The process of high harmonic generation allows for coherent transfer of infrared laser light to the extreme ultraviolet spectral range opening a variety of applications. The low conversion efficiency of this process calls for optimization or higher repetition rate intense ultrashort pulse lasers. Here we present state-of-the-art fiber laser systems for the generation of high harmonics up to 1 MHz repetition rate. We perform measurements of the average power with a calibrated spectrometer and achieved µW harmonics between 45 nm and 61 nm (H23-H17) at a repetition rate of 50 kHz. Additionally, we show the potential for few-cycle pulses at high average power and repetition rate that may enable water-window harmonics at unprecedented repetition rate.
© 2011 OSA
The process of high harmonic generation (HHG) has been studied extensively for more than two decades . It occurs when an intense light field interacts with an atom, mostly a noble gas. Due to the deformation of the atom’s Coulomb potential a valence electron can tunnel through the barrier subsequently being accelerated in the laser field. When the field reverses its sign the electron is accelerated back to the parent ion and upon recombination the kinetic and binding energy is released as a photon, typically in the extreme ultraviolet (EUV) region. One of the reasons for this process to be an extensive research field is that it allows to coherently transfer the energy to this spectral range with table-top laser systems . In addition, it happens on a timescale of attoseconds allowing for time resolved applications. When few-cycle pulses are used for interaction with the atoms isolated attosecond pulses are generated that have led to the new field of attosecond physics .
However, one of the main drawbacks is the low conversion efficiency that depending on interaction geometry, gas jet, laser system and others can reach values of 2·10−4 (ω-2ω interaction)  and ~10−5 (gas jet or waveguide) [5,6], but typically when using gas jets is rather low (<10−6) . There has been an increasing demand to boost the number of photons in the EUV spectral range. Generally, there are two possibilities being either to enhance the pulse energy (number of photons per pulse) or the number of pulses, i.e. working at a higher repetition rate. The first approach has generated impressive pulse energy of 10 µJ at a laser repetition rate of 10 Hz resulting in 100 µW of average power . This high pulse energy may enable the study of nonlinear phenomena in the EUV spectral range or the seeding of X-ray laser plasma amplifiers  or free electron lasers . However, spectroscopic applications such as photoelectron spectroscopy rather need a high number of photons per second at low pulse energy to avoid space charge effects . In the last years a number of approaches have been presented to meet this requirement. The challenge for high repetition rate high harmonic generation is the required intensity of more than 1013 W/cm2 resulting in average powers well above that of Ti:Sapphire laser systems. To circumvent the requirements on the driving laser, cavity enhancement has been proposed as a possibility to use moderate pulse energies and achieve the intensity by constructive interference of subsequent pulses inside a high finesse resonator . This scheme requires an active stabilization of the cavity . A record average power of 72 kW  inside the resonator has just recently been demonstrated holding promise for high average power high harmonic generation. But the out-coupling of the harmonics from the cavity remains a challenge in this approach. Up to now the highest average power per harmonic is 3.8 µW at 97 nm .
Another approach is to directly use a high repetition rate driving laser system, which does not require any sensitive cavity, and therefore, is more robust. The recent advances in fiber laser technology [18–20] have made possible first studies on high harmonic generation [21–23] at repetition rates of up to one MHz . However, a rather low conversion efficiency has to be expected, but has not been measured to date.
In this contribution we present the study of high harmonic generation at high repetition rates using a fiber chirped pulse amplification (FCPA) system  with MHz repetition rate. In comparison to earlier work [21–23], we carry out measurements with a calibrated spectrometer showing conversion efficiency of 1.2·10−9 when directly using a FCPA system. To improve this value a nonlinear compression of the FCPA system has been applied. We studied three different focusing conditions and were able to obtain µW level harmonics at 45 nm – 61 nm (H23-H17) with a maximum conversion efficiency of 1.2·10−7 into a single harmonic at a repetition rate of 50 kHz. These measurements solidify the importance of new fiber lasers for high field physics, and in particular, for HHG.
The principal experimental setup (Fig. 1 ) has been the same for all the harmonic generation experiments presented herein. The beam of a driving laser system is focused onto a gas (Xe, Kr, Ar), which was injected by 30 µm orifice continuously operated gas nozzle. Typical pressures in the nozzle channel were several bar, while the background vacuum pressure was about 10−3 mbar. We use two 200 nm aluminum filters placed in front of the spectrometer to filter out fundamental light and protect the sensitive CCD, which is different to earlier work where we used only one filter . The filters are placed on a slit with a width of 0.5 mm, which is expected to be large enough to transmit the whole harmonics beam.
