1. Introduction

Ultrafast lasers driving high harmonic generation (HHG) in a noble gas target have brought coherent extreme-ultraviolet light (XUV) into laboratories. In recent years, there has been a strong progress in the transition of HHG sources operating from kilohertz to megahertz repetition rates (MHz-HHG). Higher repetition rates enable shorter measurement times in space-charge-limited photoelectron spectroscopy experiments [1,2] and allow for frequency- comb applications in the XUV spectral range [3,4]. To increase the repetition rate, the driving laser system must deliver ever higher average power to maintain the pulse energy required for HHG. Nowadays, laser systems based on Yb-doped gain materials are most suitable at the required average power and several concepts capable of driving MHz-HHG have been developed.

The highest XUV average power per harmonic at MHz repetition rate is currently delivered by a high-power fiber chirped-pulse amplifier (FCPA) system driving HHG in single-pass configuration after frequency-doubling and temporal post-compressing the laser output [5].

Utilizing the field enhancement inside passive femtosecond enhancement cavities (fsEC) or inside mode-locked high-power laser oscillators is another approach suitable for reaching the required high average and peak powers for MHz-HHG at even higher repetition rates. In passive fsECs, a high repetition rate laser is coupled into an actively stabilized high finesse cavity that contains the HHG generation target [3,4]. In contrast, gain inside the cavity allows for the formation of a powerful soliton directly inside the cavity of a mode-locked thin-disk laser (TDL) oscillator. This intra-oscillator HHG approach circumvents the need for coherent coupling, enabling a single-stage XUV source [6,7].

However, in most cavity-enhanced HHG systems, higher harmonics are generated collinearly with the driving laser and need to be out-coupled. Efficient out-coupling of the XUV light without losing the intra-cavity enhancement is a major challenge and out-coupling efficiencies are often restricted to a few percent. Figure 1 shows the most-commonly used XUV out-coupling methods inside fsECs and mode-locked oscillators which will be briefly introduced in the following.

 

Fig. 1. Operation principle of common intra-cavity XUV out-coupling mechanisms. (a) Brewster’s plate method with the fundamental driving field in p-polarization. Θ_B: Brewster’s angle. (b) Coated-GIP method presented in this work with the fundamental driving field in s-polarization. Θ_D: angle of incidence on the GIP. (c) XUV diffraction grating method spatially disperses the generated harmonics. (d) Pierced-mirror method lets less diverging XUV light pass through a hole in the mirror. (e) Non-collinear crossed-beam XUV out-coupling mechanism. (f) Illustration of the enhanced XUV reflectivity of s-polarized in comparison to p-polarized light for coated GIP XUV out-coupling in comparison to the Brewster’s plate (BP) method, respectively. Angle-dependent reflectivity of s-polarized light with 25 nm wavelength (our XUV cut-off) from Ta₂O₅, the top layer of our coated GIP, in comparison to the 25 nm p-polarized one from sapphire, as in the Brewster’s plate method. The p-polarized reflectivity of 1030-nm light from sapphire vanishes at Brewster’s angle. The high reflectivity losses for the s-polarized 1030 nm light from the sapphire substrate of the GIP are reduced by anti-reflection coatings applied to both sides of the GIP (further details are described in Section 3). Depending on the desired XUV photon energies, different materials can be chosen as the top layer of the coated GIP. The s-polarized XUV reflectivity at 25 nm of sapphire, shown for comparison, is inferior to the one of Ta₂O₅ at an AoI of 60°.

