Cascaded harmonic generation from a fiber laser: a milliwatt XUV source

1. Introduction

High-order Harmonic Generation (HHG) is an unique tool to produce ultrashort pulses of spatially coherent extreme ultraviolet (XUV) radiation with table top systems [1]. HHG occurs when atoms interact with an intense laser pulse, in the 10¹⁴ W.cm⁻² intensity range. Within one optical cycle, the strong laser field ionizes the atom, accelerates the freed electron wavepacket and drives it back to recombine with the parent ion, emitting an attosecond burst of XUV radiation [2, 3]. This process repeats periodically every half laser cycle, resulting in a broad spectrum consisting of odd harmonics of the driving laser frequency, extending until a cutoff frequency determined by the laser intensity and wavelength [4].

In the past 10 years, the emergence of compact, high power, high repetition rate femtosecond lasers based on ytterbium-doped fiber amplifiers (YDFA) has opened new perspectives of applications for HHG. In 2009, pioneering experiments demonstrated the generation of high-order harmonics with repetition rates up to the MHz range [5]. Since then, a lot of investigations have been carried out to optimize the XUV photon flux of these sources [6–8]. Indeed, producing a high average XUV photon flux with a high repetition rate is optimal for experiments based on coincidence detection (e.g. COLTRIMS [9–11]) or surface photoemission measurements [12].

The low energy per pulse of YDFA lasers, compared to Ti:Sa lasers standardly used in HHG experiments, imposes tighter focusing conditions. This was initially thought to be detrimental for HHG. However important works recently demonstrated that the experimental parameters (pressure, medium length, focal length) can be scaled to keep good phase matching conditions and optimize the HHG efficiency [13–15]. When femtosecond YDFA lasers operate at ultra high repetition rate, beyond 20 MHz, the low energy per pulse can be compensated by coherently stacking pulses in a passive enhancement cavity housing the HHG process [16–18].

The second important limitation of YDFA lasers is their pulse duration, which is typically one order of magnitude longer than Ti:Sa lasers. This restricts the effective intensity that can be used for HHG before the generating medium is completely ionized, and thus the extension of the high-harmonic cutoff. Furthermore, ionization induces dispersion of the fundamental and XUV beams, which can lead to situations where the phase matching conditions are fulfilled only during a short part of the laser pulse duration (transient phase matching [8, 19]), limiting the conversion efficiency when using long pulses. Reducing the pulse duration of YDFA lasers is thus the subject of many works, using single or double postcompression stages in hollow core fibers [20–22] and more recently gas-filled multipass cells [23–25].

The highest reported XUV fluxes per harmonic from YDFA were obtained by using either postcompression (0.832 mW ± 0.2 mW produced in krypton [26]) or cavity enhancement (2 mW produced in xenon [27]). Here we show that such schemes are not necessary to produce mW-class XUV sources from YDFA lasers, leading to a significant reduction of experimental complexity. The HHG conversion efficiency is known to depend dramatically on the generating laser frequency ω_L [28–33], the process being more efficient when driven by high frequency lasers. This enhancement is mostly caused at the single-atom level by a lower spreading of the electronic wavepacket in the continuum, which leads to a higher recombining current with the parent ion. While all investigations conducted so far confirmed a general trend of XUV flux rise with increasing generating frequency ω_L, the scaling laws measured in various experimental conditions were very different: ${\omega }_L^{6-7}$ [29] in the mid-IR range, and ${\omega }_L^{4-5}$ [30, 31], ${\omega }_L^6$ [32] or ${\omega }_L^8$ [33] in the visible-UV range.

In this article we investigate the generation of high-order harmonics from the second, third and fourth harmonics of a commercial femtosecond YDFA laser system in an argon gas jet. The resulting source is extremely simple and versatile, offering the possibility to generate spectra with different energy spacing between the XUV harmonics, and in different energy ranges. We observe a strong enhancement of the harmonic conversion efficiency in the low energy region of the spectrum when HHG is driven by the third harmonic, enabling the production of 6.6 × 10¹⁴ photons/s at 18 eV in Ar, which corresponds to an average power of 1.9 mW and a conversion efficiency of 2.6 × 10⁻⁴.