The measurement of the spectrum of the high harmonics generated in that way has been done with a spectrometer, which has been calibrated at the BEAR beamline at Elletra (Trieste, Italy). It is constructed of an f=180 mm (86° angle of incidence) toroidal mirror and a 1000 lines/mm transmission grating. The spectrum is then recorded with a CCD camera (Andor DO940P-BN, 512 pixel x 2048 pixel) for subsequent analysis. For calibration of the spectrometer, narrow bands of synchrotron radiation were selected with a grating monochromator and focused in front of the spectrometer entrance. Higher diffraction orders of the monochromator were filtered with adequate foils (In, Sn, Al and Si, depending on the selected wavelength), so highly monochromatic light at several photon energies from 15 to 100 eV was obtained. A motorized aperture located behind the monochromator was used to control the beam divergence and ensure that the whole radiation was incident on the toroidal mirror and no cutting occurs by the aperture of the spectrometer grating. The beam power behind the motorized aperture was measured by a silicon diode with known sensitivity (IRD Inc. SXUV). Total spectrometer sensitivity in units of counts per Joule was then determined for each photon energy by integrating the background corrected counts recorded by the CCD camera over the first diffraction order of the spectrometer grating and dividing by CCD exposure time and beam power.
High harmonics with fiber chirped pulse amplification system
Fiber lasers are a solid-state laser concept known for the possibility of high average power levels well above the kW regime when operated in cw . However, for the amplification of ultrashort pulses to mJ level energies the challenge is to mitigate nonlinear effects that are more dominant than in other amplification schemes due to the guidance of high intensities in small size cores over lengths on the order of one meter. These effects have successfully been reduced applying the chirped pulse amplification scheme  and large mode area rod-type photonic crystal fibers . For the experiment presented here a fiber chirped pulse amplification (FCPA) system is used that is capable of generating 1 mJ, 50 kHz with a pulse duration of 480 fs leading to a peak power of 1.8 GW.
MHz high harmonics with sub-50 nm wavelength
The above-mentioned FCPA system has been operated at 1 MHz, 80 µJ (80 W average power), 500 fs and is focused to a focal spot size of 31 µm x 29 µm in a xenon gas jet resulting in an intensity of about 4.3·1013 W/cm2.
The spectrum that has been obtained by using these experimental parameters is shown in Fig. 2 together with the focal spot. The shortest wavelength that has been observed is the 21st harmonic at ~49 nm, which is well below previously demonstrated results (H15) with MHz FPCA systems . According to the cut-off law  the 21st harmonic corresponds to an intensity of 4.2·1013 W/cm2, which is in good agreement with the estimation given above. However, due to the low pulse energy and intensity the conversion efficiency is rather low (<3·10−12). The background that is apparent besides the harmonic peaks is due to residual aberrations of the spectrometer and noise of the CCD that has not been subtracted for this measurement.
Calibrated measurements of high harmonics generated with a FCPA system
In comparison to the experiments presented for the operation at 1 MHz the measurements of the average power in the EUV have been performed with the FCPA being operated at 1 mJ, 30 kHz (30 W), sub-600 fs. These pulses are focused onto a gas jet of krypton and argon with a f=150 mm focal length lens resulting in a focal spot size of 40 µm x 46 µm and an intensity of about 2.2·1014 W/cm2. The spectra of the high harmonics generated in krypton and argon are shown in Fig. 3 . As expected, shorter wavelengths are obtained when using argon, which has a higher ionization potential than krypton. Due to the higher ionization probability krypton shows higher conversion efficiency, typically about an order of magnitude higher than in argon. The strongest harmonic that has been obtained in krypton is H23 at 45 nm with an average power of 36 nW (8.1·109 photons/s) equalling a conversion efficiency of 1.2·10−9. This value has been obtained via integration over the harmonic peak and using the known spectrometer efficiency and aluminum filter transmission. Consequently, the so obtained value is the average power generated in the gas target.
µW level plateau harmonics
A main limitation of the obtainable conversion efficiency for high harmonic generation with fiber chirped pulse amplification systems is the pulse duration of several hundred femtoseconds leading to build-up of ionization before the peak of the laser pulse arrives. As soon as the accumulated ionization exceeds a certain critical value , the phase mismatch cannot be compensated by experimental accessible parameters. We have calculated the intensity that can be applied to krypton or argon before reaching the critical ionization in the pulse peak with the well-known ADK model  for different pulse durations. These calculations show that for pulses shorter than 100 fs the intensity can be increased significantly leading to higher conversion efficiency and shorter cut-off wavelengths.
