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Abstract
We report the highest intra-cavity pulse energy of 80 μJ inside a Kerr lens mode-locked thin-disk ring laser oscillator at a repetition rate beyond 10 MHz enabling observation of the 2nd and 3rd harmonic beams directly generated by the Kerr medium. By adding a tight focusing setup to the ring cavity, we could observe krypton gas flame at an intra-cavity peak intensity of ∼28 TW/cm2 yielding a conversion efficiency of 10−5 for the 3rd harmonic beam. A further upgrade of the ring oscillator could lead to realizing a table-top source of vacuum ultraviolet pulses for application in photoelectron spectroscopy.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ultrafast phenomena in atomic and molecular physics are being investigated by high-order harmonic (HH) pulses in the vacuum ultraviolet (VUV) and extreme ultraviolet (EUV) wavelength region due to superior properties of these pulses which are a high spatial coherence and a very short pulse duration in the attosecond range, which are difficult to be attained by other light sources. The perfect synchronization of HH and fundamental pulses enables us to observe dynamical response of atoms or molecules with attosecond time resolution [1]. HH pulses can be also applied in photoelectron spectroscopy of solid surfaces [2,3]. One of the most significant issues in such an application field is the space charge effect, which disturbs electron kinetic energy spectra due to the high density of electrons yielded within irradiation of a single HH pulse onto a solid surface. In order to avoid this effect and implement high-resolution photoelectron spectroscopy, one must reduce the energy of HH pulses as much as possible, while their repetition rate should be increased to keep a sufficient signal-to-noise ratio at a reasonable data acquisition time. Not only photoelectron spectroscopy, but other fields related to industrial applications such as EUV lithography mask inspection can also benefit from HH pulses with a high repetition rate specially in the MHz-class regime [4].
To boost up the repetition rate of HH pulses beyond 1 MHz, we choose thin-disk lasers as a pump source which have effective thermal management at such a high repetition rate. Progressive development of commercial thin-disk laser heads has made generation of kW average power continuous wave (CW) laser beams inside an oscillator a rather straightforward task for researchers. Once such an oscillator is Kerr lens mode-locked [5–9], femtosecond laser pulses with a pulse energy of 100 μJ can be obtained at a high repetition rate of 10 MHz. Moreover, once a tight focusing setup is added to such a cavity, high-order harmonic generation (HHG) should be possible with an advantage of not requiring precision cavity length adjustment which is mandatory in cavity enhancement technique [10–12]. This can boost up the repetition rate of HHG in the VUV spectral region well beyond several 100 kHz [13–15], and facilitate application of HH pulses in aforementioned research areas.
To achieve this, we proposed a novel route of HHG inside a mode-locked thin-disk ring oscillator [8], which could lead to an increase of the flux of HH pulses generated inside a Ti:sapphire oscillator [16], or generated after nonlinear compression in a Kagome-type hollow core photonic crystal fiber outside of a thin-disk oscillator [17]. Labaye et al. recently reported HHG inside a Yb:Lu$_2$O$_3$ thin-disk oscillator [18], while they wasted the HH pulses generated in the return path in the cavity due to the linear configuration of the mode-locked oscillator. Towards real applications, we have successfully demonstrated dual-port intra-cavity HHG in a $\sim$100 m thin-disk ring oscillator fully operated in vacuum [19]. Besides this large infrastructure, we have been also developing a smaller laser system with a repetition rate beyond 10 MHz operated mainly in ambient air towards providing a more affordable light source in the VUV spectral range at a higher repetition rate while solving technical issues faced in the larger infrastructure using a table-top experimental setup.
In this paper, we report an upgrade of our thin-disk ring oscillator with an intra-cavity pulse energy of $\sim$80 μJ with a pulse duration of 522 fs at a repetition rate of 13.08 MHz. The obtained output power of 73.6 W is lower compared to the records reported by state-of-the-art SESAM mode-locking [20–22]. However, the obtained intra-cavity pulse energy is the highest ever reported inside a Kerr lens mode-locked oscillator with a repetition rate beyond 10 MHz, to the best of our knowledge. The intra-cavity peak power is estimated to be 135 MW, which enabled us to observe the 2nd and 3rd harmonic generation by the Kerr medium itself, under an estimated peak intensity of 0.2 TW/cm2. By adding a HHG setup operated in vacuum composed of a concave mirror pair and a gas nozzle placed near the focal point, we could obtain 62.1 W of output power with a pulse duration of 507 fs at a repetition rate of 11.85 MHz. The estimated intra-cavity peak intensity at the focal point of the concave mirror pair has reached to 28 TW/cm2, which is high enough to generate HH pulses in a rare gas target. As a proof of such a high peak intensity, we observed the bright luminescence, which we call flame, from both Xe and Kr target gases injected near the focal point through a fine nozzle with the 3rd harmonic beam efficiency up to 10$^{-5}$ generated in Kr gas. We could even visualize gas dynamics of the nozzle in vacuum revealing structures of a supersonic gas jet, which is usually done using electron beam excitation [23].
