A Near Fourier-Limited Pulse-Preserving Monochromator for Extreme-Ultraviolet Pulses in the Few-Fs Regime

Abstract

We present a pulse-preserving multilayer-based extreme-ultraviolet (XUV) monochromator providing ultra-narrow bandwidth ($\Delta E<0.6\mathrm{eV}$, $E_{\mathrm{c}}=92\mathrm{eV}$) and compact footprint ($28\times 10{\mathrm{cm}}^2$) for easy integration into high-harmonic generation (HHG) or free-electron laser (FEL) sources. The temporal resolution of the novel design supports pulse durations of typical pump–probe setups in the femtosecond and attosecond regime, depending on the mirror design and focusing geometries over the tuning range of the monochromator. The theoretical design is analyzed and experimentally characterized in a laser-driven HHG setup.

1. Introduction

The availability of ultrashort and even few-cycle laser pulses has enabled high-harmonic generation (HHG) to serve as a source of ultrashort light pulses with photon energies up to the ‘water window’ region (282–533 eV) [1,2,3]. Using multilayer mirrors as band-pass filters is a standard technique for generating even shorter pulses down to 43 attoseconds (as) [4,5,6,7,8]. Spectroscopic analyses have benefited greatly from this development. Furthermore, most experiments do not require ultimate time resolution but rather a tunable, narrow bandwidth to match experimental needs. Grating monochromators are commonly used to adjust bandwidth and carrier wavelength. For ultrafast pump–probe spectroscopy in the XUV spectral range, grating monochromators have been fine-tuned to support the well-defined requirements and minimized dispersion properties [9,10,11]. However, they lead to significant temporal broadening of the pulse due to dispersion if no further action is taken, and even then the achievable pulsewidth is limited by these techniques.

Although good monochromatization and high transmission have benefits, they usually introduce temporal distortions. Additionally, the output pulses do not align with the input beam, necessitating separate paths for XUV and NIR pulses, which require active vibration stabilization schemes for a pump–probe setup. To maintain the temporal characteristics of a high-harmonic-generated XUV pulse, a multilayer mirror monochromator is a preferable setup that allows for collinear propagation and enables the easy control of dispersion properties through design [5,12,13,14]. A disadvantage of a typical multilayer mirror monochromator is the relatively small tuning range, comparably low reflectivity and resulting monochromator throughput [15]. Here, we demonstrate that the easy integration and compact footprint provides an ideal platform for existing setups to gain tunability and monochromatization with superior pulse properties and low dispersion to preserve pulse durations down into the attosecond regime. In contrast to the even smaller bandwidth achieved in HHG multilayer monachromatization for long driving pulses and in the low-order harmonic wavelength regime recently demonstrated by Guo et al. [16], the goal of the setup under investigation is the highest time resolution only limited by the reflective bandwidth of the multilayer mirrors but still resolving spin components in photoelectron spectroscopy. The initial results of these developments are presented in [17].

In typical designs, the temporal shape of the reflected pulse is often calculated based on the time–bandwidth product (TBP) of the monochromator characteristics. However, for HHG sources, the finite source distance leads to natural beam divergence, requiring basic design considerations to account for it. To maintain a nearly Fourier-limited pulse duration, a focusing mirror is typically required as part of the setup. Within the Rayleigh range, the temporal shape is preserved. Thus, the pulse duration is mainly determined by the spectral amplitude and phase. The reflectivity and phase of the multilayer coating and the HHG spectrum determine the duration in this case. Hence, an experimental setup must provide a focus at the sample position to fulfill this basic requirement.

On the other hand, achieving tunability requires an angular change resulting in an angular shift of the focus position. To account for the angular and spectral shift, a second mirror in a Z-shaped geometry adjusts the distance and angle between the two mirrors. Furthermore, correcting for a focus shift along the optical axis is achieved by moving both mirrors simultaneously along the propagation direction. Accounting for these degrees of freedom, a multilayer monochromator setup can provide a fixed focus position over the total angular tuning range.

In this study, we explore the properties of a Z-shaped, ultra-narrow bandwidth multilayer monochromator. Specifically, we examine its reflected peak photon energy and bandwidth, which determine the Fourier-limited pulse duration, as well as the pulse front distortion at realistic distances from the high-harmonic generation source, based on our experimental geometry.