2. Generation of the 515 nm, 343 nm and 257 nm beams

The experimental setup is described in Fig. 1. We used the BlastBeat femtosecond laser system at the Centre Lasers Intenses et Applications (CELIA), which consists of two synchronized 50 W Yb-doped fiber lasers (Tangerine, Amplitude Systemes [22]) delivering 135 fs pulses centered at 1030 nm (FWHM = 18.5 nm), at a repetition rate which can be continuously tuned between 166 kHz and 2 MHz. For this study, we used a single arm at 166 kHz and we converted the ω_L fundamental frequency to 2, 3 and 4ω_L (515, 343 and 257 nm) by using beta barium borate (BBO) crystals.

 

Fig. 1 Scheme of the experimental setup. We generate the harmonics (2nd, 3rd and 4th) of the YDFA fundamental laser in BBO crystals. The upconverted beam is filtered by dichroic mirrors, magnified by a telescope, and focused in an argon gas jet. The spatially-resolved XUV spectrum is measured by an imaging spectrometer, and the absolute XUV flux is measured by a calibrated photodiode.

Download Full Size | PPT Slide | PDF

To produce the second harmonic (2ω_L), we directly sent the 1030 nm beam in a 1 mm thick type-I BBO crystal and used two dichroic mirrors to select the up-converted frequency. We reached a conversion efficiency of 38 %, leading to an average power of 19 W and a pulse energy of 114 µJ. The pulse duration of the 2ω_L beam, characterized using a home-made SHG-FROG, was 130 fs FWHM.

For the third harmonic (3ω_L), we used an in-line frequency conversion setup. A first type-I 1 mm thick BBO crystal (θ = 23 °) was used to frequency double a fraction of the fundamental ω_L beam. A type-I 0.75 mm thick BBO crystal performed the sum-frequency mixing at 3ω_L. After 3 dichroic mirrors (HT ω_L-2ω_L /HR 3ω_L), we obtained a maximum average power of 12 W at 3ω_L (72 µJ, 24 % conversion efficiency). However, to avoid detrimental thermal effects in the second BBO crystal, we routinely limited the 3ω_L average power to 9.5 W (19 % efficiency). The pulse duration of the 3ω_L beam was estimated to be around 140 fs by non-linear optics calculations with the SNLO software [34].

For the fourth harmonic (4ω_L) generation, we used the 2ω_L generation setup described above, and sent the 2ω_L beam in a 200 µm type-I BBO crystal. The thickness of the BBO crystal was here limited by the large difference of group velocities between the 2ω_L (515 nm) and 4ω_L (257.5 nm) in BBO, which prevents temporal overlap over long propagation lengths. It was also necessary to avoid heating of the second BBO crystal due to two-photon absorption in the UV [35]. This was achieved by setting a -150/250 mm telescope in the 2ω_L beam before doubling it, without any loss in the efficiency. We reached a 4 % conversion efficiency from the initial laser power, i.e. 12 µJ per pulse at 166 kHz (2 W) with an estimated pulse duration about 135 fs (SNLO calculations). Note that to avoid thermally-induced wavefront distortions, only UV-grade fused-silica or high quality CaF₂ optical components were used with the 4ω_L beam.

The conversion efficiencies we obtained for the second, third and fourth harmonic generation processes are typical of what is achieved with Yb laser systems [36–38].

3. Spatial profiles of the driving laser beams

The spatial quality of the laser beams is a crucial parameter in HHG. In order to investigate the possible wavefront distortions of the beams due to thermal effects induced by the high power laser source, we performed measurements of the spatial profiles of the fundamental and upconverted beams under conditions close to the optimal ones for HHG.