2. Ring laser oscillator
2.1 Overview of the upgrade
We have upgraded our previous thin-disk ring oscillator [8,24], towards obtaining an intra-cavity pulse energy of 100 μJ inside a Kerr lens mode-locked cavity. Before providing further details, we give an overview of the upgrade here. We changed the Yb:YAG thin disk soldered on a CuW heat sink to a new one with a lower thickness mounted on a diamond heat sink provided by another manufacturer. This results in a more efficient heat removal due to the high thermal conductivity of diamond. The cavity design has been also modified in accordance with the curvature and thermal properties of the new thin disk. The whole cavity is rebuilt on a water-cooled optical table to avoid day-to-day alignment changes destabilizing mode-locking and also to reduce surface temperature of the dispersive mirrors heated under an intra-cavity average power of $\sim$1 kW to achieve a longer lifetime. We have also used a thinner Kerr medium to reduce the intra-cavity nonlinear phase shift increased due to having a longer cavity path length in ambient air to decrease the repetition rate towards 10 MHz in order to obtain a higher pulse energy. The upgraded ring oscillator is also partially manipulated by using automatic stages and mirror mounts to make the daily startup and operation easier although a fully automated startup and operation using a computer is not realized yet. Through this upgrade, we obtained superior laser parameters that will be presented in the following subsections.
Fig. 1. Properties of the thin disk. (a) Surface profile. (b) Variation of the dioptric power upon pumping the disk under non-lasing conditions. A linear fit is shown by a dashed line. (c) Surface temperature at a pump power of 405 W under non-lasing conditions. (d) Variation of the maximum temperature upon increasing the pump power. Variation of temperature at a cooling water flow rate of 2 $l$/min is shown by the rhombi with a dotted line and that at a flow rate of 2.7 $l$/min is shown by the circles together with a linear fit shown by a dashed line.
2.2 Thin disk properties
The thin disk head is provided by TRUMPF Scientific Lasers GmbH having a high damage threshold of $\sim$8 kW/cm2, which enables pumping it up to 1 kW with a medium-sized pump spot diameter of $\phi$4 mm. The wedged Yb:YAG thin disk has a thickness of $\sim$100 μm with a 10 at.% doping concentration mounted on a diamond heat sink, which is pumped by a 935 nm laser diode. The thin disk has a slightly astigmatic surface profile shown in Fig. 1(a), with a radius of curvature of $R_x$=82 m in the horizontal and $R_y$=64 m in the vertical plane. Using a Shack-Hartmann wavefront sensor in a $4f$ setup to image relay the surface of the thin disk to the sensor under non-lasing conditions [25,26], we measured the dioptric power of the thin disk shown in Fig. 1(b). The slope of dioptric power variation of the thin disk is estimated to be -2.1$\times$10$^{-4}$ (Wm)$^{-1}$. As a result, we expect a flat thin disk at a pump power of $\sim$200 W, beyond which it turns into a convex shape. An ideal thin disk with an initial stigmatic $R$=20 m curvature ($R_x/R_y\approx$1) would become flat at a higher pump power of 500 W, making the cavity design much more convenient. Although the gain of the thin disk is low due to a limited thickness, its surface temperature shown in Fig. 1(c) is less than 80$^\circ$ C at a pump power of 405 W, which results in an even higher efficiency compared to our previous thin disk [24]. To decrease the temperature of the disk, we cooled it to 18$^\circ$ C at a flow rate of 2.7 $l$/min. The maximum temperature of the disk upon increasing the pump power under non-lasing conditions is shown in Fig. 1(d), which shows a linear increase up to a pump density of $\sim$4 kW/cm2.
