1. Introduction

High harmonic generation (HHG) enables extreme ultraviolet (XUV) and soft X-ray generation by the extreme frequency conversion of a driving ultra-short laser pulse [1]. This has emerged as a complimentary technique to large-scale facilities for the generation of coherent XUV radiation [2]. A typical HHG spectrum consists of the odd harmonics of the driving laser field that are referred to as harmonic lines. These lines are usually fixed to a photon energy corresponding to the odd multiple of the central photon energy of the driving laser [2].

The unique combination of coherence, ultrashort pulse duration, spatial coherence and broad spectral coverage of these HHG-based XUV sources enabled a large variety of table top applications in recent years [2]. But these applications can be limited by the available photon flux or the comb-like structure inherent to most HHG spectra. Experiments like XUV spectroscopy [3–5], coherent diffractive imaging [6], coincidence measurements [7,8] and XUV-pump XUV-probe [9,10] measurements can benefit from a high XUV average powers to shorten acquisition times and therefore enhance the signal-to-noise ratio. Furthermore, the discrete orders of the harmonic comb limit the spectral coverage. This effect can be combatted by tunable XUV sources, extending the spectral coverage, potentially up to a quasi-continuum. Holding immense potential for material specific [11–13] or multispectral [14,15] XUV imaging techniques and aforementioned spectroscopic applications by scanning the harmonic lines over characteristic resonances of the sample.

A plethora of tunable HHG sources have been demonstrated already. The most intuitive approach is to use a tunable driving laser, either by high-order frequency mixing of the output of an optical parametric generator with a fixed frequency laser inside a gas target [16,17], by directly driving the HHG process with a tunable optical parametric amplifier [18–20] or by manipulating the driving field through soliton dynamics [21]. Furthermore, devices for spectral phase and amplitude modification allow direct control over the driving laser field [22–25]. Utilizing nonlinear propagation effects or dispersion, tuning can be accomplished through laser intensity dependent blue-shifting [26], the chirp of the driving pulse [27], or both [28,29], sometimes combined with chromatic focusing [30]. Finally, recent theoretical [31] and experimental [32,33] studies demonstrated the possibility to shift the fundamental photon energy of the driving laser pulse by interfering two pulses with an identical spectrum.

Despite the large number of possibilities for a tunable table-top XUV source, moderate photon flux, limited spectral coverage, high complexity, low tuning speeds of more than several seconds [28,32] or a combination of these continue to pose a problem. In this work, a novel XUV source is presented, combining a high photon flux of ${10^{11}}$ ph/s/eV, comparable to non-tunable state-of-the-art sources [8,34–37], and continuous tunability with full spectral coverage at high tuning speeds due to a simple experimental realization. This user-friendly combination of properties has never been shown in a table-top setup before. By simply changing the pulse energy in front a multipass cell and the subsequent waveguide-based HHG setup, utilizing nonlinear effects and pulse chirping, shifting of the generated HHG spectrum is realized. The covered spectral range, spanning from 50 eV to 70 eV is of interest for several applications, such as ultrafast magnetization dynamics of ferromagnetic materials [38,39] and coincidence measurements [8]. Nevertheless, the approach can be adapted to other XUV photon energies.

2. Experimental setup

The setup consists of three consecutive parts: a coherently combined chirped pulse amplification (CPA) fiber laser system delivering ultrashort pulses, a gas-filled multipass cell for nonlinear pulse compression and a waveguide-based high harmonic generation with subsequent spectral and spatial characterization (Fig. 1). The coherently-combined fiber-based CPA system as presented in [40] is set to emit pulses with an energy of 1.3 mJ and a duration of 160 fs at 64 W average power, 50 kHz repetition rate and a center wavelength of 1032 nm. The following combination of a half-wave plate and a thin-film polarizer allows for continuous adjustment of the pulse energy entering the argon-filled multipass cell. The multipass cell setup is fully described with all relevant parameters in [41]. Herein, the laser pulses are spectrally broadened by self-phase modulation in 450 mbar of argon, depending on the pulse energy set by the half-wave plate and thin-film polarizer combination. Compared to the original publication, the pressure in the multipass cell was reduced to accommodate for a higher pulse energy and shorter pulse duration. Subsequently, the pulses are compressed to 35 fs FWHM duration by a set of negatively chirped mirrors with a fixed group delay dispersion of −1400 fs². The following Schiefspiegler-telescope consists of a concave mirror with a focal length of 500 mm and a convex mirror with -1000 mm to focus the beam into the waveguide with a spot size diameter of 128 µm according to [42]. The Schiefspiegler-type telescope is used to mitigate aberrations for efficient incoupling. The waveguide is a capillary with a core diameter of 200 µm and an outer diameter of 2400 µm. It consists of two capillaries stacked inside each other. The inner one has an octagonally-shaped, fluorine-doped ring that guides light escaping the core by total internal reflection. This protects the fiber mount from direct laser illumination, making it high power capable. The outer capillary, made of fused silica, ensures mechanical stability by its significantly larger diameter. The fiber is slit to its core by a 300 µm wide wet saw blade. The cuts are 13 mm apart and are located 4 mm away from the end of the fiber facing the XUV spectrometer. The capillary is firmly mounted within a water-cooled stainless-steel pipe by a set of high temperature capable rubber gaskets pressed against the outer cladding. This creates a vacuum-tight seal around the capillary, allowing a targeted infusion of argon gas through the slits into the fiber with a defined backing pressure. The whole unit containing the capillary is connected to its adjacent vacuum chambers by two bellows, which allow adjusting the waveguide with respect to the laser beam for efficient coupling of the laser radiation into the capillary.