2. Theory of Multilayer Mirrors

The fundamental working principle of a multilayer mirror involves the interference of light that reflects from the interfaces of two alternating thin layers of materials having high and low refractive indices [18,19]. Such reflection causes partial transmissions and reflections at the layer interfaces as described by the Fresnel equations. For s-polarized light, the transmittance t and reflectance r as a function of the angle of incidence (AOI) $\alpha$ and the angle of refraction $\beta$ are determined by

$$t_s=\frac{2sin\beta cos\alpha }{sin(\alpha +\beta )}{r}_s=-\frac{sin(\alpha -\beta )}{sin(\alpha +\beta )}$$

(1)

and for p polarized light, one obtains

$$t_p=\frac{2sin\beta cos\alpha }{sin(\alpha +\beta )cos(\alpha -\beta )}{r}_p=\frac{tan(\alpha -\beta )}{tan(\alpha +\beta )}$$

(2)

Each interface that has a transition from a high refractive index to a low refractive index results in partial reflection. The reflected beams interfere constructively in accordance with Bragg’s law, which is defined as $m\lambda =2dsin\left(\theta \right)$. Here, m is the refraction order, $\lambda$ is the wavelength, d denotes the distance between the reflective interfaces or the double-layer thickness, and $\theta$ refers to the angle between the front surface and the incident beam. Thus, for a given multilayer design, wavelength tunability can be achieved simply by rotating the mirror, resulting in a virtual change in the double-layer thickness. The total reflectivity curve of a multilayer mirror is determined by the thickness of the double layer, the thickness ratio and the total number of bilayers in a periodic design. For customized spectral phases, aperiodic designs are selected, resulting in a single-layer definition of thickness and corresponding double-layer ratio as demonstrated in [5,20,21]. The basic Z-shaped geometry allows for any combination of mirrors and their layer structure and phase. Nevertheless, a periodic design is beneficial for a wide tuning range and a minimal influence on the pulse properties.

Depending on the experimental requirements, it is important to consider that a finite source distance and natural beam divergence may necessitate additional focusing, causing temporal distortion based on the pulse wavefront following classical optics rules. When using focusing mirrors with collimated light sources at an infinite distance, the focal distance is defined by the radius of curvature (ROC). Taking into account a finite and divergent source, the relation between the distance of the source and the focal length f results in the formation of a real image when the source distance is greater than the focal distance, an imaginary image when the source distance is less than the focal distance, or no image when the source distance is equal to the focal distance. Based on these initial considerations, the wavefront in the image plane appears to be relatively flat. Translating this behavior to ultrashort pulses, it shows only a minor effect on the lateral temporal structure, resulting in minimal temporal smearing. Outside the image plane, the wavefront distortion impacts the temporal pulse shape in a way that causes pulse arrival times to scatter due to wavefront distortion, with the pulse arriving earlier or later at the center than on outer regions. This requires using a focusing mirror to recollimate or focus the initial beam and adjust the radius of curvature to the divergence and finite source distance to minimize wavefront distortion and temporal deviation, referred to as the pulse front in ultrafast optics.

In Gaussian beam optics, the Rayleigh range $z_{\mathrm{R}}$ is the distance where a beam doubles in the lateral area [22]:

$$z_{\mathrm{R}}=\frac{n·\pi ·w_0^2}{{\lambda }_0}$$

(3)

Here, $w_0$ is the focal beam waist. In the following investigations, we assume the wavefront to be nearly constant within the Rayleigh range.

3. XUV Monochromator Design

The design of this monochromator is based on specific experimental needs, which are evident in the narrow-bandwidth mirror design. The ability to integrate the setup into an existing HHG beamline without altering the beam path allows for tunability and a desired footprint to be achieved.

The complete design fulfills the following boundary conditions:

• Peak reflectivity at 92 eV;
• Minimum tunability ±2 eV;
• Reflected bandwidth <0.8 eV (FWHM);
• Collinear setup with small beam offset;
• Small overall footprint to incorporate the monochromator in standard HHG pump–probe setups;
• The monochromator needs to preserve the pulse according to the desired temporal resolution for pump–probe spectroscopy experiments.

These specifications are satisfied with the multilayer mirror monochromator design in a Z-shape geometry as shown in Figure 1.

The monochromator’s tunability is achieved through mirror rotation (${\theta }_{M1},{\theta }_{M2}$), which causes a shift in peak reflectivity. To maintain a fixed beam offset, the relative distance between the mirrors is adjusted. The setup utilizes motorized linear and rotational stages for both mirrors, enabling in-situ wavelength tuning and focus distance correction. Two motorized mirror mounts are incorporated to manipulate overall beam pointing. The setup is presented in Figure 1, which also illustrates the degrees of freedom for all optical components.