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The simplest XUV out-coupling method is based on placing a thin dielectric plate, typically sapphire, under Brewster’s angle for the p-polarized fundamental driving field into the cavity [Fig. 1(a)]. The difference in the refractive index of the plate for the XUV and the fundamental light leads to a partial reflection of the XUV light. However, the reflectivity of the sapphire plate is relatively narrowband and limited to a maximum of 17% at 25 eV [8]. From ∼600 µW of generated XUV average power in a single harmonic at 15 eV and 50 MHz, only 77 µW were out-coupled (12% XUV out-coupling efficiency) from the fsEC in [9]. Thanks to its technical simplicity, until now, all intra-oscillator HHG TDL systems utilized the sapphire Brewster’s plate XUV out-coupling method [6,7,10]. Recently, 0.4 µW of XUV average power at 30 eV and 11 MHz were generated inside a ∼100-fs Kerr-lens mode-locked (KLM) Yb:YAG TDL oscillator [10], but only 0.06 µW were out-coupled (14% XUV out-coupling efficiency).

XUV out-coupling via an XUV diffraction grating etched into the top layer of one of the highly reflective cavity mirrors is a method successfully implemented in fsECs [Fig. 1(c)] [11]. While this method features the advantage of no material propagation inside the cavity, the out-coupled XUV light is spatially dispersed and the XUV extraction efficiency typically reaches only around 10% [8,11]. Using this method, the up to now highest generated XUV average power inside a fsEC, amounting to 2 mW at 13 eV and 77 MHz, was demonstrated [12]. Nevertheless, just 130 µW were out-coupled, resulting in a 7% XUV out-coupling efficiency.

Another XUV out-coupling method successfully implemented in fsECs is the pierced mirror [Fig. 1(d)]. The concept is based on the smaller divergence of the short-wavelength XUV light in comparison to fundamental driving field. The less-divergent XUV light can escape the cavity through a small on-axis hole, typically in the ∼100-µm diameter range [13], drilled into one of the cavity mirrors. The out-coupling efficiency increases strongly towards higher photon energies and is spectrally not limited. In the 18-MHz fsEC in [14] for example, only 14 µW of XUV average power were out-coupled with 5% efficiency at 37 eV while towards higher photon energies, the XUV out-coupling efficiency increased to 45% at 60 eV.

Recently, a new XUV out-coupling mechanism based on a non-collinear crossed-beam geometry was experimentally demonstrated inside a fsEC [Fig. 1(e)]. The mechanism was proposed before [15] and utilizes a cavity that is twice as long as the driving laser cavity, enabling two pulses to circulate inside the cavity which meet simultaneously in the gas target. The generated harmonics and the fundamental driving field propagated in different directions and can thus be easily separated, e.g., by a gap in between two mirrors. A record high power level of 600 µW at 13 eV and 154 MHz was out-coupled with >60% efficiency using this method [16].

XUV out-coupling of intra-cavity high harmonics by a coated grazing-incidence plate (GIP) was proposed by [8]. The mechanism is based on the higher reflectivity of s-polarized light in comparison to p-polarized light for large angles of incidence (AoI) [Figs. 1(b),(f)]. For the s-polarized near-infrared (NIR) driving laser field, a low-loss transmission is enabled by NIR-anti-reflection (AR) coatings on both sides of the GIP. Despite the common use of GIPs to separate XUV and NIR light in single-pass HHG systems [17,18], XUV out-coupling of intra-cavity high harmonics by a coated GIP has not been experimentally demonstrated until now. Even the by [8] produced coated GIP was characterized extra-cavity only. Potential reasons preventing so far an intra-cavity application might have been the introduced losses of the coated GIP for the fundamental light, thermal lensing, nonlinear effects, or the damage threshold of the coated GIP due to the high intra-cavity average and peak powers [8].

In this work, we demonstrate for the first time out-coupling of intra-cavity high harmonics by a coated GIP [Fig. 1(b)]. We designed and produced a 60°-AoI coated GIP in our ion-beam-sputtering (IBS) coating facility and placed it inside the cavity of a high-power ultrafast TDL oscillator. We present the coating structure and design parameters of our GIP and discuss the trade-off between XUV reflectivity and bandwidth of the AR coatings for the NIR fundamental driving field. As shown by Fig. 2, our intra-oscillator HHG source based on GIP XUV out-coupling approaches the state-of-the-art out-coupled XUV power levels per harmonic of fsEC sources at comparable photon energies.