2.3 Construction of the ring oscillator
The layout of the ring oscillator is shown in Fig. 2. In short, we have a ring cavity consisted of a 7% output coupler (OC), a $\phi$6.2 mm ceramic hard aperture in front of it to assist Kerr lens mode-locking (KLM) startup and remove a CW component from the spectrum, 32 GTI (Gires-Tournois interferometers) mirrors specially designed to have a high dispersion but a low loss to compensate for the nonlinear phase shift accumulated by the laser due to self phase modulation (SPM) in the air proving a total group delay dispersion (GDD) of $-$42,000 fs2, a telescope pair in front of the thin disk to compensate for its bending after pumping, and finally a turning mirror to get back to the OC. Eight of these GTI mirrors (Type-T2k) have a higher dispersion of GDD=$-$2000 fs2 shown by green squares in Fig. 2. Since they have a relatively large radius of curvature of $R$=$-$360 m with a convex shape after coating, we have placed them together in a group before the OC in order to have an easier management of their curvature effect on the cavity design. This enabled us to consider them as a curved optic with an equivalent focal point of $f$=$-$22.5 m, which can not be neglected in a ring laser oscillator with a larger cavity length of $\sim$22.9 m.
Fig. 2. Schematic of the thin-disk ring oscillator. CMOS: Complementary Metal Oxide Semiconductor sensor used for measuring the beam profile. He: helium gas. Type-T2k GTI mirrors are shown in green.
In the KLM setup, a concave mirror pair with a radius of curvature of $R$=2000 mm is used, which focus the laser beam inside the Kerr medium to a beam radius of $\sim$210 μm estimated from ABCD matrix formalism. One of the mirrors is fixed in position and the other one is placed on a $\pm$20 mm range translation manual stage (Sigmakoki, TSD-65121S-M6) to optimize the KLM performance. As a Kerr medium we used a high-quality sapphire plate with a thickness of 4 mm and a low impurity, which is inserted at the Brewster’s angle behind the focal point. It is water-cooled using a copper holder to avoid its degradation under a high intra-cavity pulse energy. The KLM setup was placed inside a vacuum chamber buffered by 10 mbar of helium (He) gas to avoid its degradation and reduce SPM in the air, near the focal point. The Kerr medium is placed on a motorized stage (Newport, 9063-X-P-M) with a travel range of 25.4 mm to optimize the KLM performance.
The thin-disk ring oscillator is placed on a 3$\times$1.5 m2 water-cooled optical table (Nihon Boushin, WHBL-3015TJS) to avoid alignment changes in the long ring cavity. The optical table is separated to 3 plates to yield a homogeneous temperature. To stabilize the temperature of the optical table, we have used a chiller (SMC, HRS024-W-20) set to 19$^\circ$ C with a temperature stability of $\pm$0.1$^\circ$ C and a flow rate of 3$\times$1.8 $l$/min. The temperature of the air inside the laboratory fluctuates up to 20$\pm$0.8$^\circ$ C with a period of $\sim$1 h, while that of the optical table is almost constant after sufficient warmup of 1.5 h. This temperature difference of $\sim$1$^\circ$ between the optical table and the laboratory environment helped us stabilize the temperature of the optical table, otherwise the temperature was fluctuating in resonance with that of the air and was difficult to be kept almost constant. As a result, we obtain the same alignment in the cavity from day to day requiring a minimal adjustment of the whole cavity for daily operations.
Fig. 3. KLM properties. (a) A broadband spectrum. (b) Measured autocorrelation trace. (c) Pulse trains measured by a 20 GHz sampling oscilloscope. (d) A spectrogram showing KLM stability up to 30 min.
2.4 Kerr lens mode-locking
At a pump power of 305 W, CW oscillation with an output power of 104.5$\pm$0.23 W (RMS 0.22$\%$) was obtained. The output power is measured by a water-cooled thermal head (Ophir, L1500W-LP) with a response time of 2.7 s. We usually take more than 180 samples with a time interval of 1 s (total 3 min) to measure the average power and determine its deviation. The maximum optical-to-optical efficiency was 34.7$\%$ with a slope efficiency of 38.7$\%$. We could start mode-locking by a gentle vibration in the vibrating mirror arm placed behind the output coupler after inserting the ceramic hard aperture in front of it. Unidirectional oscillation is achieved by using the vibrating mirror arm that destabilizes laser oscillation in the opposite direction that the laser output is coupled back into the ring cavity [8,27]. We also monitor the pulse trains in the opposite direction using a photodiode and once unidirectional oscillation is achieved, the power collapses to the background level.