The beam offset remains fixed at 20 mm for the parallel input and output beams to allow easy accessibility and create additional space for a differential pumping stage between the HHG source (S_HHG) and the experimental chamber (OP). To maintain high transmission by minimizing the total number of reflections, the focusing mirror M2 provides a free focus spot at a finite distance of L2 behind the monochromator. In the optical simulation, the high-harmonic generation (HHG) source is modeled as a Gaussian source featuring a beam waist of $w_0=5.0\mathsf{\mu }$m and a source distance of 750 mm to the first mirror M1. A Gaussian beam profile at ${\lambda }_{\mathrm{c}}=13.5\mathrm{nm}$ (∼92 eV) is assumed. In order to simulate an untruncated Gaussian intensity profile, the radius of the aperture of the entrance beam is defined as $401.156\mathsf{\mu }$m. The average group delay dispersion (GDD) is retrieved by the second derivative of the numerical date from Figure 2 in the linear part of the phase to be $\mathrm{GDD}\approx -0.157$ fs².

The second mirror’s curvature radius must deliver either a finite distance focus or a recollimated output beam. Otherwise, wavefront distortion results in temporal delay or pulse front distortion. This effect is especially crucial when using the monochromator as the focus setup of two overlapping pulses of varying wavelengths in a pump–probe geometry. An optimized pulse front establishes the minimum overall temporal resolution for this configuration as discussed in Section 4.3. As demonstrated by this analysis, the pulse front is ideally maintained within the Rayleigh range and in a 1:1 imaging geometry.

4. Simulations

4.1. XUV Multilayer Design

The multilayer mirrors are designed to obtain a peak reflectivity at 91.6 eV at ${15}^{\circ }$ angle of incidence. In the targeted photon energy range, the material combination of alternating molybdenum and silicon layers is known as the standard. The manufactured design is based on a Mo/Si stack and presented in Figure 2. Further design details are the intellectual property of OptiXfab GmbH, Jena.

The peak reflectivity is optimized for a fixed angle of incidence of ${15}^{\circ }$ as a compromise between the specified tunability with a compact geometrical footprint and minimized optical aberrations as discussed in the next section.

4.2. Spectral Tunability Simulation

The total reflectivity of the monochromator setup after two reflections from the multilayer mirrors is calculated from the individual reflectivity curves of the single mirrors by $R_1\left(E_{\mathrm{ph}}\right)\ast R_2\left(E_{\mathrm{ph}}\right)$. For identical XUV mirrors, $R_1=R_2=R$, the total reflectivity is given by $R^2$. In Figure 3, the reflectivity is shown as a false color plot versus the angle of incidence from $0^{\circ }$ to ${30}^{\circ }$.

The photon energy with maximum reflectivity depends on the angle of incidence and shifts to higher photon energies with increasing angle of incidence. The peak reflectivity of approximately $14\%$ is reached for 90 eV photon energy at ${10}^{\circ }$, which is the smallest AOI accessible by the monochromator due to its limiting geometry. Up to ${20}^{\circ }$ AOI, the total transmission drops by only $3\%$. Within a tunable range of ${27}^{\circ }$ AOI, the peak energy shifts from 90 eV to 98 eV corresponding to the maximum energy tunability of this monochromator setup.

4.3. Evaluation of Temporal Performance

The reflectivity’s angular dependence is presented in Figure 3a, while Figure 3b displays the temporal performance of the multilayer design, estimated using the time–bandwidth relation for Gaussian shaped pulses, utilizing the fit parameters obtained from fitting all spectra of Figure 3a.

A consistent temporal performance is noted within the angular range of ${10}^{\circ }$ to ${26}^{\circ }$, featuring a pulse duration of approximately ∼3.5 fs. The pulse duration marginally increases within the angular range of ${26}^{\circ }$ to ${28}^{\circ }$, which denotes the limit of angular tuning. A significant increase in pulse duration occurs when the angle of incidence is larger than ${28}^{\circ }$, which is attributed to the reflectivity spectrum approaching the silicon $L_{\mathrm{III}}$ absorption edge and becoming narrower.