 

Fig. 2. Overview of intra-cavity XUV sources based on fsEC and intra-oscillator HHG. The plot shows the out-coupled XUV average power per harmonic and the color code represents the photon energy of the out-coupled harmonic. The applied XUV out-coupling mechanism is distinguished by the marker symbol. Intra-oscillator sources are labeled by year of publication. The dashed line indicates the progress of our intra-oscillator HHG system and the stars at “2022” show the results we achieved in argon and xenon using the here presented coated GIP for XUV out-coupling. References: [3,6,7,9–14,16,19–23].

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2. Experimental setup

The scheme of our KLM TDL oscillator is shown in Fig. 3. The oscillator is housed in a vacuum chamber with a footprint of 0.8 m × 1.6 m and operates at <1·10⁻² mbar pressure, limiting reabsorption of the generated XUV light. Most characteristics of the TDL setup are described in our recent publication [24]. Compared to the publication, we mode-lock the laser using a 2-mm-thick Kerr medium to decrease the intra-cavity power of the TDL due to a power limitation we observe when using the coated GIP (more details in Section 4). Furthermore, the laser operates in s-polarization which is required for efficient XUV out-coupling through the coated GIP.

 

Fig. 3. Schematic of the KLM Yb:YAG TDL oscillator with double pass over the disk. High harmonics are generated in the tight focus between two concave mirrors, CM3 and CM4. A coated GIP placed after the tight focus is used to couple the generated XUV light out of the oscillator. As indicated by the double arrow, CM3 is mounted on a translation stage used for fine-tuning of the laser cavity during mode-locked operation. HA: hard aperture; CM1/2: concave mirror; KM: Kerr medium; DM: dispersive mirror; OC: output coupler.

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The output-coupling arm of the oscillator contains a tight focus extension for HHG, which consists of two concave mirrors (CM3 and CM4). Due to the different peak intensity requirements for driving HHG in argon and xenon, we employed CM3 with a radius of curvature (RoC) of 100 mm and 150 mm, respectively, while CM4 always had a RoC of 250 mm. The noble gas is injected into the focus with a tapered glass gas nozzle with a ∼100-µm opening diameter. The gas nozzle is placed on a motorized xyz-stage to fine-adjust the XUV generation point. The coated GIP is placed after the focus between CM3 and CM4 to out-couple the XUV light out of the oscillator. The XUV light is directed by an unprotected gold mirror in the case of xenon or another extra-cavity coated GIP in the case of argon towards a 248/310 McPherson spectrometer and a photodiode. The overall XUV flux is measured with an aluminum coated AXUV100Al photodiode, while an additional 200-nm-thick aluminum filter is inserted to block the residual NIR. We use tabulated values for the transmission of the aluminum filter, for the reflectivity of the gold mirror, and for the reflectivity of the Ta₂O₅ top layer of the GIP to determine the generated and out-coupled XUV flux. For the determination of the flux in a single harmonic order, we assume a flat spectral response of the XUV spectrometer [10]. CM3 is placed on a motorized linear stage, allowing to compensate the lens effect of the plasma in the generation gas on the oscillator.

The optical coatings of the dispersive mirrors as well as of the coated GIP were designed inhouse and grown in our IBS coating facility. The Kerr medium and the coated GIP are purged with oxygen from both sides to prevent contamination during laser operation [10].