The initial waist of the unfocused laser beam is about 1.3 mm (radius at I_max/e²). In order to reach high intensities for HHG while keeping all the focusing optics outside the vacuum chamber, we used telescopes to increase the beam size before focusing it. We found out that whatever the wavelength used from 1030 nm to 257 nm, UV fused silica introduces wavefront distorsion at high power when the beam size is close to or below 1 mm. Therefore all-reflective telescopes based on spherical dielectric mirrors were used to enlarge the beams. For the fundamental and second harmonic beams, we used a combination of −100 mm/300 mm focal spherical mirrors, followed by a f = 300 mm lens. The resulting focal spots, measured by a CCD camera with a 3.75 µm resolution, are shown in Fig. 2(a-b). The fundamental beam shows excellent focus quality, with a beam waist w₀ of 26 µm. The second harmonic has a waist of 20 µm and shows a slightly cross-like shape, indicating some wavefront distortions, possibly due to small thermal effect in the SHG BBO crystal. We monitored the evolution of the fundamental and second harmonic focii as a function of the laser power, and observed no significant variation of their size. We also measured the initial waist of the laser before focusing w₁ by sending directly the beam on the CCD. We then estimate the deviation from the diffraction limit (DDL) by applying the formula DDL = πw₀w₁/(λ f), where f is the focal length and λ the driving wavelength. DDL is equal to 1 for a perfect gaussian beam and increases if the wavefront is distorted. We obtain DDL of ~ 1/1.2 in the horizontal/vertical direction at ω_L and ~ 1.2 at 2ω_L in both directions, indicating a rather good spatial quality of the beams.

We performed similar measurements on the 3ω_L beam, after a -100 mm/500 mm dielectric mirror telescope and a focal lens of 300 mm. The spatial profile of the resulting focus at 7 W average power is shown in Fig. 2(c). Even if the profile seems nice, its size was found to change with average power. We thus characterized the beam waist at focus w₀ and the beam waist before the focusing lens w₁ as a function of the average power of the 3ω_L beam (Fig. 2(e)). The near field waist w₁ diminishes from to 6.5 mm to 3.5 mm when the 343 nm power increases from 0.5 to 8 W. This is accompanied by an increase of the spot size at the focus of the lens, from 8.5 µm to 13 µm. This is probably due to thermal effects in the BBO crystal. These measurements lead to a DDL of 1.4 at high power.

Last, we measured the near-field profile of the 4ω_L after a -100 mm/500 mm dielectric mirror telescope (Fig. 2(d)). The resolution of our UV camera was insufficient to measure the focus. The beam becomes 30% elliptical at high power, but the mean waist stays around 2.0 mm. The elliptical shape is caused by a temperature increase in the BBO crystal due to non-linear absorption of the 257 nm [35], which changes the angular acceptance of the phase-matching process.

 

Fig. 2 Measurement of the laser beam spatial profiles. (a) Focus of the ω_L beam at 50 W average power, after a -100 mm/300 mm telescope and f=300 mm lens. (b) Focus of the 2ω_L beam at 19 W after a -100 mm/300 mm telescope and f=300 mm lens. (c) Focus of the 3ω_L beam at 7 W after a -100 mm/500 mm telescope and f=300 mm lens. (d) Near-Field of the 4ω_L beam at 1.75 W after a -100 mm/500 mm telescope. (e) Beam waist measurement versus average power at 3ω_L after a -100 mm/500 mm telescope (w₁) and at focus (w₀) with f=300 mm. (f) Beam waist measurement versus average power at 4ω_L after a -100 mm/500 mm telescope (w₁) and its projection on the x (w_x) and y axis (w_y).

