# Raman Red-Shift Compressor: A Simple Approach for Scaling the High Harmonic Generation Cut-Off

Katherine Légaré, Reza Safaei, Guillaume Barrette, Loïc Arias, Philippe Lassonde, Heide Ibrahim, Boris Vodungbo, Emmanuelle Jal, Jan Lüning,

Nicolas Jaouen, et al.

► To cite this version:

Katherine Légaré, Reza Safaei, Guillaume Barrette, Loïc Arias, Philippe Lassonde, et al. Raman Red-Shift Compressor: A Simple Approach for Scaling the High Harmonic Generation Cut-Off. Advanced Photonics Research, 2021, 2 (11), pp.2100113. 10.1002/adpr.202100113. hal-03961246

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# Raman Red-Shift Compressor: A Simple Approach for Scaling the High Harmonic Generation Cut-Off

Katherine Légaré, Reza Safaei, Guillaume Barrette, Loïc Arias, Philippe Lassonde, Heide Ibrahim, Boris Vodungbo, Emmanuelle Jal, Jan Lüning, Nicolas Jaouen, Zhensheng Tao, Andrius Baltuška, François Légaré,* and Guangyu Fan*

The use of ultrashort laser pulses with long wavelengths as drivers is a relevant strategy for scaling high harmonic generation (HHG) to higher photon energies. Here, stimulated Raman scattering enhanced by the formation of multidimensional solitary states in a molecular gas-filled hollow-core fiber as the mechanism to produce a versatile HHG driver is reported on. This recently discovered method allows to red shift and to compress conventional subpicosecond laser pulses with a simple experimental apparatus, ultimately increasing the generated photon energy, while assuring a high photon flux. The adaptability, simplicity, and stability of this method make it attractive for tailoring HHG sources to individual applications at specific photon energies. Measurements of resonant magnetic scattering in a cobalt/platinum multilayer sample are presented as a demonstration of the relevance of this approach for photon-hungry applications in the extreme ultraviolet.

## 1. Introduction

Over the past decade, the development of large-scale X-ray facilities delivering ultrashort pulses able to probe ultrafast phenomena in matter with high spatial and temporal resolutions has been continuously motivated by their rich potential for fundamental and applied science in multiple fields, including physics, chemistry, and biology.[1] In parallel, intense research activities

have been pursued to develop compact X-ray sources based on nonlinear and relativistic laser-matter interactions such as hard X-ray radiation from laser wakefield electron acceleration,[2,3] incoherent hard X-ray plasma sources,[4] and high harmonic generation (HHG) from laser-ablated plumes,[5] plasma mirrors,[6,7] and gases.[8] The HHG approach in gases is ideal to generate X-ray radiation spanning from the extreme ultraviolet (XUV) to the soft X-rays with pulse durations down to 43 attoseconds.[9]

Along with the development of HHG, attosecond science has emerged as a vibrant research field to observe and control electronic dynamics in atoms,[10] molecules,[11] and solids.[12] In addition to its unique temporal resolution, HHG

enables the generation of supercontinua, covering specific absorption edges of different materials, which can be used to track dynamics with element specificity.[13-15] Furthermore, HHG radiation with its high spatial coherence has become a practical tool for high spatial resolution imaging of, for example, nanostructures in multielement systems.[16,17]

To facilitate such novel space- and element-dependent dynamic studies, the development of advanced HHG methods

K. Légaré, R. Safaei, G. Barrette, L. Arias, P. Lassonde, H. Ibrahim, F. Légaré, G. Fan
Institut National de la Recherche Scientifique
Centre Énergie Matériaux et Télécommunications
1650 Boulevard Lionel-Boulet, Varennes, Québec J3X 1S2, Canada
E-mail: legare@emt.inrs.ca; guangyu.fan@emt.inrs.ca

B. Vodungbo, E. Jal
Laboratoire de Chimie Physique - Matière et Rayonnement
CNRS
LCPMR
Sorbonne Université
75005 Paris, France

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adpr.202100113.