A broadband spectrum shown in Fig. 3(a) with a calculated Fourier-limited pulse duration of 517 fs was obtained. The measured intensity autocorrelation trace without any dispersion compensation is shown in Fig. 3(b), resulting in a pulse duration of 522 fs with assumption of a sech2 pulse shape. Moreover, the oscillation is unidirectional and we have confirmed single pulse operation in the sub-ns range shown in Fig. 3(c) within the dynamic range (25 ps) and frequency response (20 GHz) of an InGaAs fast photodiode (EOT, ET-3500) and a sampling oscilloscope (Tektronix, DSA8300). A spectrogram showing stability of the ring oscillator up to 30 min is shown in Fig. 3(d). We could not obtain stable KLM operation beyond 1 h, due to a vertical misalignment in the cavity near the thin disk. By compensating for this misalignment using a mirror holder placed right after the thin disk, we could get it back to normal operation.
Furthermore, CW mode-locking has been confirmed using a spectrum analyzer (Agilent, N9322C) at a resolution bandwidth (RBW) of 30 kHz. The radio frequency (RF) spectrum measured at a central frequency of 13.08 MHz is shown in Fig. 4(a) and the harmonics of the fundamental RF spectrum are shown in Fig. 4(b) which were not modulated. The beam profile shown in Fig. 4(c) has a nearly Gaussian shape ideal for tight focusing. Besides, the beam is slightly diffracted due to measurement behind the hard ceramic aperture. Using a measurement setup composed of a $f$=500 mm achromatic doublet, an automatic stage, and a CMOS sensor [28], we measured a beam quality factor of M2(x)=1.09 in the horizontal and M2(y)=1.06 in the vertical plane. The caustic is shown in Fig. 4(d). The far-field beam profile having a Gaussian profile is shown in the inset. The beam radius is calculated using the D4$\sigma$ method based on the second moment of the intensity distribution.
Fig. 4. Further properties of the laser pulses. (a) Fundamental RF spectrum. (b) Harmonics of the fundamental RF spectrum. (c) Near-field beam profile measured behind the ceramic hard aperture. The beam is slightly diffracted at this position due to using the hard aperture. (d) Caustic with a Rayleigh range of 54.3 mm in the horizontal and 50.9 mm in the vertical plane showing a nearly diffraction-limited beam. The far-field beam profile is shown in the inset.
The output power was 73.6$\pm$0.43 W (RMS 0.58%), from which we can estimate an intra-cavity pulse energy of 80 μJ, and an average power beyond 1 kW corresponding to a peak power of 135 MW. To the best of our knowledge, this is the highest intra-cavity pulse energy obtained in a Kerr lens mode-locked oscillator at a repetition rate beyond 10 MHz. The increase of the average power and a higher beam quality compared to that of our previous ring oscillator [8,24], is owing to the efficient heat removal at a higher pump power using a thin disk mounted on a diamond heat sink. However, since the laser propagates a longer distance in ambient air, the obtained pulse duration is longer, and this has resulted in just a slightly higher intra-cavity peak power. This confirms a limit to the attainable intra-cavity peak power inside a thin-disk ring oscillator partially operated in ambient air inside which a single pulse is propagating with a high pulse energy.
2.5 Harmonic generation by the Kerr medium
Since the intra-cavity peak power is 135 MW, a very interesting phenomena was observed for the first time, to the best of our knowledge. While optimizing the KLM setup, by placing a card beyond the second concave mirror having a UVFS substrate, we could observe a blue light concentric with the profile of the fundamental beam. This blue light was only present when the cavity was mode-locked. To further verify this effect, we placed a UVFS prism behind the concave mirror and diffracted the beam. The result was observation of a weak 2nd harmonic beam together with a brighter 3rd harmonic beam. The 2nd harmonic generation (SHG) in a sapphire substrate is a very interesting phenomenon because the 2nd order nonlinear susceptibility $\left (\chi ^{(2)}\right )$ of sapphire is regarded as 0. In addition, we had no observation of such harmonic generation from the Kerr medium in a mode-locked oscillator using a bulk Yb:Lu$_2$O$_3$ ceramic developed in a previous study [29].
The spectrum of the 2nd harmonic beam is shown in Fig. 5-(a). The peak wavelength was 515.3 nm, which is exactly the same as the half-wavelength of the fundamental beam. The spectrum of the 3rd harmonic beam is also shown in Fig. 5-(b). The peak wavelength was 343.6 nm, which is consistent with that expected from the fundamental beam. We could not accurately determine the spectral width of the 2nd and 3rd harmonic beams due to the low resolution of the spectrometers, while the bandwidth of the spectra indicate that these do not correspond to fluorescence. The beam profile in the inset of Fig. 5-(b) shows a Gaussian profile similar to the profile shown in Fig. 4(c). The 2nd harmonic beam was too weak for measurement using a neutral density filter (OD=1.0) in front of a CMOS camera, but we could observe it by naked eyes. These harmonic beams could have been generated on the surface of the Kerr medium. A thermal power meter head was not sensitive enough to measure the power.