Download Full Size | PPT Slide | PDF

4. Spatially resolved HHG spectrum

The experimental setup to produce the high order harmonics is described in Fig. 1. After dichroic mirrors and a telescope, the laser beam was focused into a continuous argon gas jet produced by a 250 µm nozzle, whose absolute density profile was measured during experiments [39]. The emitted XUV radiation was characterized by a flat field XUV spectrometer, consisting of a 1200 grooves/mm holographic cylindrical grating with variable groove spacing (Shimadzu) and a set of dual micro-channel plates coupled to a P46 (fast) phosphor screen (Hamamatsu). A 12-bit cooled CCD camera (PCO) recorded the spatially-resolved high-harmonic spectrum.

The spectrum produced by the 1-4ω_L in optimized conditions are displayed in Fig. 3. Each spectrum is constituted of odd harmonics of the laser frequency. As expected, the cutoff is much higher at ω_L and reaches 49.2 eV (H41) – close to the Cooper minimum of argon [40,41] around 53 eV – and decreases to 36 eV (H15) at 2ω_L, 25.2 eV (H7) at 3ω_L and 24 eV (H5) at 4ω_L. The spectral width of the harmonics in the plateau region is too narrow to be resolved by our spectrometer. Spatially, we observe an up/down clipping due to a slit ensuring a differential pumping outside of the HHG chamber and occluding a large part of the laser power. The excellent spatial beam quality of the high-order harmonics produced from YDFA laser demonstrates the potential of this source for imaging purposes.

 

Fig. 3 (a)-(d) Spatially resolved high-harmonic spectrum generated in argon using a driving laser at 1,2,3 and 4ω_L, with respective intensities of 1.5, 2.8, 3.4 and 1.6 × 10¹⁴ W.cm⁻². The peak density in the generating medium is 4.5 × 10¹⁸ at./cm³ at ω_L and 3.5 × 10¹⁸ at./cm³ at 2,3 and 4 ω_L. The spectra at 1 and 2 ω_L are recorded after reflection on two Nb₂O₅ plates. The spectra at 3 and 4 ω_L are recorded after transmission through an Al filter.

Download Full Size | PPT Slide | PDF

5. HHG flux measurements

To measure the high-harmonic photon flux, we used an XUV photodiode calibrated by the Physikalisch-Technische Bundesanstalt Berlin, in front of a 157 nm thick Al filter whose transmission was measured directly with our XUV spectrometer. The measured filter transmission is plotted in Fig. 4(a) as a function of the photon energy. Each set of data corresponds to a different Al filter. The transmission maximizes around 45% in the 32-50 eV range, significantly below the expected 70% from CXRO [42]. This is the signature of an oxidation of the Al filter. A few Angströms of Al₂O₃ on each side of the filter are enough to significantly decrease its overall transmission. Different levels of transmission are are measured around 33 eV, illustrating the level of oxidation of the different filters. The low energy decay of the transmission occurs above the expected 20 eV cutoff. This was observed in previous works, and interpreted as the result of multiple reflections of the XUV light in the filter (see Supplementary Information in [32]). The filter used for the 515 nm case was clearly less oxidized than others.

 

Fig. 4 (a) Transmission of the 157 nm Al filters used at different driving wavelengths. The filters used in each configuration are different. (b) XUV reflectivity after two Nb₂O₅ plates in s- and p- polarization at ~ 70° incidence angle.

Download Full Size | PPT Slide | PDF

Aluminum filters melt as soon as they are exposed to a few watts of average laser power. When HHG is driven by 3ω_L or 4ω_L beams, the average power is sufficiently low to preserve the filters. However for measurements using the fundamental or second harmonic, it is necessary to attenuate the laser power before reaching the Al filter. To that purpose, we used two fused silica plates under 20° grazing incidence, coated by a layer of Nb₂O₅. The measured reflectivity for the set of two plates at 1030 nm is 42% in s-polarization and 0.7% in p-polarization. At 515 nm this reflectivity is 60% in s- and 0.5% in p-polarization. We calibrated the XUV reflectivity of the plates by comparing the high-harmonic spectra with and without the two Nb₂O₅ plates (Fig. 4(b)). The XUV reflectivity for two plates lies in the 20% - 55% range in s-polarization and 5% -30% range in p-polarization.