© 2021 The Authors. Advanced Photonics Research published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/adpr.202100113

J. Lüning
Helmholtz-Zentrum Berlin für Materialien und Energie
Hahn-Meitner-Platz 1, 14109 Berlin, Germany

N. Jaouen
Synchrotron SOLEIL
L'Orme des Merisiers
91192 Gif-sur-Yvette, France

Z. Tao
State Key Laboratory of Surface Physics
Department of Physics
Fudan University
Shanghai 200433, China

A. Baltuška
Photonics Institute
Vienna University of Technology
Gusshausstrasse 27-387, A-1040 Vienna, Austria
with scalable flux at higher photon energy is still a subject of
intense research. In this perspective, mainly four knobs, or
degrees of freedom, are accessible to influence the maximum
photon energy generated from the HHG process. They are evi-
denced by the cut-off equation, $h\nu_{\text{cut-off}} = I_p + 3.17 U_p$, where
$h\nu_{\text{cut-off}}$ is the highest generated photon energy, $I_p$ is the ioni-
zation potential of the generation medium, and $U_p$ is the ponder-
omotive energy, which scales with the laser intensity and the
square of the driving wavelength.[18] The first knob is the choice
of the generation medium. Gases with a larger $I_p$ can provide a
higher cut-off, but suffer from a much lower single-atom conver-
sion efficiency.[19] The second knob is the intensity of the driver.
The cut-off may increase using more intense driving pulses;
however, to drive HHG efficiently, the ionized fraction of the
generation medium has to remain below a critical level.
Therefore, beyond a certain medium-dependent saturation inten-
sity, the cut-off cannot extend any further. The third knob is the
duration of the driving pulses. With shorter pulses, the satura-
tion intensity is reached at a higher field amplitude, consequently
scaling the HHG cut-off favorably.[20,21] This effect is a strong
motivation for the development of high-power few-cycle drivers,
for instance, by the incorporation of advanced nonlinear com-
pression techniques with state-of-the-art ytterbium lasers deliver-
ing relatively long pulses (subpicosecond).[22,23] Finally, since the
cut-off energy scales with the square of the driving wavelength,
the fourth knob is the central wavelength of the driver. However,
in the single-atom response, the generated photon flux decreases
rapidly with increasing wavelength ($\lambda^{-5-6}$).[24] Therefore, to
avoid loss in conversion efficiency, the optimal driving wave-
length should remain as short as possible, while ensuring that
the harmonic spectrum covers the target photon energy. So
far, the most useful approach for extending the central wave-
length of ultrashort laser pulses has been optical parametric
amplification (OPA), which often requires complex stages and
has a limited conversion efficiency. Furthermore, this nonlinear
process is unsuitable for directly tuning the pump wavelength by
small amounts due to the absorption of the long wavelength idler
by the amplification crystal. For example, an OPA built with beta
barium (BBO) crystals and pumped by a titanium-sapphire laser
(Ti-Sa, 800 nm) can produce tunable pulses from 1100 to
2500 nm (signal + idler range), leaving a "gap" of 300 nm
between the pump and the signal range.[25]

Recently, nonlinear pulse compression via the stimulated Raman scattering (SRS) process in molecular gases has drawn attention as an alternative solution to generate pulses at slightly longer wavelengths than the driver. Various approaches based on SRS have been reported in gas cells,[26,27] hollow-core photonic crystal fibers,[28,29] and large-diameter hollow-core fibers (HCF).[22,23,30-32] Particularly, in the study by Safaei et al.[32], we describe a new regime of nonlinear propagation in HCFs that derives from the spatiotemporal nonlinear Raman enhancement observed with subpicosecond driver pulses. This mechanism allows for scaling the peak power by producing broadband, self-frequency shifted solitons driven by subpicosecond pulses. As these high-energy multidimensional solitary states (MDSS) exhibit a clean negative quadratic spectral phase, they are easily compressed to few-cycle durations by linear propagation in a simple piece of glass with positive dispersion. Therefore, by

reshaping the spatiotemporal properties of the driver beam via
the generation of highly stable multimode states, we propose
a new route toward the generation of bright HHG.