Fig. 5. Properties of the harmonic beams generated by the Kerr medium. (a) Spectrum of the 2nd harmonic beam generated by sapphire. (b) Spectrum of the 3rd harmonic beam generated by sapphire. The near-field beam profile is shown in the inset. (c) Spectrum of the 2nd harmonic beam generated by quartz. The near-field beam profile is shown in the inset. (d) Spectrum of the 3rd harmonic beam generated by quartz.
Changing the Kerr medium to quartz ($t$=4 mm), we could observe a bright 2nd harmonic beam together with the 3rd harmonic. The spectrum of the 2nd harmonic beam is shown in Fig. 5-(c) having a peak wavelength of 515.2 nm together with its near-field beam profile in the inset. The spectrum of the 3rd harmonic beam is shown in Fig. 5-(d) having a peak wavelength of 343.8 nm. The 2nd harmonic beam was relatively brighter so that it was difficult to measure only the profile of the 3rd harmonic beam in the limited space. Using a CaF2 plate, still both the 2nd and the 3rd harmonic beams were observable. However, we could not observe the 5th harmonic beam outside the vacuum chamber buffered by He gas even using this plate having the lowest absorption at 206 nm which can be easily absorbed by the other Kerr media having a high thickness. The peak intensity at the focal point of the concave mirror pair ($R$=2000 mm) focusing the beam into the Kerr medium is estimated to be 0.2 TW/cm2. Therefore, we expect that a peak intensity above 10 TW/cm2, which is typically required for HHG in a gas medium, could be achieved at an additional focal point of a telescope consisted of a tightly focusing concave mirror pair ($R$=200–300 mm) to be inserted into the cavity as the next step towards observation of intra-cavity HHG.
3. Towards intra-cavity HHG
3.1 Ring oscillator upgrade
We further upgraded the ring oscillator towards intra-cavity HHG at a repetition rate beyond 10 MHz. The main differences with our previous design are placing the Kerr medium inside a small vacuum chamber buffered by 10 mbar of He and adding another vacuum chamber which contains the HHG setup. Therefore, there are 4 windows inside the cavity that seal these chambers from the rest of the cavity which is operated in ambient air. The windows are composed of a UVFS plate ($t$=1 mm) sealed at a Brewster’s angle to a nipple. After adding these chambers, the length of the ring oscillator is increased to 25.4 m. The schematic of the ring oscillator after this upgrade is shown in Fig. 6. We used 29 GTI mirrors in the cavity proving a total GDD of $\sim$-31,000 fs2. We removed Type-T2 GTI mirrors in order to simplify the cavity design and not include the effect of their curvature on the oscillator performance since the cavity length is much longer than their effective focal length ($f$=$-$22.5 m).
Fig. 6. Schematic of the ring oscillator after adding the HHG setup and placing the Kerr medium inside another compact vacuum chamber buffered by He gas. A picture of the setups is shown in the inset.
The ceramic hard aperture had a reduced diameter of 5.6 mm to completely remove a CW component from the spectrum. Since the beam propagates a long distance between the concave mirror pair, two nipples with a length of 650 mm are attached to the vacuum chamber filled with a low-pressure He gas to decrease the intra-cavity nonlinear phase shift of the air upon focusing the laser beam. For HHG, another concave mirror pair (R=200–300 mm) is used which focus the laser beam down to a beam radius of 17–25 μm. Since we did not insert any out coupler for HH pulses in the VUV spectral range at the Brewster’s angle, the beam suffers from slight astigmatism due to using this concave mirror pair having a short focal length.
To further stabilize the temperature of the experimental setup and avoid excessive air flow coming from the air conditioners in the laboratory, we placed it in a clean booth. However, we still observe a periodical misalignment of the ring cavity in the vertical direction, which should be due to temperature fluctuation of the air since it is observed even when the thin disk is not pumped. Such an alignment change in a long ring oscillator required fine adjustment of the position of the ceramic hard aperture to avoid decreasing of the output power and spectral narrowing, which were usually observed after $\sim$40 min of laser operation. To further decrease this minimal drift of alignment, we plan to place the whole experimental setup in a box to avoid air flow perturbations and further stabilize the temperature.