The XUV photodiode provides the total XUV flux. To obtain the flux generated in each harmonic order, we redistribute the total flux amongst the harmonics measured with the XUV spectrometer, and calibrate out the transmission of the Al filter and Nb₂O₅ plates when used. We also take into account the spatial clipping of the XUV beam by the setup: we perform a gaussian fit of the clipped profile of each harmonic, and estimate the energy in the wings of the harmonics which do not reach the detector. For the most divergent harmonics, this missing energy was 30% of the total signal. We estimate the uncertainity in the flux measurement to ±20% because of this spatial clipping and the typical current fluctuations of the photodiode. Note that the signal is not corrected for partial reabsorption of the harmonics by the residual gas [26] and corresponds to the available XUV photons flux for experiments.

6. HHG optimization

6.1. Introduction

The optimal generating conditions are determined by three processes: (i) the single atom response, which increases nonlinearly with laser intensity; (ii) XUV reabsorption, which increases with medium density and length; (iii) phase matching, whose dependency on density and intensity is complex.

From the single atom response, the harmonic flux is expected to scale as $I_q\propto I_L^{q_{\text{eff}}}$, where I_L is the laser intensity and q_eff the effective nonlinearity of the process, which is typically 4 in the plateau region. This dependency can be expressed as a function of the laser pulse energy E_L and beam waist at focus $w_0:I_q\propto {\left(E_L/w_0^2\right)}^{q_{\text{eff}}}$. It thus seems that the tighter we focus, the higher is the flux. However, this statement must be nuanced. If the intensity is too high, the atoms are fully ionized on the rising edge of the pulse and no more ground state population is available to produce HHG when the driving laser pulse intensity reaches its maximum. An optimization procedure thus has to be defined to produce the highest possible HHG flux.

6.2. Experimental results

Our method of optimization of the high-harmonic flux aims at finding the focus waist w₀ producing the optimal laser intensity to maximize the XUV conversion efficiency. Experimentally, we proceed as follow : we tune the mirrors spacing of the telescope and the focal length of the lens to set w₀, then we increase step by step the pulse energy E_L and measure the HHG flux at each step. If we observe a saturation of the flux while increasing the energy, this means that we focused too tightly. We then increase w₀ until we reach the maximum flux at the maximum pulse energy. Since we found out that the size of the 3 and 4ω_L beams change with power, we have to adapt our protocol. For these driving wavelengths, we keep the beam at maximum power and tune the intensity at focus by setting pinholes with different diameters before focusing. We measure the transmitted power for each pinhole diameter, and we estimate the size of the focal waist using basic Fourier optics. Note that for each driving wavelength, we also optimize all the other experimental parameters such as focus position, length and density of the Ar gas jet.

In order to illustrate this method, we plot in Fig. 5(a) the total efficiency for two different focusing geometries at 1030 nm. The total efficiency is defined as the ratio between the average power of all high-harmonics from 15 eV to the cutoff energy, and the average power of the driving beam. In the tightest focusing geometry (w₀ = 16 µm), we observe a saturation of the conversion efficiency at 2 × 10¹⁴ W.cm⁻² where the efficiency scales almost only linearly with intensity $\left(I_L^{1.2}\right)$. This is the signature of a too tight focusing. We thus increase the focus beam waist to 26 µm, and observe a continuous growth of the HHG efficiency as $I_L^3$ until I_L = 1.5 × 10¹⁴ W.cm⁻². This second geometry leads to a higher conversion efficiency (4.8 × 10⁻⁸). The optimized high-harmonic spectra obtained in the loose and tight focusing conditions are shown in Fig. 5(b). Working at lower intensity naturally leads to lower cutoff, while the tight focusing enables us to extend the spectrum till 60 eV and observe the Cooper minimum around 50 eV. Since we aim at optimizing HHG in the low energy range (15-50 eV), we use the loose focusing conditions in the following, which provides a better efficiency around 40 eV.