In this work, MDSS pulses are exploited to extend the cut-off of HHG spectra, while maintaining a strong XUV photon flux. This is achieved without the use of OPAs and by keeping argon, an atom with a good HHG conversion efficiency due to its large recombination cross section, as the generation medium. To demonstrate experimentally the pertinence of our approach for space- and element-dependent applications, the generated XUV beam is used to carry out X-ray resonant magnetic scattering (XRMS) measurements on a Co/Pt ferromagnet sample, a relevant prototype system for future spintronic devices.[33] The XRMS technique requires a high flux of photons near the M edge of cobalt at 60 eV, which is not readily accessible when driving high harmonics in argon with pulses delivered from a standard Ti–Sa laser system as the photon energy cut-off is typically below 50 eV.[34] Here, we demonstrate that by driving the HHG process with submillijoule red-shifted MDSS pulses, scattering images of the magnetic nanostructures in a Co/Pt ferromagnet sample can be resolved in a short exposure time (≈500 laser shots), due to the high conversion efficiency of HHG in argon. A comparison with harmonics generated in neon, a gas with a higher $I_p$, from more energetic Ti–Sa driver pulses shows that the MDSS method is at least as effective to generate a high photon flux. We argue that the MDSS method offers global and technical advantages that make it attractive for such photon-demanding element-specific applications.

**2. Multidimensional Solitary States**

The experiments were conducted at the Advanced Laser Light Source (ALLS) facility. To obtain a high flux of 60 eV photons from the Ti–Sa laser system, the MDSS process enabled to shift the central wavelength to around 960 nm. This wavelength was chosen to ensure that the cut-off would be ≈15 eV above the desired photon energy, thereby increasing the stability of the light source around 60 eV and loosening the optimization constraints. Indeed, as the HHG stability near the cut-off energy is highly sensitive to the characteristics of the driver pulses, it is preferable to work with photon energies that are in the plateau region of the HHG spectra. A layout of the experimental setup is shown in Figure 1a. The output pulses of the Ti–Sa laser system (40 fs, 8 mJ pulses with a repetition rate of 100 Hz) are first stretched to 400 fs by displacing the compressor gratings to introduce a positive chirp. Then, the beam is focused with a 3 m focal length and coupled to a 3 m-long stretched HCF with a core diameter of 500 µm (few-cycle Inc.). The reduced intensity from the long pulse duration allows to couple higher pulse energies into the HCF. Still, the fiber is filled with a differential pressure of N₂ to avoid any ionization or self-focusing at the fiber input, which is pumped in a primary vacuum. As described in the study by Safaei et al.,[32] near the fiber input, the beam is coupled into high-order modes (HOMs) by self-focusing, resulting in intermodal four-wave mixing (IFWM) and the generation of new frequencies. Once the bandwidth of the newly generated frequencies covers the Raman gain, intermodal SRS starts to occur. The nonlinearity from these intermodal processes
<figure><img src="image_2.png" /><figcaption>**Figure 1.** a) Experimental setup. The pulses at the HCF output are collimated with a concave silver mirror with a focal length of 3.5 m, compressed by linear propagation in CaF₂ plates and characterized with a spectrometer and SHG-FROG. Alternatively, the beam is focused in an 8 mm-long cell filled with argon for HHG. After generation, the HHG spectra can either be characterized by a XUV spectrometer or refocused to the magnetic sample, where XRMS measurements are carried out. In the latter case, a concave multilayer mirror is used to select a narrow bandwidth around the desired photon energy (60 ± 2.5 eV) and the fundamental beam is blocked by two 200 nm-thick aluminum filters. The XUV beam is then transmitted through a Co/Pt multilayer sample with out-of-plane magnetic anisotropy. The directly transmitted beam is blocked by a beamstop, whereas the scattered photons are captured by a CCD camera. b) Beam profile of the MDSS and SPM beams after collimation. The MDSS beam diameter is 9.0 mm at $1/e^2$, whereas the SPM beam diameter is 11.3 mm, a size difference that is attributed to the presence of HOMs in the MDSS beam.</figcaption></figure>

balances diffraction and dispersion, resulting in highly spatio-temporally localized solitary (MDSS) pulses. At the HCF output, the MDSS pulses comprised in the red-shifted part of the spectra exhibit a stable self-trapped beam. As shown in Figure 1b, this beam is smaller than a beam generated from the self-phase modulation (SPM) process in the same HCF filled with an atomic gas. We assume that this is due to the presence of HOMs in the MDSS pulses. In these experimental conditions, the typical fiber transmission drops from 50% to 35% when the gas is present due to the energy transfer to the molecular system in the frequency down-conversion process of SRS and the attenuation of HOMs during propagation. At the fiber output, submillijoule MDSS pulses are formed in the long-wavelength part of the spectra. It should be noted that the overall efficiency of the MDSS process is tied to a combination of several parameters such as the characteristics of the input pulses and the specifications of the HCF. While these parameters were chosen to maximize the output energy with minimal consideration for the MDSS conversion efficiency in this work, superior outcomes have already been demonstrated.[32]