Thus, from the simulation, the temporal performance is expected to remain nearly constant over the entire tuning range from ${10}^{\circ }$ to ${28}^{\circ }$. To achieve an even more consistent temporal behavior, the tuning range should be limited to an angular range of ${10}^{\circ }$ to ${26}^{\circ }$. It is worth noting that this behavior is linked to the coating design and may vary for other coatings. Further research is required to effectively constrain the angular tuning range for the desired temporal performance.

This evaluation determines the overall temporal performance of the monochromator, excluding any distortions due to optical aberrations. The mirror M2 of the setup is designed to create a focus spot in the observation plane (OP). As a result, an increasing angle of incidence introduces optical aberrations that lead to a temporal distortion of the reflected pulse. To further investigate this phenomenon, we evaluate wavefront distortions for different radii of curvature at the design angle of ${15}^{\circ }$.

To simulate the resulting temporal delay within the lateral plane, we use a ray transfer matrix analysis. Here, the Gaussian beam is described by the complex beam parameter $q_0=i{z}_{\mathrm{R}}$ at its waist position. The HHG source parameters defined above are as follows:

• Gaussian beam waist $w_0=5\mathsf{\mu }$m;
• Central wavelength ${\lambda }_{\mathrm{c}}=13.5\mathrm{nm}$;
• Beam-quality factor $M^2=1$;
• Mirror angles ${\theta }_{M1}={\theta }_{M2}={15}^{\circ }$;
• Distance between the two mirrors $L=34.64\mathrm{mm}$ leading to a beam offset of $20\mathrm{mm}$.

The source distance ($L1$) is a variable parameter in these simulations.

We calculate the wavefront distortion along the propagation axis for fixed radii of curvature ($ROC$) of $3000\mathrm{mm}$, $1500\mathrm{mm}$, $1000\mathrm{mm}$ and $500\mathrm{mm}$. The analysis is performed in an observation plane ($OP$) at a fixed position of $L2=1\mathrm{m}$ behind the focusing mirror $M2$, which may not be the ideal focus position in an experiment. For evaluation, the source distance $L1$ is changed, and the complex beam parameter $q_{OP}$ is calculated:

$$\left[\begin{array}{c}{q}_{OP}\\ 1\end{array}\right]=k\left[\begin{array}{cc}1& L2\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& 0\\ -2/ROCcos\left({\theta }_{M2}\right)& 1\end{array}\right]\left[\begin{array}{cc}1& L/cos\left(2{\theta }_{M1}\right)\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& L1\\ 0& 1\end{array}\right]\left[\begin{array}{c}{q}_0\\ 1\end{array}\right]$$

(4)

Here, k is a normalization constant chosen to keep the second component of the ray vector equal to 1. This parameter $q_{OP}$ provides information about both the beam waist $w_{OP}$ and its radius of curvature $R_{OP}$:

$$\begin{array}{cc}\hfill w_{OP}& ={\sqrt{-Im\left[\frac{1}{q_{OP}}\right]\frac{\pi n}{{\lambda }_{\mathrm{c}}}}}^{-1}\hfill \end{array}$$

(5)

$$\begin{array}{cc}\hfill R_{OP}& =Re{\left[\frac{1}{q_{OP}}\right]}^{-1}\hfill \end{array}$$

(6)

Finally, the RMS spotsize ($RMS$) and the wavefront distortion ($WD$) are calculated in the observation plane:

$$\begin{array}{cc}\hfill RMS& =\frac{1}{\sqrt{2}}{w}_{OP}\hfill \end{array}$$

(7)

$$\begin{array}{cc}\hfill WD& =\frac{|R_{OP}|-\sqrt{R_{OP}^2-w_{OP}^2}}{c}\hfill \end{array}$$

(8)

The evaluation of the wavefront distortion for the different curvatures as a function of source distance is shown in Figure 4a.

A relatively small pulse front distortion for this geometrical setup is found for $R=1000\mathrm{mm}$. Here, the source distance is approximately the ROC or the double focal distance that results in a 1:1 image of the HHG source at the focus position. For very short source distances of $0.1$ to $0.3\mathrm{m}$, a mirror with a smaller ROC of $R=500\mathrm{mm}$ resulting in a real magnified image in the observation plane ($OP$) also results in a flat curve at the focus position, but at longer source distances, the wavefront distortion grows very rapidly. A mirror with ROC of $3000\mathrm{mm}$ leads to a divergent outgoing beam, resulting in a virtual image since the source distance is smaller than the focal length. The inset Figure 4a shows the behavior for very long source distances of several meters.