 

Fig. 5 (a) Intensity dependency of the total HHG efficiency at 1030 nm in two focusing conditions. The intensity was tuned by changing the laser energy. (b) Efficiency per harmonic at the highest power in the two focusing conditions.

Download Full Size | PPT Slide | PDF

At 2ω_L, the best conditions were obtained with a −100 mm/300 mm dielectric mirror telescope and a f = 200 mm lens, leading to a beam waist at focus w₀ = 13 µm. The signal increases with laser intensity and saturates when I_L reaches around 2 × 10¹⁴ W.cm⁻². The conversion efficiency is two orders of magnitude higher than the one obtained with 1030 nm pulses (Fig. 6(a)).

At 3ω_L, we used a -100 mm/500 mm dielectric mirror telescope followed by a f=300 mm lens, leading to w₀ = 8 µm. The efficiency reaches the 10⁻⁴ range and saturates around I_L ~ 1 × 10¹⁴ W.cm⁻² (Fig. 6(a)). The intensity was varied here by using pinholes, because of the spatial variations of the beam with average power as we discussed previously. The highest conversion efficiency is achieved with a 10 mm diameter pinhole, transmitting 7.3 W of 3ω_L and resulting in a waist of 12.8 µm at focus.

 

Fig. 6 (a) Intensity dependency of the total HHG efficiency at 1,2,3 and 4 ω_L. The intensity was tuned by changing the laser energy at 1 and 2ω_L, and was changed by setting different pinhole diameters at 3 and 4ω_L. (b) Maximal flux at each harmonic generated from 1,2,3 and 4ω_L beams. (c) Total efficiency for the detected harmonics as a function of generating frequency, at the interpolated intensity of 1.5 × 10¹⁴ W.cm⁻². The dashed line is a power fit of the efficiency made from 1 to 3 ω_L.

Download Full Size | PPT Slide | PDF

Last, at 4ω_L we used a -100 mm/500 mm telescope, increasing the beam to a waist of ω₁ = 4 mm, followed by a f=200 mm lens. Assuming DDL = 1.4 (same as 3ω_L), we estimate the focal spot size to w₀ = 5.5µm. The HHG efficiency is more than two orders of magnitude lower than the one obtained at 3ω_L, and hardly shows any variation with the laser intensity.

6.3. Discussion

In order to interprete the experimental results, two relevant quantities can be derived to characterize the efficiency of the HHG process: the absorption length and the phase matching density.

The absorption length is determined by the photoabsorption cross section of the gas, and by the gas jet density which we directly measure in our experiment [39,43]. At ω_L, the HHG process was optimized when the gas jet has a 360 µm FWHM profile with a 4.5 × 10¹⁸ at./cm³ peak density. For HHG from the 2-4ω_L, the signal was optimal for lower gas densities, about 3.5 × 10¹⁸ at./cm³ with the same jet length. The absorption length at 27 eV in argon is thus equal to 65 µm at 4.5 × 10¹⁸ at./cm³ and 85 µm at 3.5 × 10¹⁸ at./cm³. With a jet length of 360 µm FWHM, we ensure that the medium length is at least three times larger than the absorption length [44].

The influence of phase matching in the HHG process leads to the existence of an optimal medium density [14, 15]:

In the absence of ionization (η = 0), at ω_L with w₀ = 26 µm, the phase-matching density $d_{PM}^0$ is 4 × 10¹⁸ at./cm³ at 27 eV (where Δδ ~ 7.1 × 10⁻⁴ [42]). At 2, 3 and 4 ω_L, $d_{PM}^0$ is respectively 2.8, 1.5 and 4.0 × 10¹⁸ at./cm³. These calculated densities are close to the ones used in our experiment.