As shown in Figure 2a, the $N_2$ pressure in the HCF is adjusted to 1450 mbar such that the output spectra extend up to 1050 nm. The red-shifted part of the spectra is selected by a long-pass filter (>830 nm), setting the central wavelength at 958 nm (center of

<figure><img src="image_3.png" /><figcaption>**Figure 2.** a) Normalized Ti–Sa output spectrum (gray area), spectrum broadened by the MDSS process in nitrogen (blue), and spectrum broadened by the SPM process in neon (red). The blue shaded area denotes the part of the spectrum selected for compression by the long-pass filter. b) Measured and c) reconstructed spectrograms for MDSS pulses. d) In black, spectral intensity profile (solid lines, left axis) and phase (dashed line, right axis) for the reconstructed MDSS pulses including the added spectral phase caused by their propagation through CaF₂ plates. In blue, measured spectral intensity profile. The disparity between the measured and reconstructed spectra for short wavelengths is due to the presence of uncompressed HOMs in this spectral region and to the limited dynamic range of the SHG-FROG. e) Retrieved temporal intensity profile (solid lines, left axis) and phase (dashed lines, right axis) of the shortest MDSS pulses (blue) and SPM pulses (red). The retrieved duration of the pulses at full width half maximum is 11.7 and 14.8 fs, respectively.</figcaption></figure>

mass). In the same figure, the spectra of SPM pulses with a bandwidth capable of supporting few-cycle pulse durations are shown. Note the contrast between the symmetric SPM spectra and the strong asymmetry of the red-shifted MDSS spectra. Here, the SPM pulses serve to make a comparison between HHG driven by red-shifted MDSS pulses and by ultrashort pulses centered at 800 nm. The SPM pulses are obtained by replacing nitrogen with neon and propagating 2 mJ, 40 fs pulses into the HCF. At the HCF output, the beam is either directed toward spectral and temporal characterization devices (respectively Avantes AvaSpec-ULS2048XL and home-built second-harmonic generation frequency resolved optical gating—SHG-FROG) or to the vacuum chamber where HHG is conducted in a pressure-controlled argon-filled gas cell. Following its generation, the XUV radiation is characterized by a XUV spectrometer based on a 1200 gr mm⁻¹ diffraction grating and a microchannel plate detector. Alternatively, the grating can be moved out of the beam path, in which case the remaining fundamental photons are blocked by an aluminum filter. The XUV beam is transmitted
and 60 eV photons comprised in a 5 eV bandwidth are selected by a multilayer mirror (Ultrafast Innovations GmbH). Then, the XUV beam is sent directly to a water-cooled charge-coupled device (CCD) camera (PIXIS-XO, Princeton Instruments) for characterization of the HHG flux, which is estimated by converting the total counts measured by the camera in a given exposure time to a number of photons by taking into account the quantum efficiency and conversion gain of the CCD camera, the reflectivity of the multilayer mirror, and the transmissivity of the aluminum filters. To carry out XRMS measurements, the beam is focused by the same multilayer mirror onto a magnetic sample placed in front of the camera.

One attractive feature of MDSS is that, in the normal dispersion regime, the pulses can be compressed directly with a simple piece of glass with positive dispersion due to the natural formation of negative chirp through intermodal interactions. Here, to compress the MDSS pulses, CaF₂ plates were chosen due to the low third-order dispersion coefficient of this material. Propagation through air and through the input window of the HHG chamber also contributes to compensating the negative quadratic phase of the pulses. To characterize the pulse duration, SHG-FROG measurements of the uncompressed field were taken and propagation through CaF₂ plates was numerically simulated by the addition of the spectral phase induced by the dispersive material. The measured and reconstructed SHG-FROG traces corresponding to the shortest attainable pulse duration of ≈12 fs are shown in Figure 2b,c, along with the retrieved spectral and temporal profiles and phases in Figure 2d,e. The retrieved temporal shape of the SPM pulses compressed to a similar duration by a chirped mirror (HD1401, UltraFast Innovations GmbH) is also shown in Figure 2e. As SPM pulses are known for their clean spatial profile and monotonic spectral phase, they serve here as a reference of high temporal quality.[35] Regardless of the long, low-intensity pedestal displayed by the MDSS pulses, as much as 65% of the total energy is contained in the main pulses, which makes them suitable as efficient drivers for the HHG process, as shown in the following sections.