In Figure 4b, the corresponding rms spot size is evaluated. For the $1000\mathrm{mm}$ mirror, the image distance is around $0.9\mathrm{m}$. Angular tuning slightly changes the source distance. Within $100\mathrm{mm}$ shift, the increase in the spot size remains small compared to a ROC of $R=500\mathrm{mm}$, where the optimum source distance is about $0.25\mathrm{m}$. For ROC $=3000\mathrm{mm}$, the optimum is at extremely long source distances, but the position of the evaluation is comparably short such that the change in the spot size remains small over the full simulation range of 10 m. Here, the limited rms spot size results from the aperture of the $1/2$ inch mirrors of the monochromator themselves.

The Rayleigh range is $0.58\mathrm{m}$ according to Equation (3) for the source spot radius of $5\mathsf{\mu }\mathrm{m}$, which is nicely reproduced for a ROC = 1000 mm including an AOI of 15°.

The calculations above were performed for a monochromatic wave at $13.5\mathrm{nm}$ with a Gaussian intensity profile. Under typical experimental conditions, the reflected HHG spectrum is modulated, reproducing the odd multiples of the driving laser frequency with a finite bandwidth for each harmonic in the plateau region. Even in the cut-off region, the spectral amplitude drops rapidly for increasing photon energy for the chosen laser characteristics.

To simulate our experimental conditions, the reflectivity matrix of the multilayer mirror monochromator is multiplied with an HHG spectrum in the given spectral range. From this, we obtain the angle-dependent transmission expected for our HHG experiment. Figure 5 shows the reflectivity curve of the monochromator versus AOI. The amplitude modulation from the distinct harmonic peaks is clearly visible. The highest reflectivity is obtained for an angle of ${13}^{\circ }$ resulting from the maximum of the HHG spectrum used for convolution at ∼91 eV.

The spectra with peak reflectivity for AOI ${13}^{\circ }$, ${20}^{\circ }$ and ${25}^{\circ }$ are analyzed with a Gaussian fit to determine the peak photon energy $E_{\mathrm{c}}$ and the FWHM bandwidth $\Delta E_{\mathrm{c}}$, respectively, and presented in

Table 1. Results of the Gaussian fits of Figure 5b.

Theoretical Data
AOI	${\mathit{E}}_{\mathrm{c}}$ [eV]	$\Delta {\mathit{E}}_{\mathrm{c}}$ FWHM [eV]
${13}^{\circ }$	$90.8193\pm 0.0017$	$0.5120\pm 0.0054$
${20}^{\circ }$	$93.9104\pm 0.0005$	$0.4550\pm 0.0013$
${25}^{\circ }$	$96.9979\pm 0.0002$	$0.4134\pm 0.0005$

. The results show a bandwidth clearly below the design guidelines of <0.8 eV in the covered tuning range of the monochromator. Furthermore, we can expect near-Fourier-limited pulses according to the phase behavior of the multilayer presented in Figure 2, which exhibits the expected performance of the monochromator for the reflection by two plane mirrors. For better comparison,

Table 2. Results of the Gaussian fits of Figure 6b.

Experimental Data
AOI	${\mathit{E}}_{\mathrm{c}}$ [eV]	$\Delta {\mathit{E}}_{\mathrm{c}}$ FWHM [eV]
${13}^{\circ }$	$90.7321\pm 0.0015$	$0.5184\pm 0.0038$
${20}^{\circ }$	$93.7924\pm 0.0042$	$0.5196\pm 0.0111$
${26}^{\circ }$	$97.4789\pm 0.0023$	$0.5171\pm 0.0059$

presents the results of the experimental verification from the following section. Note that the maximum energy analyzed deviates by an AOI of $1^{\circ }$ in the experimental dataset due to the typical experimental deviations in HHG.

Taking the wavefront mismatch and thus the pulse front distortion into account, if $M2$ is chosen to be a focusing mirror, the ideal performance with a distance $L1=0.9\mathrm{m}$ and $L2=1\mathrm{m}$ is provided by a mirror with ROC = 1000 mm showing a local minimum in pulse front distortion and spot size according to the analysis presented in Figure 4. This defines a lower limit caused by wavefront distortion in a pump–probe geometry with copropagating pulses substantially <250 as. We denote that for the given design restrictions, this setup is thus limited by the bandwidth of the mirrors and could even be used for spectral tuning in the attosecond regime.