3.2 Mode-locking performance
At a pump power of 305 W, CW oscillation with an output power of 99.3$\pm$0.58 W (RMS 0.58$\%$) was obtained. The RMS instability of the output power is increased after installing the clean booth due to poor removal of dust particles, which is under improvement by adding an extra HEPA (High Efficiency Particulate Arrestance) filter. The maximum optical-to-optical efficiency was 35.2$\%$ with a slope efficiency of 40.3$\%$. A broadband spectrum shown in Fig. 7(a) with a calculated Fourier-limited pulse duration of 498 fs was obtained. The measured intensity autocorrelation trace without any dispersion compensation is shown in Fig. 7(b), resulting in a pulse duration of 514 fs with assumption of a sech2 pulse shape. Moreover, the oscillation is unidirectional and we have confirmed single pulse operation in the sub-ns range shown in Fig. 7(c), using a sampling oscilloscope. A spectrogram indicating stability of the ring oscillator up to 30 min is shown in Fig. 7(d).
Fig. 7. KLM properties after inserting the HHG setup. (a) A broadband spectrum. (b) Measured autocorrelation trace. (c) Pulse trains measured by a 20 GHz sampling oscilloscope. (d) A spectrogram showing KLM stability up to 30 min. (e) Near-field beam profile measured behind the ceramic hard aperture. The beam is slightly diffracted at this position due to using the hard aperture. (f) Caustic with a Rayleigh range of 55.5 mm in the horizontal and 49.3 mm in the vertical planes showing a nearly diffraction-limited beam. The far-field beam profile is shown in the inset.
The repetition rate was 11.76 MHz and we could obtain CW mode-locking confirmed by measuring the RF signal using the spectrum analyzer. The beam profile shown in Fig. 7(e) has a nearly Gaussian shape ideal for tight focusing. There is a slight astigmatism in the beam due to tight focusing in the HHG setup resulting in a horizontal beam radius of 1.6 mm and a slightly longer vertical beam radius of 1.78 mm. Besides, the beam is slightly diffracted due to measurement behind the hard ceramic aperture. We measured a beam quality factor of M2(x)=1.02 in the horizontal and M2(y)=1.01 in the vertical plane. The beam quality has improved after inserting the tight focusing setup in the cavity since we had more flexibility in obtaining single mode oscillation. The caustic is shown in Fig. 7(f). The far-field beam profile shown in the inset is also slightly astigmatic. In spite of having placed the setup inside a clean booth, we could not obtain stable KLM operation beyond 1 h yet due to a vertical misalignment in the cavity. However, this level of stability was sufficient to observe rare gas flames and should be long enough for measuring the spectrum of the HH pulses and further applications.
The output power was 61.7$\pm$0.56 W (RMS 0.92%), from which we can estimate an intra-cavity pulse energy of 75 μJ, and an average power of 880 W corresponding to a peak power of 128 MW. From ABCD matrix formalism we expect a beam radius of $\sim$25 μm, which should result in an intra-cavity peak intensity of $\sim$13 TW/cm2 near the focal point. Since the HHG setup is placed in a vacuum chamber, replacing the concave mirror pair from $R$=300 mm to $R$=200 mm did not change the intra-cavity nonlinear phase shift and it only resulted in negligible changes in laser parameters. Therefore, further reduction of the beam path length in ambient air by placing part of the ring oscillator in the vacuum chamber should result in a higher intra-cavity peak power even at a high pulse energy. After this replacement, the obtained power was 62.1$\pm$0.83 W (RMS 1.33%) at a repetition rate of 11.85 MHz with a pulse duration of 507 fs. Since the laser beam is focused to a beam radius of $\sim$17 μm from ABCD matrix formalism, we expect a peak intensity of $\sim$28 TW/cm2 near the focal point of the HHG setup.