3. Design of the coated grazing-incidence plate

The coated GIP out-coupling method utilizes the increasing Fresnel reflection at the vacuum-top layer interface with increasing AoI in s-polarization for the XUV light [8]. In comparison to [8], we chose Ta₂O₅ as top layer instead of SiO₂ due to its higher XUV reflectivity, especially for a moderate AoI of 60°. Since the XUV light is typically absorbed in the first tens of nanometers in the top layer, interference with all underlying layers can be neglected. This allows to freely minimize the reflectance of the NIR light for s-polarization at the same AoI by using the interference of the material interfaces in the layer stack. The chosen materials are transparent in the NIR. Especially for the coated GIP that is placed inside a cavity, it is important that the NIR pulse with its full spectral bandwidth experiences low losses and therefore the AR-coating properties in the NIR needs to cover this bandwidth. Low losses at the GIP for the NIR pulse are achieved by applying the same coating on both sides of the GIP. Benefitting from gain in the cavity, we can tolerate higher losses compared to fsECs. Recently, we showed operation of our TDL oscillator with an intra-cavity peak power of more than 1 GW at an output coupling rate of 8.5% [24]. In the following, we assume that 0.5% per coating, resulting in 2% losses per cavity round-trip, can be easily tolerated.

The design of a coated GIP and the choice of the AoI is based on a trade-off between a desired high XUV reflectivity and low reflection losses over the spectral bandwidth of the driving NIR pulse. While a larger AoI favors a higher XUV reflectivity, low reflection losses for the fundamental NIR pulse become increasingly more difficult as the supported spectral bandwidth decreases. To visualize this trade-off, we designed several GIP coatings, each optimized for a different AoI and maximal NIR bandwidth (reflectivity <0.5% per coating), yet not exceeding a total coating thickness of 3.5 µm, allowing reliable production [Fig. 4]. A larger NIR bandwidth at high AoI could be potentially realized by designing thicker AR coatings, but this is outside of the scope of this investigation since it comes with other challenges related to the manufacturing of such coatings [8]. The design study in Fig. 4(a) shows the wavelength and AoI-dependent XUV reflectivity of the Ta₂O₅ top layer whereas Fig. 4(b) visualizes the AoI-dependent supported spectral bandwidth of the AR coatings for the NIR pulse.

 

Fig. 4. Coated GIP design study and trade-off parameters for AoI ranging from 60° to 85°. (a) Wavelength-dependent reflectivity of s-polarized XUV light from the Ta₂O₅ top layer of the GIP. The steps in the reflectivity curves are due to the use of two different reference data sets – high energy side is from [25] and low energy side from [26]. The p-polarized XUV reflectivity from a sapphire plate placed under Brewster’s angle (60.4°) is shown for comparison (blue dashed line). (b) Wavelength dependent reflectivity of the fundamental driving field. The maximum bandwidth (reflectivity <0.5%) for the respective AoI of the GIP is shown in the legend of (a). A transform limited soliton spectrum of a 45-fs pulse is shown for comparison (shaded gray area).

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Due to our broadband pulses (∼45 fs), we choose a 60°-AoI design of the coated GIP. Furthermore, the choice of an AoI of 60° simplifies the comparison to the sapphire Brewster’s plate method (Brewster’s angle of 60.4°), which is commonly used for intra-cavity applications, in this first proof-of-principle experiment. Another reason is that for the intra-cavity use of a coated GIP, in comparison to its single-pass application, it is crucial to minimize any influence on the NIR beam propagation, which becomes more challenging for larger AoIs. Due to slight production deviations, the produced coated GIPs turned out to be centered at an AoI of 62° for the laser wavelength. Figure 5(a) shows the wavelength dependent reflectivity of the s-polarized fundamental wavelength at 1030 nm of the coated GIP device with the same coating applied on both sides. The measured reflectivity of a single AR coating is below 1% in the 1000 nm to 1060 nm wavelength range. In comparison, the reflectivity of the p-polarized fundamental light of the applied AR coating is >6%. The high difference in reflectivity for s- and p-polarized radiation should thus enable an automatic selection of an s-polarized laser operation without the need of an additional polarization selecting intra-cavity element. The design of the AR coating and the s-polarized electric-field distribution of the fundamental light is shown in Fig. 5(b). The coating has a total thickness of 3.35 µm and consists of alternating layers of SiO₂ and Ta₂O₅. To further enhance the XUV reflectivity, the 263-nm-thick top layer is made from Ta₂O₅, a high refractive index material in the XUV range. Our coated GIP with 60° AoI features a broadband XUV reflectivity >25% for photon energies between 10 and 60 eV. For higher AoIs, the reflectivity could be increased to >50% while simultaneously extending the high photon energy cut-off. In comparison, a sapphire plate placed under Brewster’s angle for the p-polarized fundamental light would feature a narrower reflectivity band with a maximum of 17% at 25 eV [Fig. 4(a)].