### 3. High Harmonic Generation

Because HHG is a highly nonlinear process, the cut-off and the XUV flux are very sensitive to the temporal shape of the driving pulses and consequently are an excellent gauge of their spatiotemporal quality. Here, the measurement of HHG spectra is used to compare the performance of the compression mechanism of MDSS pulses to that of standard SPM pulses. Experimentally, both pulses are focused by a CaF₂ lens with a focal length of 75 cm in an 8 mm-long gas cell filled with argon, ensuring that the length of the generation medium exceeds the absorption length for 60 eV photons in argon by at least three times in the operation pressure range ($L_{abs}$ = 1.4 mm for a pressure of 260 mbar).[36] The argon pressure as well as the position of the focus with respect to the gas cell are adjusted to optimize HHG phase matching conditions (Figure 3a,b). For the MDSS pulses, the cut-off is maximized by inserting a few millimeters of CaF₂ in the beam path (Figure 3c), which is consistent as a large part of the pulse energy in the 830–1050 nm bandwidth

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Harmonic spectra generated by compressed 800 µJ a) SPM pulses and b) MDSS pulses for different argon pressures in the generation chamber to show optimal phase-matching conditions. c) Harmonic spectra generated by MDSS pulses obtained for the optimal pressure and different CaF₂ thicknesses in the beam path. The highest cut-off, which indicates optimal compression, is obtained with glass thicknesses between 5 and 7 mm. Due to limitations in the geometry of the experimental vacuum chambers, some reabsorption occurs for low photon energies (<40 eV), which explains the missing harmonics. The dashed horizontal lines in (a–c) show the argon pressure and glass thickness conditions for the spectra presented in (d). d) Harmonic spectra driven by ≈12 fs, 800 µJ MDSS pulses (blue) and by ≈15 fs, 800 µJ SPM pulses compressed by chirped mirrors (red) for the optimized argon pressure and glass thickness. The vertical dashed lines show the experimental position of the cut-off for each case. The dashed gray line shows the expected cut-off of the MDSS-driven HHG based on the cut-off equation and the shadowed area represents an error bar the width of one harmonic on this value. Arrows indicate positions of absorption edges of relevant elements.</figcaption></figure>

is compressed by propagating through materials with positive linear dispersion.

To demonstrate the spatiotemporal quality of the compressed pulses, the cut-off energies of HHG driven by MDSS pulses and SPM pulses are compared. As the pulses have similar durations, the cut-off should be influenced by the different central wavelengths only. In agreement with the cut-off equation, it is then expected that the highest photon energy should scale quadratically with the wavelength, as stated by the three-step model.[18] In both cases, a driver pulse energy of 800 µJ is chosen, which
implies a higher intensity in the generation medium for the SPM
beam (see Figure 1b). Indeed, the diameter of the focal spot of
the SPM pulses (at 1/e²) is 79 µm, whereas it is 135 µm for the
MDSS pulses. For SPM, the chosen pulse energy ensures
saturation of the HHG process and maximization of the cut-off
photon energy. For MDSS pulses, saturation is approached only
for well-compressed pulses of high peak intensities, making the
effects of the compression apparent in the HHG spectra.
As scanning the intensity of the MDSS pulses in the focal spot
is not possible in this setup, without affecting the characteristics
of the pulses, saturation could not be ensured. However, a lower
cut-off would be expected in the case of unsaturated HHG.
The results are shown in Figure 3d. The cut-off energy, defined
as the first harmonic for which the intensity drops below 10% of
the highest harmonic intensity, falls at 57.7 eV for the SPM
pulses. According to the cut-off equation in argon (I<sub>p</sub> = 15.76 eV),
the cut-off energy expected with the red-shifted MDSS pulses is
ħν<sub>MDSS</sub> = I<sub>p</sub> + (ħν<sub>SPM</sub> - I<sub>p</sub>)λ<sup>2</sup><sub>MDSS</sub>/λ<sup>2</sup><sub>SPM</sub> = 77.3 eV. Considering
a spacing of 2.6 eV between the discrete harmonics, the experi-
mental value of 75.2 eV falls less than one harmonic away from
the expected cut-off. This result attests to the high spatiotemporal
quality of the MDSS pulses and indicates that the weak pedestal is
not detrimental to efficient generation of high harmonics. For the
47th harmonic, nearest to the M<sub>2,3</sub>-edge of cobalt, the energy
conversion efficiency is 3 × 10<sup>-7</sup>, which yields a photon flux of
3 × 10<sup>7</sup> photons/pulse. It should be noted that other generation
configurations have been shown to reach comparable or greater
conversion efficiencies in this spectral range.<sup>[37-39]</sup> In particular,
in the study by Kim et al.,<sup>[38]</sup> a conversion efficiency of 5 × 10<sup>-5</sup>
has been reported from a two-color scheme using helium.
Furthermore, harmonics generated in argon near 40 eV from
800 nm drivers have been reported to reach conversion efficien-
cies between 5 × 10<sup>-7</sup> and 10<sup>-5</sup>.<sup>[36,40,41]</sup> However, a substantial
reduction in efficiency is expected for the generation of 60 eV pho-
tons from a 960 nm driver due to the unfavorable single-atom
response for long driver wavelengths which cannot be entirely
compensated by macroscopic phase matching.<sup>[42]</sup> In general,
although such photon flux is obviously orders of magnitude lower
than what can be produced at large facilities such as free-electron
lasers,<sup>[43]</sup> it has the benefits of being generated using a table-top
laser in a small-scale laboratory and of being intrinsically free of
temporal jitter, an important asset for time-resolved experiments.

