high enough to observe an HHG signal. Such a tight focus has the drawback of poor phase matching due to the Gouy phase and limited interaction volume with the medium.

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To show the cut-off energy improvement with higher pulse energies [45, 46], we numerically studied HHG by solving the 3D propagation of the driver pulse [47] with the three-step model HHG [24]. Figure 7 shows also a simulation of the cut-off energy under the experimental conditions (black triangles and connecting line) and one with the saturation of the cut-off energy, occurring with a few mJ driver energies (red circles and connecting line). Both in the experiments and in the simulations we considered as cut-off energy the photon energy at which the signal drops by one order of magnitude with respect to the plateau region. The simulations show that with more pulse energy than possible with the current OPA, one could reach higher cut-off energies. This happens because one could use higher peak intensities without focusing the driver pulses tightly. Phase matching, which is particularly critical for higher energy photons, also becomes easier with looser focusing due to a lower Guoy phase. In our earlier measurement with higher pulse energy (1 mJ) of 400 nm driver [31], we were able to reach experimentally a cut-off at 71 eV. In this work, we investigated the cut-off scaling of HHG driven by a continuously tunable OPA at low pump energy.

Due to the low driver energy, we observed only a 10⁻⁹ visible-to-EUV conversion efficiency per harmonic order in the plateau region, corresponding to ∼10⁴ photons/shot at 100 eV, from the 589 nm driver wavelength. To show the improvement in efficiency with higher pulse energies, we simulated the efficiency for three different He gas jet pressures, as shown in figure 8. In the simulation, we compared the total efficiency between 80 and 90 eV for a 589 nm driver pulse. The pulse duration is the same as in the experiments, 34 fs, and we fixed the peak intensity to 7.7 × 10¹⁴ W cm⁻² (corresponding to the experimental value) by changing the beam size accordingly. Figure 8 shows that, as the pulse energy increases from 120 µJ to a few mJs, the simulated efficiency improves by two or three order of magnitude due to the loose focusing and the longer interaction length (up to 10^−(6–7) in the example considered here). Before reaching the asymptotic value, the efficiency curves show some oscillatory behaviour due to phase matching. Further optimization of the gas jet position in the simulation may result in efficiencies higher than those shown in figure 8, but this does not affect the main conclusion that a looser focusing can help phase matching and give an improvement by a few orders of magnitude. Previous simulations [24] predicted even higher efficiencies in the range of 10^−(4–6). The difference can be explained because the simulations in [24] considered 1D propagation and an ideal case with perfect phase matching and infinitely long interaction lengths, while in this paper, we consider 3D propagation and a 2 mm interaction length, which we estimate to be the same as in the experiments.

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Despite this increased efficiency one would still need multi-mJ driver energies to reach a nJ EUV energy in order to seed an FEL [18]. Hundreds of µJs through mJ could be enough in the case of shorter driver wavelengths, due to the favourable efficiency scaling (λ^−(5–6)), at the expense of a slightly lower cut-off energy. The necessary energy could be further reduced by using more efficient gases, like argon, again at the expense of lower cut-off energy. In addition to the energy requirements, repetition rates as high as 100 kHz–1 MHz are desired to match future FEL repetition rates [48].

These requirements would be too restrictive for an OPA scheme, and one should use an optical parametric chirped pulse amplifier (OPCPA). Scaling to mJ energies, even at higher repetition rates, seems to be possible by using Yb-pump laser technology [49, 50].

Tunability is a crucial characteristic for a seed source because it makes it possible to finely match the photon energy of the seed with the photon energy of the FEL. In FELs, for example, one can think of tuning the pump, or probe, wavelength to excite, or observe, certain dynamics in a pump-probe experiment which occur at those particular wavelengths, and it is necessary to have a continuously tunable seed source to follow the photon energy of the FEL [51].