Over the last year’s two approaches, i.e. optical parametric chirped pulse amplification [29, 30] and nonlinear compression in hollow core fibers [31,32], have proven to be a way to maintain the average power advantages of fiber laser while shortening the pulse duration to the required values of less than 100 fs [31,32] down to the few-cycle regime [29,30]. Due to its simplicity the nonlinear compression seems to be ideally suited for the purpose of high harmonic generation. It uses self-phase modulation in a noble gas filled hollow core fiber to broaden the input spectrum of the FCPA to several tens of nanometer. When removing the imposed chirp by appropriate mirrors shorter pulses with an enhanced peak power can be obtained. In order to achieve the highest possible peak power a numerical simulation based on a split-step Fourier algorithm has been performed. The propagation of Gaussian laser pulses with a pulse energy of 900 µJ, which corresponds to 90% coupling efficiency, and a pulse duration of 480 fs propagating along hollow core fibers with different inner diameters and lengths has been calculated, while also considering the losses occurring in such fibers . The nonlinearity is provided by a xenon gas filling (n2/p=8.1·10−23 m2/(W·bar)) with the pressure being set to pmax=0.148·λ2/(n0·Ppeak·n2)=1.1 bar , i.e. the pressure where self-focusing sets in. A Fourier-transform of the spectrum after propagation allows us to obtain the highest possible peak power. The results of the simulation show an optimum at an inner diameter of ~250 µm and a fiber length of 1 m. It has to be noted that our simulation has been restricted to 1 m fiber length due to practical reasons (manageability). An experimental setup based on our numerical optimization has been realized. The fiber chirped pulse amplification system has been operated at 1 mJ, 50 kHz, 480 fs for the nonlinear compression. By using a single 1 m long (250 µm inner diameter) fiber with a xenon pressure of 1 bar the input spectrum can be broadened to a −10 dB width of 82 nm (Fig. 4 ).
The pressure used in the experiment is somewhat lower than the pressure used in the simulation, but is the maximum we were able to use before seeing an increase in propagation losses in addition to reduced stability. Compression is achieved by a chirped mirror compressor with an overall group delay dispersion (GDD) of −2900 fs2. Due to the low propagation loss and the high reflectivity of the mirrors used in the compressors the compressed pulse energy is as high as 580 µJ (29 W average power). The compressed pulses have been characterized with an intensity autocorrelator (Fig. 4) giving an autocorrelation width of 65 fs. This corresponds to a pulse duration of 45 fs with a peak power of 7.5 GW, when adapting our propagation code to the experimental conditions. Due to the systematic numerical study we were able to find an optimized configuration with a performance significantly exceeding previous results . This fourfold increase in peak power combined with order of magnitude shorter pulses and excellent beam quality (inset of Fig. 5 ) poses an ideal source for high harmonic generation.
For the generation of high harmonics this laser system and three different focusing geometries have been used. The focal spots of 50 µm x 50 µm (f=150 mm), 67 µm x 69 µm (f=200 mm) and 93 µm x 94 µm (f=300 mm) are shown in Fig. 5. When using the estimated peak power from above the corresponding intensities are 7.6·1014 W/cm2 (f=150 mm), 4.1·1014 W/cm2 (f=200 mm) and 2.2·1014 W/cm2 (f=300 mm). The gases for HHG were krypton and argon. The spectrum has been recorded by the calibrated spectrometer described earlier.
For the largest focal spot size we still were able to observe the aluminum edge at 17 nm (Fig. 6 ). Via cut-off law  this corresponds to an intensity of 1.82·1014 W/cm2. Since we were not able to detect radiation below 17 nm, due to the filter transmission properties, we can conclude that the intensity was even higher. This agrees with our intensity calculation based on the peak power estimation given above. The spectra (before calibration) that have been obtained by using different focal lengths and gases are shown in Fig. 6.
They clearly show that the aluminum edge has been observed in argon for all focal spot sizes. Advantageously, the spectrometer efficiency increases at wavelengths below 35 nm making this observation easier.