 

Fig. 1. Experimental setup for continuously tunable high harmonic generation between 50 eV and 70 eV (GIPs: grazing incidence plates). The CPA system and the multipass cell are simplified. Inset: end facet of the capillary used as a waveguide. The core, an inner octagonal fluorine-doped cladding and an outer fused silica cladding are visible.

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After the generation of high-order harmonics in the waveguide, the collinearly propagating fundamental infrared and XUV beams are separated by means of two grazing incidence plates (GIPs) [43] followed by thin metal foils. The GIPs have a custom-designed broad-bandwidth antireflective coating for the driving laser (R < 1%) and a high refractive index top layer for high XUV reflectivity, placed at a grazing angle to the incident beam. The driving laser light is transmitted through the first GIP and is monitored by a power meter and a camera. After the second GIP, less than 50 mW of the driving laser remains, not posing a danger to the thin metal foils. The reflected XUV beam is transmitted through three thin aluminum foils, two of which have 2 µm thickness and an additional one having 0.2 µm thickness. They fully block the remaining driving laser light and attenuate the XUV beam to protect the subsequent camera from oversaturation. Finally, the XUV beam is spectrally and spatially characterized by a flat field spectrometer using a 1200 lines/mm grating in combination with an Andor Newton CCD camera.

3. High harmonic generation

In the first part of the experiment, the photon flux is optimized and characterized. The experimental optimization for achieving phase matching at a given capillary diameter is an iterative process with the following three steps. Step one: adjusting the combination of gas pressure within the multipass cell and the pulse energy delivered by the CPA system. This results in compressed laser pulses with different pulse energies but the same pulse length to achieve the correct phase matching intensity. Step two: the capillary gets adjusted with respect to the laser beam. This adjustment of the capillary is done on a micrometer level in five axes as shown in Fig. 1. Step three: the backing pressure is optimized with respect to the photon flux.

This optimization process leads to the highest photon flux at 125 mbar of argon backing pressure, 450 mbar of argon in the multipass cell and 0.88 mJ, 35 fs driving laser pulses. A gas flow analysis of the experimental setup conducted with Ansys Fluent revealed a lower particle density in the core of the capillary equivalent to a pressure of 85 mbar at room temperature. The corresponding pressure scan is shown in Fig. 2(a)). These findings are supported by a phase matching simulation with a one-dimensional model [44,45], indicated by an orange line in Fig. 2(a)).

 

Fig. 2. Pressure scan and flux characterization of the HHG emissions from a 2.5 cm long waveguide with an inner diameter of 200 µm. a) Pressure scan for argon at 60 eV with the corresponding simulation of the phase matching process. The pressure in the interaction zone, between the cuts of the fiber is shown. b) Measured HHG spectrum, ranging from 50 eV to 70 eV. The spectrally integrated power of the harmonic lines in µW can be found over each respective line.

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The generated photon flux of $> {10^{11}}$ ph/s/eV between 50 eV and 70 eV at the maximum of the harmonic lines (Fig. 2(b))) represents an HHG source with a state-of-the-art photon flux compared to other HHG sources in this spectral range [8,34–37]. To evaluate the generated photon flux, the measured spectra are corrected by the transmission through the residual gas in the chamber, the theoretical reflectivity of the grazing incidence plates, the measured transmission of the aluminum filters, the efficiency of the diffraction grating and the sensitivity of the CCD camera of the spectrometer.

4. Spectral tunability

The typical lines in an HHG spectrum are the odd multiples of the wavelength of the driving laser pulse. If this driving pulse is chirped, the instantaneous wavelength changes over its relative time. For efficient HHG, the high harmonics are generated at the intensity peak of the driving pulse [1]. Thus, to determine the spectral position of the generated harmonics, the instantaneous wavelength at the intensity peak of the driving pulse must be analyzed. A shift in this wavelength is directly translated to a shift of the generated harmonic lines. In addition to the chirp, nonlinear propagation effects can influence the spectrum of the driving laser pulse and therefore, the instantaneous wavelength driving the HHG.