In order to estimate d_PM more accurately, we calculated the ionization fraction by performing simulation with the Yudin-Ivanov model [45]. At 1030 nm, at the peak of a 135 fs laser pulse of 1 × 10¹⁴ W.cm⁻² intensity, the ionization fraction reaches η ~ 2% while η_crit ~ 4% at 1030 nm and 25 eV in Ar. This leads to a phase matching density d_PM ~ 8 × 10¹⁸ at./cm∼3, above the peak density of our gas jet (4.5 × 10¹⁸ at./cm³). This means that the phase-matching conditions are not perfectly fulfilled in the whole medium, and during the whole pulse duration : we have a transient phase-matching. The transient phase-matching allows a good build-up of the XUV over the leading edge of the pulse, when the ionization is almost zero and the medium density is optimal. When the laser intensity is increased to 1.5 × 10¹⁴ W.cm⁻², the ionization fraction at the peak of the pulse reaches η ~ 20% which is above η_crit meaning that the HHG is not phase matched at the peak intensity. This restricts the duration over which the HHG process is efficient. Yet, the experimental results show that the HHG signal produced at 1.5 × 10¹⁴ W.cm⁻² is higher than the one produced at 1 × 10¹⁴ W.cm⁻². This means that the enhancement of the single-atom response with increasing intensity is stronger than the degradation of the phase matching.

The simulations show that the ionization yield increases with increasing laser frequency: at 1×10¹⁴ W.cm⁻², η = 10, 40 and 80 % at 2,3 and 4 ω_L respectively. These high ionization fractions are fortunately less problematic for phase matching at short driving wavelengths, because η_crit increases with laser frequency, to 15, 35 and 45% around 25 eV for 2,3 and 4ω_L respectively [46]. Transient phase matching can be fulfilled in the leading edge of the pulses, explaining why the high-harmonic emission can be optimized in high ionization conditions.

7. HHG flux and efficiency

To illustrate the versatility of our XUV source, we display the maximum flux (Fig. 6(b)) of the high-harmonics driven by the four wavelengths. Table 1 summarizes the main results of this investigation. At ω_L, the XUV photon flux reaches almost the 10¹¹ photons/s level around 35-40 eV (500 nW), from 45 W of fundamental average power. Switching to 2ω_L increases the flux by two orders of magnitude, reaching 2.1 × 10¹³ photons/s (90 µW) at 26.4 eV from 19 W of driving laser. The HHG process is even more efficient at 3ω_L where we produce 6.6 × 10¹⁴ photons/s at 18 eV from 7.3 W. This brings the source to the mW level – 1.9 mW average power at 18 eV and 166 kHz.

Table 1. Most Relevant XUV Photon Flux in Ar.

View Table

At 4ω_L the flux drops at 8 × 10¹¹ photons/s (3.3 µW) from 2 W of driving laser but is still higher than the flux at ω_L. The low efficiency at 257 nm could first seem surprising. However the ponderomotive energy at this wavelength is very low, such that the cutoff frequency expected at 1.5 × 10¹⁴ W.cm⁻² is around 17 eV. The harmonic we observe at 24 eV is thus beyond the cutoff. In order to reach a 24 eV cutoff energy, we would need a much higher laser intensity, around 4.5 × 10¹⁴ W.cm⁻². At this intensity, the medium would be fully ionized at the beginning of the pulse, and we would still be below the regime where HHG can be efficiently produced from ions (typically 5 × 10¹⁵ W.cm⁻² [33]). Generating efficiently harmonics from the 257 nm pulses would thus require much tighter focusing. The flux of 8 × 10¹¹ photons/s is still high enough for applications, and an important advantage of the HHG at 4ω_L is the large spacing between consecutive harmonics (9.6 eV), which makes their spectral selection for applications easier.