3.3 Observation of rare gas flames
To generate HH pulses we applied xenon (Xe) gas with a back pressure up to 5 bar to a $\phi$125 μm nozzle placed near the focal point of the concave mirror pair ($R$=300 mm). We note that there was no notable instability of the mode-locking at the moment of gas introduction owing to the robustness of the mode-locking condition against the slight change of the dispersion and nonlinear phase shift caused by the gas target. The nozzle is consisted of a stainless steel tube with an inner diameter of 1 mm, to the tip of which a zirconium tube is inserted. The gas nozzle setup is compatible with Swagelok fittings and can be easily replaced. The vacuum chamber has a volume of $320\times 1140\times H=240$ mm3. When the vacuum chamber was evacuated using a scroll pump (Edwards, nXDS6i), the pressure was $8 \times 10^{-1}$ mbar with continuous injection of Xe gas through the nozzle. We observe a bright structured luminescence near the exit of the gas nozzle, which we call flame, as shown in Fig. 8(a). The bright luminescence is the evidence that the intensity of the laser pulse is sufficiently high to induce multi-photon/tunneling excitation/ionization of atoms in the gas target, and this intensity, typically more than 10 TW/cm2, is equivalent to that required for HHG. Thus, this observation was consistent with the intensity estimated at the focal position described in subsection 3.2, and it ensures HHG in the gas target, even though we did not measure the spectra of the HH pulses. The outcoupling of the HH pulses from the cavity will be realized by inserting a Brewster plate reflecting them at the downstream of the focal position [19].
Fig. 8. Rare gas flame properties. (a) Xe flame at a back pressure of 5 bar when the turbo pump was off. (b) Xe flame when the turbo pump was on. (c) Kr flame at a back pressure of 6 bar when the turbo pump was on.
We can classify the typical structures of the Xe gas density in a supersonic gas jet by observing the luminous parts of the flame as shown in the magnified part of Fig. 8(a). The Xe gas jet at the exit hole of the nozzle expands in the ambient Xe and the jet pressure is reduced to less than the ambient Xe pressure at some distance, where the Xe gas jet is recompressed by a pushing-back force of the ambient Xe, resulting in forming high-density wall structures of Xe atoms. The wall normal to the jet axis is called Mach disk, the cylinder wall with a swollen belly surrounding the jet axis is called barrel shock, and the region enclosed with these walls is called zone of silence. The forming process of these structures in a supersonic gas jet are still actively studied in the field of fluid dynamics [30], and it is important how the density structures of transparent fluid can be revealed in that scientific field. In this sense, our observation of the flame structures utilizing multi-photon/tunneling excitation/ionization with intense femtosecond laser pulses might give a novel technique to identify the structures of a supersonic gas jet, because this kind of observation had been previously performed only by applying a more sophisticated technique of electron beam excitation [23].
From the point of view of HHG, however, the formation of the Mach disk and the barrel shock were unfavorable because they ensured that the ambient Xe gas pressure is high enough to push back the Xe gas jet from the nozzle. The ambient Xe generally absorbs the HH pulses in the VUV spectral range resulting in the reduction of the HH yield. Therefore, we operated a turbo molecular pump (Pfeiffer, HiPace400) set in front of the scroll pump. Once the turbo pump was turned on, the pressure of the vacuum chamber was reduced to $2 \times 10^{-2}$ mbar. The luminous walls disappeared with this reduction of pressure inside the vacuum chamber as shown in Fig. 8(b). This might be owing to the fact that the wall structures moves far from the exit hole of the nozzle and the densities of the walls significantly decreased as was demonstrated with numerical simulations in Ref. [30]. As a result, the Xe gas jet was more widely expanded than that under the previous condition. The extensions of red fluorescent lines on the propagation axis of the laser pulse supported this assumption. We note that the evacuation using a turbo pump had no effect on KLM stability unless it was heated up while evacuating a high Xe gas pressure, which resulted in a huge vibration. To avoid this, we limited the rotation frequency of the turbo pump and applied water cooling, which helped us continue to operate the ring oscillator while flowing a high pressured gas near the focal point. A gas jet dump will be introduced to improve the pressure condition [18], in the future.
Fig. 9. The power of the 3rd harmonic beam generated in Xe gas ($R$=300 mm, $\phi$125 μm) is shown by the rhombi fitted to a parabola shown by a dotted curve. The power of the 3rd harmonic beam generated in Kr gas ($R$=200 mm, $\phi$200 μm) is shown by the solid circles fitted to a parabola shown by a dashed curve.