Spectral tuning of the harmonic lines in the experiment is achieved in the following way: while the parameters of the CPA system remain constant at 1032 nm, 50 kHz, 160 fs and 1.3 mJ, the pulse energy entering the multipass cell is continuously changed with a half-wave plate and a thin-film polarizer. Due to a constant gas pressure in the multipass cell, the pulses pick up different spectral phases, depending on the pulse energy. The following recompression with negatively chirped mirrors adds a constant amount of negative group delay dispersion (GDD) to these pulses. Thus, for most pulse energies there is a mismatch of spectral phase acquired in the multipass cell and negative GDD added in recompression, leading to chirped pulses. These chirped pulses are focused into the 200 µm capillary and propagate through a certain amount of argon gas at high intensities. Here, spatiotemporal propagation effects must be considered, such as the Kerr effect, ionization and dispersion [46]. This further reduces the instantaneous wavelength of the driving pulse, leading to changing generation conditions for the high harmonics due to the ionization-induced blueshift, depending on the pulse energy launched into the multipass cell.

In this work, a specific combination of Yb-amplifier, multipass cell and waveguide geometry is chosen, but the general concept for tunable HHG can be applied to similar setups with the same three integral parts. First, a laser source delivering ultrashort pulses and an element to seamlessly adjust the pulse energy is needed. Second, these pulses are spectrally broadened and compressed with a fixed GDD, introducing a spectral phase mismatch. Third, these chirped pulses drive HHG while experiencing an ionization-induced blueshift in the generating medium.

4.1 Simulation

To gain a deeper understanding of the interaction of the involved effects, a two-stage simulation is carried out, including the propagation through the multipass cell and the gas-filled capillary. The pulse propagation through the multipass cell is based on [47], solving the nonlinear envelope equation [48] in radial symmetry [49], including self-phase modulation, self-steepening, diffraction, dispersion to all orders and the mirror reflection bandwidth [50]. Starting with the spectral parameters of the CPA system and the pulse energies used in the experiment, this first stage of the simulation delivers spectrally broadened and chirped pulses, compressed by the addition of the constant negative GDD from the compression mirrors. The resulting pulses are then propagated through the gas-filled capillary based on a field-resolved multimode propagation equation according to [46]. This includes self-phase modulation, self-steepening, Kerr-driven self-focusing and plasma defocusing. Both parts of the simulation are explained in greater detail in [50,51].

The chirp of the pulse in combination with the aforementioned nonlinear effects acts on the temporal shape of the electrical field (Fig. 3(a))). The peak of the envelope of the electrical field of the pulse leaving the capillary gets shifted slightly to earlier relative times, compared to the pulse entering the capillary. The frame velocity in this simulation is the group velocity of the driving pulse. The arrows in Fig. 3(a)) indicate the cycle with the highest intensity within the peak of the envelope of the electrical field. Furthermore, the frequency at the pulse peak is shifted to higher frequencies (${f_{\textrm{peak}/\textrm{in}}} < {f_{\textrm{peak}/\textrm{out}}}$). Tunability of the generated HHG signal is then achieved by changing the pulse energy launched into the multipass cell and therefore also the intensity in the capillary. Increasing the pulse energy has two effects. First, the second order spectral phase of the pulse decreases due to different acquired spectral phases in the multipass cell and the fixed negative GDD compression in the multipass cell. Second, the higher the intensity in the capillary, the stronger is the ionization-induced blueshift acting on the pulse. Thus, both effects increase the frequency of the pulse peak with increasing pulse energy in roughly equal proportions. From this peak frequency, an effective driving wavelength can be calculated, as it is shown in Fig. 3(b)). This change in driving wavelength is directly translated into a wavelength change of the generated higher order harmonics, resulting in the tuning of the generated XUV spectrum.

 

Fig. 3. Influence of nonlinear effects on driving electrical field. a) Visualization of the peak frequency of the driving laser pulse and its shift induced by nonlinear effects during the propagation through the capillary. The simulated electrical field before entering the capillary (in) and after leaving the capillary (out) for a pulse energy of 0.88 mJ is shown. ${f_{peak}}$ is the frequency at the peak intensity of the driving laser pulse. The peak frequency of the outgoing pulse is higher compared to the incoming pulse. The blue line is offset by $7\cdot {10^{10}}\; V/m $ for better visibility. b) Simulated wavelength at the peak of the laser pulse for different driving pulse energies. The wavelength is shown in the expected interaction region for HHG. The dotted line is a guide to the eye.