To demonstrate the potential of MDSS-driven HHG for XUV
applications, XRMS measurements are carried out on a Co/Pt
multilayer sample. XRMS occurs in materials that present a mag-
netic structure of domains with magnetization along the direc-
tion of light propagation. Light scatters on those magnetic
structures when the photon energy is tuned to a magnetically
dichroic absorption edge.[44] In the far field of the XUV beam,
after its transmission through the sample, a scattering pattern
of the magnetic domain network is formed. This method is
now widely used to track ultrafast magnetization dynamics,[45,46]
but the low scattering efficiency (≈10⁻⁶) means that a high pho-
ton flux is required to obtain a signal. Here, as the magnetic
domain network of the sample is prepared such that the domains
align in parallel stripes (Figure 4b), the scattering pattern is
composed of two spots, whose separation is determined by
the average domain size and whose spread depends on the

domains' deviations in size and orientation (Figure 4a). The peaks become visible after just a few seconds (≈5 s) of exposure time as a result of the high photon flux. Previously, the same Ti–Sa laser system (prior to the HCF) has been used to generate a comparable flux at 60 eV (2 × 10⁷ photons/pulse) by driving the HHG in neon using a loose focusing geometry and 40 fs pulses.[47] In those experimental conditions, the required driver pulse energy was one order of magnitude larger (13 mJ) than that with the MDSS approach presented here. In addition, the longer driver pulse duration resulted in inferior temporal resolution for that XUV source, making it less desirable for the study of ultrafast dynamics. These results suggest that, for many applications, using MDSS pulses as drivers of the HHG process represents a potential benefit as it allows reaching higher photon energies in media with good XUV conversion efficiencies, while simultaneously increasing the temporal resolution of the XUV source. Moreover, given that the manipulation of high-energy pulses is likely to introduce technical challenges, the implementation of the MDSS process is overall quite convenient. Indeed, the intermodal SRS process is seeded by long pulses with relatively low peak intensity and results in sub-millijoule MDSS pulses. While reflective optics are required when generating harmonics in neon from 13 mJ pulses, the MDSS pulses can be focused in the HHG chamber with a regular lens. Furthermore, separating the harmonic beam from the driver is much easier in the case of a low-energy MDSS driver as the thin aluminum filters used to reject the infrared are rather delicate. Alternatively, generating similarly red-shifted, millijoule-level ultrashort pulses with an