An important characteristic of secondary XUV sources is their conversion efficiency, defined as the fraction of generating laser power converted in the XUV range. The conversion efficiency in HHG from the ω_L is about 1 × 10⁻⁸ (500 nW from 45 W) in the 30-40 eV spectral range. The efficiency gains orders of magnitude when the process is driven by 2ω_L, reaching 5 × 10⁻⁶ (90 µW from 19 W) at 26.4 eV in argon.

The highest conversion efficiency is obtained from the 3ω_L beam (343 nm) and reaches about 2.6 × 10⁻⁴ at 18 eV (1.9 mW with 7.3 W of 343 nm). This is above the value reported using 400 nm pulses of ~ 50 − 75 fs duration in krypton (5 × 10⁻⁵) [32], and slightly lower than the one measured from much shorter (25 fs) 270 nm pulses in argon (5 × 10⁻⁴ at 22 eV) [33]. Our efficiency could be further improved by avoiding reabsorption of residual gas with a better design of the gas jet [47].

In order to investigate the scaling of the HHG process with laser frequency, we integrate the conversion efficiency over all detected harmonics for each driving wavelength, and interpolate it at a common intensity of 1.5 × 10¹⁴ W.cm⁻²(Fig. 6(c)). The evolution in log-log scale is linear when the generating frequency increases from ω_L to 3ω_L, and can be fitted in this range as a ${\omega }_L^{\alpha }$ scaling with α = 7.7 ± 0.4 in a 2 σ interval. This value seems a bit far from the expected ${\lambda }^{-5.5}\equiv {\omega }_L^{5.5}$ predicted by TDSE calculation of the single-atom response [48]. However we also have to take into account propagation effects in the highly ionized medium where short driving wavelengths are less perturbated than long wavelengths. This increases the ω_L dependency, as already observed by Popmintchev et al. [33] who found a ${\omega }_L^8$ scaling law in a highly ionized medium. This high dependency underlines the benefit to generate VUV with short wavelengths.

It is finally worthwhile to compare our results to recent works on optimization of HHG from high repetition rate sources. Klas et al. [26] reported a conversion efficiency of 7 × 10⁻⁶ from 120 W - 300 fs YDFA, and produced 0.83 mW at 21.3 eV in krypton after postcompression. Porat et al. [27] obtained a 2.5 × 10⁻⁵ conversion efficiency from 80 W - 120 fs YDFA, in a cavity enhancement configuration, reaching an XUV average power of 2 mW at 12.7 eV and 0.9 mW at 19.7 eV in xenon. Both approaches require a high level of expertise in optics and use expensive gases as the generating medium. The overall efficiency of our cascaded high-harmonic generation, calculated by dividing the measured XUV power of 1.9 mW at 18 eV by the 50 W of 1030 nm light, is 3.8 ± 0.8 × 10⁻⁵. Noteworthy, these flux and conversion efficiency are obtained in argon, which is commonly considered as less efficient in this spectral range. Our results thus demonstrate that a simple setup, based on a turnkey laser, standard nonlinear crystals and an affordable generating gas, can be used to produce record XUV flux. This should ensure a broad spreading of the technique for application experiments.

8. Conclusion

Cascaded harmonic generation from YDFA provides an ideal source for applications in the 15-30 eV spectral range. The simplicity of the setup and the very high conversion efficiency open the route to a broad range of experiments in photoionization, photoemission, or transient absorption spectroscopy. This conclusion is however not valid at higher XUV photon energy, since the HHG cutoff frequency decreases with decreasing generating wavelength. The limiting factor to push the high-harmonic cutoff is here the laser pulse duration. In our conditions, ionization calculations [45] show that the ionization fraction is higher than the critical ionization before reaching the maximum intensity of the laser pulse. This means that the high-order harmonics are only produced during a fraction of the pulse. Reducing the pulse duration from 135 to 15 fs [22] could thus enable further optimization of conversion efficiencies. Furthermore, shorter pulses duration would yield higher cutoffs, typically in the 60-120 eV range, enabling important absorption edges to be reached.