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4.2 Experiment

In the experimental realization, the pulse energy in front of the multipass cell is adjusted by simply turning the half-wave plate in front of the thin-film polarizer, representing a simple method, delivering reliably and reproducibly the desired tuning setting. In contrast to other spectral tuning methods, no physical or spectral changes in the CPA system, multipass cell or HHG setup itself are required.

To achieve full tunability in the spectral region between 50 eV and 70 eV (41^st to 55^th harmonic order), the driving pulse energy has to be changed between 0.88 mJ and 1.28 mJ, while the driving pulse duration remains relatively constant between 35 fs and 41 fs. Figure 4(a)) shows the spectral positions of the maxima of every harmonic line with different driving pulse energies. At the highest driving pulse energy, the photon energy of every line at least reaches the photon energy of the next harmonic order at the lowest driving pulse energy, demonstrating full tunability. Considering the simulation results of the instantaneous driving wavelength in Fig. 3(b)), the expected photon energies of the higher harmonics can be calculated by simply multiplying the photon energy of the driving laser pulse with the order of the harmonic line. The expected XUV photon energies are shown in Fig. 4(a)) and match the experimental results.

 

Fig. 4. Characterization of the fully tunable high harmonic lines for a variety of driving pulse energies. a) Spectral positions of the maxima of each harmonic line while tuning, showing the full tunability between 50 eV and 70 eV. The dotted lines show the expected photon energies of each harmonic line at every driving pulse energy, based on the simulation results shown in Fig. 3(b)). b) Normalized peak flux, bandwidth and full-angle divergence of the 47^th harmonic line. The respective maximum values are shown in the inset.

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Over the whole tuning range, the peak flux of a line of one harmonic order stayed relatively constant with a maximum deviation of 25% between the strongest and weakest measured signal. To explain this, microscopic and macroscopic effects must be considered. With increasing driving pulse energy, the driving wavelength is decreased (as shown in Fig. 3(b))) leading to a higher HHG conversion efficiency [52]. Further, the increased pulse energy leads to a slightly increased intensity in the interaction region, resulting in a higher single-atom response in the HHG process [45,53]. However, these two effects which are acting positively on the conversion efficiency are counteracted by decreased phase matching conditions. Because the backing pressure is optimized for the lowest driving pulse energy and is kept constant during the tuning, only one driving pulse energy and therefore only one intensity is fully phase matched, leading to a comparably constant peak flux over the whole tuning range. While the bandwidth of the generated harmonics stays comparably constant over the full tuning range the divergence is declining nearly by a factor of two. This can partially be explained by an increase in source size [1]. The higher the driving pulse energy and therefore intensity in the interaction region the larger is the XUV-emitting area. A full characterization of the parameters peak flux, bandwidth and divergence for the 47th harmonic order is shown in Fig. 4(b)).

4.3 Pulse-to-pulse tunability

The tuning mechanism for the generated XUV radiation in this work relies on the continuous change of the driving pulse energy in front of the multipass cell and the subsequent waveguide-based HHG setup. The tuning speed is only limited by the turning speed of the half-wave plate, requiring less than one second for tuning over the full line spacing. If the combination of half-wave plate and thin-film polarizer is replaced by an acousto-optic modulator (AOM), the speed of change in pulse energy can be drastically increased, enabled by the high modulation speeds of an AOM. If the laser parameters from this experiment are considered, the Kerr nonlinearity of an AOM crystal is a limiting factor. Therefore, placing the AOM in a beam path with lower intensities and thus stretched pulses is essential. In the used CPA system this would be possible in front of the main compressor, providing pulse lengths of several nanoseconds [40]. This would enable the modulation of pulse energies well beyond millijoules with a quartz crystal based AOM. Considering typical focal spot diameters and AOM geometries, modulation speeds in the low MHz range are possible. This would enable continuous, on-demand pulse-to-pulse switching of the XUV photon energy over the whole line spacing of the generated harmonic signal which provides additional experimental possibilities.

5. Conclusion

In conclusion, a continuously tunable XUV source with state-of-the-art photon flux and full spectral coverage between 50 eV and 70 eV is presented. The underlying tuning mechanism of chirped and blue shifted driving laser pulses is experimentally realized by a change in driving pulse energy in front of the pulse compression and the waveguide-based HHG setup. These findings are supported by numerical simulations, revealing a blue shift of the instantaneous wavelength in the intensity peak of the driving pulse. Due to these features and the simple experimental realization, this kind of novel table-top XUV source is suitable for a broad range of applications. With little experimental effort, pulse-to-pulse tunability can be implemented.