<figure><img src="image_5.png" /><figcaption>**Figure 4.** a) Raw XRMS image after 5 s of exposure. The two spots highlighted by black ellipses correspond to the scattering pattern expected from the sample's magnetic domain network.[44] The bright, red regions are residual background photons that were not blocked by the sample or the beamstop. b) Magnetic force microscopy image of a 10 × 10 µm region of the sample showing its magnetic domain network. The sample composition is Ta 3 nm/Pt 2 nm/[Co 0.6 nm/Pt 0.8 nm] × 20/Al 3 nm. c) Stability of the XRMS signal over 50 min. One XRMS image with an exposure time of 20 s is recorded every minute. The blue points represent intensity in the scattered peaks for each image. The black line serves to guide the eye. The standard deviation is 7% of the average signal and between the first and the last 5 points, the signal decreased by 5%, which is due to a slow drift in our nonstabilized beam pointing.</figcaption></figure>
OPA system would not be straightforward. It would require
multiple stages of nonlinear interactions, for example, by first
generating pulses near 1920 nm before frequency doubling
them, and then an additional compression stage would be
necessary. In contrast, the MDSS approach can create ultrashort
red-shifted pulses with a tunable bandwidth in a single stage and
with a simple apparatus.

Figure 4c shows the measured intensity in the scattering pat-
tern over 50 min. A standard deviation of 7% is observed along
with a small long-term drift (5% loss). As no significant change
was observed in the spectra or intensity of the MDSS pulses over
the same period of time, it is likely that much of the instability is
due to the long, uncovered propagation path in the air (≈7 m)
before the HHG chamber. Therefore, the implementation of a
beam-pointing feedback loop would be sufficient to avoid such
instability. In an environment with controlled temperature
and humidity, this source is expected to reliably operate for many
hours or even days with minimal adjustments, allowing for long
acquisitions of data with low signal-to-noise ratios and support-
ing a move toward table-top time-resolved experiments with high
long-term stability requirements in the XUV.

4. Conclusion

In conclusion, we show that the nonlinear Raman process
enhanced by the formation of MDSS pulses can be a powerful
driver for HHG. The spatiotemporal quality of the MDSS pulse
is verified by comparing the cut-off energy obtained from
harmonics generated with MDSS pulses and SPM pulses.
Furthermore, the convenience of this method for photon-hungry
applications in the XUV is demonstrated through resonant mag-
netic scattering measurements on a Co/Pt multilayer, a valuable
technique for studies of spatially resolved ultrafast magnetic
dynamics that requires a high photon flux due to its low
efficiency. Ultimately, driving HHG with compressed MDSS
pulses is attractive for many applications that benefit from a
slight increase in the cut-off energy of the XUV spectrum, while
keeping a strong photon flux and a good long-term stability and
while avoiding the technical challenges related to using high-
energy drivers. In contrast to OPAs, MDSS pulses are generated
with a simple scheme and are not limited to the generation of
long wavelengths; they can be used to induce a small red shift
to the driver in a single stage, while simultaneously compressing
the pulses. Consequently, our approach is especially attractive for
state-of-the-art high-power Ytterbium laser systems with long
pulse duration. In addition, because the central wavelength of
the MDSS pulses can be modified with ease through the control
of the gas pressure in the fiber, this method is versatile and can
readily be adapted to different applications. More research is
required to achieve a thorough understanding of the capabilities
and limitations of the MDSS process. For example, the duration,
intensity, and wavelength of the input pulses along with the fiber
parameters presumably play a role in the extension of the spec-
trum and in the conversion efficiency of the process. As such,
this method has the potential to improve both efficiency and
in reaching longer wavelengths. Eventually, it could be used,
for example, as a spatiotemporal engineered source for the
generation of photons in the spectral region of the water window

(280–530 eV). Despite significant advances,[48] the generation of
ultrashort pulses in the water window and beyond remains chal-
lenging. Thus, the extension of MDSS Raman shifting into the
midinfrared could significantly extend their utility, and we are
confident that such femtosecond X-ray sources derived from
ultrafast lasers will be major players in the landscape of X-ray
sources available to the scientific community.

Acknowledgements

K.L. acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) Ph.D. scholarship program. R.S. acknowledges financial support from the Fonds de Recherche du Québec sur la Nature et les Technologies (FRQNT) Ph.D. scholarship program. G.B. acknowledges financial support from the NSERC and FRQNT undergraduate scholarship programs. The research received funding from the Canada Foundation for Innovation (CFI), the Ministère de l'Économie et de l'Innovation du Québec, the NSERC, and the FRQNT.

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

Research data are not shared.

Keywords

extreme ultraviolet sources, high harmonic generation, multidimensional
solitary states, resonant magnetic scattering, stimulated Raman scattering

Received: June 1, 2021

Revised: June 25, 2021

Published online: September 21, 2021

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