 

Fig. 5. Characterization and design properties of the fabricated coated GIP. (a) Reflectivity of the s- and p-polarized fundamental light from the both-side AR-coated GIP at an AoI of 62°. The curves according to the design and the measured data are shown. A transform-limited soliton spectrum of a 45-fs pulse is shown for comparison (gray shaded area). (b) Coating design of the GIP for an AoI of 60°. The red line shows the light intensity distribution of the fundamental laser light within the dielectric coating.

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4. Experimental results

Table 1 summarizes the laser parameters and XUV performance of our TDL oscillator. In the here presented experiment, we operated our TDL oscillator based on Yb:YAG as gain material with sub-50-fs pulse duration at ∼17 MHz repetition rate. The optical bandwidth of the sub-50-fs pulses exceed the gain bandwidth of Yb:YAG by a factor of more than two. Such short pulses from Yb:YAG are enabled by operating the oscillator in a regime of strong self-phase-modulation inside the laser cavity [27]. Without the coated GIP introduced into the oscillator, our TDL oscillator delivers 43-fs pulses at 220 W of pump power. Intra-cavity, we achieve a peak and average power of 950 MW and 800 W, respectively. When the coated GIP is introduced into the oscillator, the performance was limited to less than 500 MW of intra-cavity peak power. We assume that this limitation comes from a thermal lens originating from the coatings of the GIP, which is for the argon experiment at an incident average intensity on the GIP of ∼10 kW/cm² and for xenon at ∼40 kW/cm². The respective incident peak intensities and peak fluences on the GIP are ∼20 GW/cm² and ∼1 J/cm² for argon and ∼80 GW/cm² and ∼5 J/cm² for xenon. Please note that the stated intensities and fluences are error-prone due to their high sensitivity to the respective length measurements of the HHG focus to the GIP. During the experiment we did not observe damage of the coated GIP.

Table 1. Summary of the laser parameters and XUV performance of our TDL oscillator with HHG in argon and xenon.

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We inject argon with a backing pressure of 5 bar and use a CM3 with 100-mm RoC. At a pump power of ∼200 W, the laser operates with 46 fs pulse duration at an intra-cavity peak and average power of 480 MW and 430 W, respectively. The optical spectrum [Fig. 6(b)] is centered at 1024.9 nm with a FWHM bandwidth of 24.5 nm. The ∼5-nm blueshift of the optical spectrum away from the gain peak of Yb:YAG at 1030 nm is explained by the ionization blue-shift in the plasma. The harmonic spectrum is shown in Fig. 7 and extents up to the 43^rd harmonic (52 eV). We out-couple an XUV average power of 1.3 µW in the 31^st harmonic (37 eV). With an XUV out-coupling efficiency of ∼30%, 1.3 µW of out-coupled correspond to 4.3 µW of generated XUV average power.

 

Fig. 6. Characterization of the KLM Yb:YAG TDL oscillator with HHG in argon (a) to (c) and xenon (d) to (f). (a), (d) Intensity autocorrelation with fit for sech²-soliton pulses. (b), (e) Optical spectrum with central wavelength (λ₀), spectral FWHM bandwidth (Δλ), and sech² fit. (c), (f) Radio-frequency (RF) spectrum of the fundamental repetition rate (f_rep) measured with 10-kHz resolution bandwidth (RBW).