The experimental conditions, i.e. gas pressure and position of the gas jet, have been optimized to obtain the highest possible average power. In agreement with the study of Salières et al.  we found the optimum conditions when the gas jet is placed somewhat behind the focus. The interesting fact is that the generation conditions we used is known to generate a Gaussian like harmonics beam , which is favourable for most applications.
The integrated average power of the harmonics generated in krypton and argon is shown in Fig. 7 with respect to the harmonic order. For both gases the loosest focusing has enabled the highest average power. This can be understood by phase matching considerations. The most critical parts contributing to phase mismatch are the Gouy phase shift, whose gradient is larger for tighter focusing, and the contributions of the free electrons caused by ionization.
We have calculated the weighted ionization rates, i.e. the ionization rate multiplied with the fractional ground state population, with the ADK model . It shows that the number of cycles contributing to ionization is larger for longer focal lengths while the peak value of the weighted rates is similar. In combination with looser focusing the phase mismatch is therefore significantly reduced for f=300 mm, which leads to the highest efficiency in our experiment. This is in agreement with a study of HHG optimization by Constant et al. .
When using krypton gas the plateau harmonics with an f=300 mm lens have an average power of 1.7 µW (H17, 60.6 nm), 3 µW (H19, 54.2 nm), 3.2 µW (H21, 49 nm) and 1.3 µW (H23, 44.8 nm), while all the harmonics up to the 31st order have an average power well above 100 nW. The highest conversion efficiency of 1.2·10−7 is therefore achieved for H21 in krypton gas resulting in 7.9·1011 photons/s at 49 nm. This is an increase in conversion efficiency by two orders of magnitude compared to the use of the FCPA system alone. The average power after the aluminum filters (400 nm thickness), which is what can be used for experiments, is still as high as 0.7 µW (H17, 60.6 nm), 1.2 µW (H19, 54.2 nm), 1.3 µW (H21, 49 nm) and 0.5 µW (H23, 44.8 nm).
Approaching the few-cycle regime with double stage nonlinear compression
As demonstrated in , the peak power and pulse duration of the driving laser system can be further scaled using a second nonlinear compression stage. Here the second stage is realized with an 250 µm inner diameter fiber with a length of 40 cm. The output from the first stage is coupled to this fiber, which is filled with argon at a pressure of 0.75 bar. Compression is achieved with a broadband mirror compressor with an overall GDD of −450 fs2. The pulse energy after the second compressor was 430 µJ at a pulse duration of 25 fs (Fig. 8 ), which corresponds to only 7 cycles at a central wavelength of 1030 nm.
The combination of high pulse energy and ultrashort pulses leads to a peak power of 10 GW. While the peak power is only slightly improved compared to a single stage setup, the reduced pulse duration could be beneficial for generation of even shorter wavelengths via HHG. The shorter pulses would allow for higher intensities without exceeding the critical ionization leading to shorter cut-off wavelengths. This may enable the generation of water-window harmonics at high repetition rates in the near future.
In this contribution we show calibrated measurements of HHG by state-of-the-art high repetition fiber lasers systems. Such systems are now emerging as a powerful tool for high field physics at high repetition rate. We show that sub-50 nm harmonics can be generated at 1 MHz repetition rate, however, with rather low conversion efficiency (<3·10−12).
The conversion efficiency of mJ class fiber chirped pulse amplification system operated at 30 kHz repetition rate is measured to be 1.2·10−9 resulting in 36 nW (8.1·109 photons/s) of average power in a single harmonic at 45 nm.
Additionally, a nonlinear compression scheme is used to enhance the conversion efficiency by two orders of magnitude resulting in 3.2 µW (7.9·1011 photons/s) at 49 nm and a repetition rate of 50 kHz. These parameters are well suited for a variety of high repetition HHG applications. Due to the high repetition rate, the performance of e.g. photoelectron spectroscopy experiments can be increased significantly in the future by employing the presented laser system . With the possibility of further power scaling of the employed fiber laser systems mW level harmonics are in reach.
Furthermore, we have already presented the possibility for further pulse shortening down to the few-cycle regime, which is a prerequisite for water-window harmonic generation at unprecedented repetition rates.
This work has been partly supported by the German Federal Ministry of Education and Research (BMBF), Grant 05 ES7GU1, the Helmholtz Institute Jena and the European Research Council under the European Union’s Seventh Framework Program (FP7/2007-2013)/ERC Grant agreement no . We thank Christian Rödel (Institute of Optics and Quantum Electronics, Friedrich Schiller University Jena) for assistance with the spectrometer.
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