Figure 9 shows several spectra measured while tuning the driver wavelength in Ar, Ne and He gases. Note that the spectra for helium are not necessarily the same as the ones used in the cut-off energy study. We focused the beams with f = 150 mm for argon, f = 100 mm for neon and argon. We estimated the driver intensities to be (0.9 ± 0.2) × 10¹⁴ W cm⁻² in Ar, (6.6 ± 1.0) × 10¹⁴ W cm⁻² in Ne, and (1.6 ± 0.9) × 10¹⁵ W cm⁻² in He. We measured the efficiencies per harmonic (referring to the highest HHG peak) to be (0.9–4) × 10⁻⁷ for Ar, ∼1 × 10⁻⁹ for Ne, and (0.4–10) × 10⁻¹⁰ for He, respectively. In the case of argon, we observed the maximum EUV signal at a gas pressure of 42 mbar, corresponding to a backing pressure of 1.5 bar. Varying the aperture of the beam with an iris before the chamber controls the intensity at the focus in the chamber and with it the ionization level and phase matching. For the cases of neon and helium, we used the full beam to maximize the delivered pulse energy.

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The HHG spectra show a broad continuous tunability, allowing for the production of any photon energy between 25 and 100 eV. The tuning range of the nth-order harmonic is larger than two times the central frequency of the driver pulse, which is the spectral gap between two consecutive harmonics. For example, figure 9(a) shows that the 13th-order harmonic peak is found to be tunable up to ∼8 eV, which is > 3 × 2.5 eV (2.5 eV is the photon energy for 490 nm). Note that in the region 80–100 eV the tunability is limited to ∼2 times the driver's central frequency because only the long wavelength OPA drivers allow for the production of these photon energies. This still allows for full tunability because the harmonic peaks are closer for longer driver wavelengths. We exploited the HHG tunability by adjusting the OPA central wavelength (i.e. by changing only the birefringent phase-matching angles and the delays of the three OPA stages), the target gases and the focusing lenses. This is similar to what has been done with an infrared driver [44, 52–54]. Compared to the continuum-like EUV generation covering broad bandwidths when using long wavelength drivers, the strong high-order harmonic structure observed here with visible drivers is more advantageous in terms of the amount of energy concentrated in one harmonic as long as the tunability is sufficiently maintained. Therefore, due to the high expected maximum efficiency achievable with higher driver pulse energies, the HHG source demonstrated here is very promising in high-energy or high-flux seeding over a narrow EUV bandwidth. The EUV laser line width is typically a few times narrower than the HHG line width, which is advantageous for robust seeding. A source similar to this, after proper scaling of the energy and of the repetition rate, can be used for seeding EUV FELs, which have typically the same spectral range as the HHG source demonstrated here, and is eventually a good candidate for seeding hard-x-ray FELs using cascade schemes. In this way, the coherence, stability and reproducibility of FEL pulses could be greatly improved, provided that high enough seed energy is obtained as a seeding source. In addition, the photon energy at ∼92 eV (∼13.5 nm), which can be obtained with helium from long wavelength visible drivers, is of interest for applications such as mask and optics inspection for EUV lithography [30].

We developed a fully tunable source in the EUV range based on HHG driven by a broadly tunable visible OPA. The OPA produces pulses with hundreds of µJ energy between 450 and 650 nm, and pulse durations around 30 fs. With these pulses we drove HHG in different gases, and studied the dependence of the cut-off energy up to 100 eV on the driver wavelength. We found a λ^1.7±0.2 experimental scaling law, which agrees well with previous experimental works in the literature. We showed by simulations that the values of the cut-off energy and efficiency could be further optimized by scaling the output energy of the OPA to the mJ level.

The EUV spectra show full spectral coverage between 25 and 100 eV with continuous tunability. All photon frequencies in this range can be produced by changing the crystal orientations and pump-seed delays of the OPA, the focusing lens, the species (Ar, Ne, He) and the pressure of gas in the HHG chamber.

HHG driven by a visible OPA (or an OPCPA) provides full tunability in the proper range for EUV FEL seeding, while maximizing the conversion efficiency, in contrast to Ti:sapphire technology, which operates at a fixed wavelength, limiting the HHG tunability. Thus, phase-matched and absorption limited HHG driven by a tunable source like an OPCPA in the visible range pumped by a Yb amplifier gives the most for seeding FELs when fine wavelength tuning is needed. The scaling study conducted here shows the possible choices in driver wavelengths for seeding at a desired EUV FEL photon energy.

This work was supported by the Air Force Office of Scientific Research under contract FA9550-10-1-0471, and the Center for Free-Electron Laser Science, DESY, Hamburg, and by Progetto Roberto Rocca. AS acknowledges support by the Alexander von Humboldt Foundation. PK acknowledges support by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.