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Fig. 7. Detected XUV spectra in argon and xenon filtered by a 200-nm-thick aluminum filter. Harmonics are labelled with harmonic order, energy, and out-coupled XUV average power per harmonic. The s-polarized XUV reflectivity of the Ta₂O₅ top layer of the 60°-AoI GIP is shown for comparison. The step in the reflectivity curve is due to the use of two different reference data sets – high energy side is taken from [25] and low energy side from [26].

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Due to the lower ionization potential of xenon, we use a slightly larger focus with a 150-mm RoC for CM3. At a pump power of ∼200 W, the laser operates with 45 fs pulse duration at an intra-cavity peak and average power of 410 MW and 360 W, respectively. The optical spectrum is centered at 1031.1 nm with a FWHM bandwidth of 26.9 nm [Fig. 6(e)]. The harmonic spectrum in xenon with a backing pressure of 3 bar extents up to the 25^th harmonic (30 eV) and we out-couple an XUV average power of 5.4 µW in the 21^st harmonic (25 eV) [Fig. 7]. With an XUV out-coupling efficiency of ∼30%, 5.4 µW of out-coupled correspond to 18.0 µW of generated XUV average power.

While driving HHG in both gases, the intensity autocorrelation traces [Figs. 6(a),(d)] and the optical spectra [Figs. 6(b),(e)] agree well with the fit for sech²-soliton pulses. The radio-frequency spectra measured at the fundamental repetition frequency of ∼17 MHz show no side peaks [Figs. 6(c),(f)], indicating clean soliton mode-locking. Within a few hours of XUV experiments, we did not observe degradation of the coated GIP.

5. Conclusion and outlook

We have, for the first time, experimentally implemented a coated GIP for efficient and broadband XUV out-coupling of intra-cavity generated high harmonics. We have designed and produced a 60°-AoI GIP, tailored specifically for the high demands of intra-cavity HHG. We have shown that XUV sources based on intra-oscillator HHG can deliver µW power levels, approaching the state-of-the-art of out-coupled XUV power levels delivered by fsECs at comparable photon energies [Fig. 2].

In comparison to previous intra-oscillator HHG in argon inside a ∼100-fs KLM Yb:YAG TDL oscillator where ∼0.06 µW of XUV were out-coupled in the 25^th harmonic (30 eV) by a sapphire Brewster’s plate [10], the combination of increased driving laser performance with more efficient XUV out-coupling by the coated GIP allowed us to out-couple 1.3 µW in the 31^st harmonic (37 eV). Hence, we have increased the out-coupled XUV average power by a factor of 20 while simultaneously increasing the photon energy. With xenon as generation gas, our out-coupled XUV average power has increased even further and has reached 5.4 µW in the 21^st harmonic (25 eV).

Currently, the intra-cavity HHG laser performance of our TDL oscillator is limited, which presumably originates from a thermal effect in the AR coatings of the GIP. By investigating and optimizing the residual absorption of the employed AR coatings, we expect to be able to increase our laser performance and the XUV output. Further possibilities to increase the XUV output of the system, including, e.g., the implementation of a high-pressure gas target, have been discussed in our previous publication [10].

In a future study, we plan to optimize the structure of our coated GIP. A first parameter is the design angle of the coated GIP, which can be used to further optimize the discussed trade-off between XUV reflectivity and supported driving laser pulse duration. Also, the top-layer material can be changed. Instead of Ta₂O₅, also the low index material SiO₂ can be used [8]. This brings the advantage of having the low index material at the interface to vacuum, simplifying the AR coating. Alternatively, also the high index material Ta₂O₅ can be exchanged by another one such as Nb₂O₅, Al₂O₃, or HfO₂. A change of the substrate material from sapphire to fused silica (lower refractive index in the NIR) reduces the complexity of the NIR AR coatings, leading potentially to lower NIR losses. This would be beneficial for the use of a coated GIP in a fsEC, which is more sensitive to losses than a TDL oscillator.

We have shown that efficient and broadband intra-cavity XUV out-coupling by a coated GIP is a well-suited approach to improve the performance of intra-cavity XUV sources based on fsECs or TDL oscillators.