We observed the 3rd harmonic beam behind the focusing concave mirror with a radius of curvature of 300 mm, the substrate of which was made of UVFS transmitting the UV 3rd harmonic beam but terminating the HH beams in the VUV spectral range. Efficient generation of the 3rd harmonic beam in a gas flame is one of the milestones towards intra-cavity HHG. To measure the power of the 3rd harmonic beam generated in the flame, we placed a power meter behind the concave mirror. The third harmonic beam was focused to a filter (Thorlabs, NENIR60B) in front of the power meter to cut the fundamental field. The power of the 3rd harmonic beam is shown by the rhombi in Fig. 9, fitted to a parabola shown by a dotted curve. The power was increased either upon decreasing the distance of the nozzle to the focal point or even getting away from it to cover the whole Rayleigh range. The conversion efficiency was $2.8 \times 10^{-6}$ considering the transmission of the filter when the gas nozzle was close to the focal point. The low conversion efficiency should be due to a long Rayleigh range of 1.9 mm, which can not get fully covered by the nozzle. Therefore, we switched to covering the whole Rayleigh range while the nozzle was placed near the focal point to benefit from both of the high-conversion regions.
For further increase of the conversion efficiency, we replaced the concave mirror pair to R=200 mm in order to obtain a tighter focus so that the nozzle could cover a shorter Rayleigh range of 0.9 mm. We also increased its hole size to $\phi$200 μm. Unfortunately, we ran out of Xe gas and had to switch to Kr gas. The observed flame using Kr gas with a back pressure of 6 bar is shown in Fig. 8(c) while the pressure of the chamber was increased to $8.7 \times 10^{-1}$ mbar although the turbo pump was on. Power of the 3rd harmonic beam upon increasing the back pressure of Kr gas is shown in Fig. 9 by the solid circles fitted to a parabola shown by a dashed curve, leading to a conversion efficiency up to $10^{-5}$. Conversion efficiency of the 3rd harmonic beam is even higher when we flow the gas to the focal point at a higher vacuum level and decreases after the vacuum level gets poor. Therefore, we expect to increase the efficiency by installing a gas jet dump and boosting the evacuation ability using multiple turbo pumps. We also observed the 3rd harmonic beam using argon (Ar) gas although we could not observe the Ar gas flame itself. This confirms that the intra-cavity peak intensity is not sufficient for observing multi-photon/tunneling excitation/ionization in Ar gas due to having a higher ionization energy compared to Xe and Kr.
4. Conclusion and future prospects
We have observed rare gas flames in Xe and Kr inside a Kerr lens mode-locked thin-disk ring oscillator at a repetition rate of 11.85 MHz. To the best of our knowledge, this is the first time that Kr flame is observed inside a thin-disk ring oscillator at a repetition rate beyond 10 MHz. To out couple the HH pulses, we inserted a sapphire plate ($t$=1 mm) behind the focal point of the HHG setup. The pulse duration became 60–80 fs longer and it was difficult to get a shorter pulse duration by adjusting the intra-cavity negative dispersion. Laser performance highly depends on the quality of this plate and we should decrease its thickness to avoid getting longer pulses. By optimizing the gas nozzle design and using Xe gas, we expect to further increase the conversion efficiency of the 3rd harmonic beam up to 2 orders of magnitude. We plan to pump the thin disk at 969 nm towards obtaining a higher intra-cavity peak power while keeping the repetition rate beyond 10 MHz towards observation of Ar flame and out coupling HH pulses using a SiC plate. The latter upgrades should enable us to move towards application of the HH fields in photoelectron spectroscopy and EUV lithography mask inspection.
Funding
Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT); Grant-in-Aid for Scientific Research (26247068, 26220606).
Acknowledgment
We are grateful for the non-stop efforts of M. Sugiura and K. Tamura of Tokai Optical Co. Ltd., for development of the low-loss GTI mirrors and K. Tsuchiya of Nihon Boushin Co. Ltd., for development and installation of the water-cooled optical table. We are also grateful to T. Metzger of TRUMPF Scientific Lasers GmbH, M. Larionov of Dausinger+Giesen GmbH, and T. Imahoko of Cyber Laser Inc., for fruitful discussions. Besides, we appreciate Y. Yamagata and T. Hosobata of the Advanced Manufacturing Support Team of RIKEN for giving us unlimited access to their precision measurement tools. AAE is grateful to the Endeavour Fund-Research Programmes of the Ministry of Business and Innovation & Employment (MBIE) of New Zealand.
This work is part of the Leading-edge Research Infrastructure Program in collaboration with the Advanced Photon Science Alliance (APSA) project commissioned by the Ministry of Education, Culture, Sports, Science, and Technology of Japan (MEXT). Y.N. and K.M. gratefully acknowledge a financial support from Grant-in-Aid for Scientific Research No. 26247068 and No. 26220606.
Disclosures
RIKEN Center for Advanced Photonics and TRUMPF Scientific Lasers GmbH have signed a confidentiality and non-use agreement of thin-disk laser components for the development of thin-disk ring oscillators.
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