5. Experiment

5.1. Laser System and HHG

For the experimental characterization of the monochromator transmission and tunability, a commercial Ti:sapphire chirped-pulse amplifier (CPA) is used with the following specifications:

• $\Delta \tau =35\mathrm{fs}$;
• $E=5\mathrm{mJ}$;
• Center wavelength: 803 nm;
• Repetition rate: 3 kHz;
• CEP stability: $320\mathrm{mrad}$ rms
• gas-filled hollow-core fiber (HCF) compression to $\Delta \tau =5.3\mathrm{fs}$.

The laser system provides the general capability to use either the direct output pulse with a duration of 35 fs for HHG as well as the cut-off spectrum from the HCF-compressed pulses. For spectral characterization of the multilayer monochromator, we chose the longer pulse for HHG to demonstrate the ability to isolate a spectral bandwidth defined by the XUV mirror coating from the HHG plateau range. Experimentally, this provides a much higher photon flux than using the HHG cut-off range for characterization.

The laser pulses are focused with a $f=250\mathrm{mm}$ spherical mirror into a neon gas target for HHG. The gas target is a steel tube with an inner diameter of 4 mm with a backing pressure of $200\mathrm{mbar}$. To suppress the fundamental laser pulse, a 200 nm-thin Zr filter is used.

A commercial slit grating spectrometer (McPherson 251MX XUV) with two flat-field gratings covering a total spectral range $\Delta E$ from $15.5\mathrm{eV}$ to $248\mathrm{eV}$ is used for spectral characterization. The spectrally resolved HHG is detected by a Newton 940 back-thinned XUV CCD camera (Andor Technology Ltd., Belfast, UK). The camera is cooled down to −50 °C during the measurement for improved signal-to-noise ratio.

5.2. Multilayer Mirror Monochromator Characterization

Figure 6a shows the monochromatized high-harmonic spectra measured with the XUV spectrometer after polynomial background subtraction. We analyze the three intensity peaks at AOI ${13}^{\circ }$, ${20}^{\circ }$ and ${26}^{\circ }$. The corresponding spectra are shown in Figure 6b, and the data are summarized in Table 2. The same analysis as in the theoretical investigation is used to determine the center photon energy and the FWHM bandwidth of the monochromatized beams.

From the experimental data, one can see that the bandwidth is nearly constant at 518 meV, providing a constant pulse duration over the tuning range analyzed according to the measurements performed. For further investigation, a time-resolved pump–probe experiment would be required to directly determine reflected bandwidth and XUV pulse duration.

6. Conclusions and Discussion

We presented the design, simulation and experimental characterization of an ultra-narrowband multilayer XUV monochromator. The designed mirror pair allows using this setup as a time-preserving XUV monochromator limited by the given bandwidth of the mirrors found to be $0.52\mathrm{eV}$ and capable of even higher temporal resolution much below <250 as with a geometrically limited spectral tuning range of roughly 8 eV. The total reflectivity reaches up to 13% for the design wavelength. The operation regime of the monochromator can be adapted by tailoring the multilayer coating to the required experimental conditions. For experiments requiring a dedicated photon energy, this monochromator offers the smallest known footprint with the benefit of a quasi-inline setup. The small footprint allows to insert this monochromator even in compact experimental setups. The peak intensity in the experiment is reached at ${13}^{\circ }$ and $90.73\mathrm{eV}$ with a FWHM bandwidth of $0.52\mathrm{eV}$. To our best knowledge, this is the smallest bandwidth reported for a multilayer monochromator in the given energy range, even for pure monochromatization.

The final design supports a narrow bandwidth that is even smaller than the comparable arrangements in the combination of multilayer coated gratings. Kleineberg et al. [12] demonstrated a monochromator for microspot-XPS experiments using synchrotron radiation at BESSY I at 95 eV with a corresponding bandwidth of 0.7 eV. Further experiments with HHG sources demonstrate a reflected bandwidth in the range of 1.5 eV and 2.5 eV [13,14] in the 40 eV to 70 eV range, respectively.

The bandwidth of the monochromator design presented here is substantially smaller and will provide even better spectroscopic resolution with respect to the inner-shell photoelectron spectroscopy using the high harmonic source presented by Drescher et al. [23].

An upper limit for the contrast ratio to neighboring harmonics is better then 20% based on the sensitivity of the back-thinned CCD camera used in this experiment (Newton 940, Andor Technology Ltd.). With respect to comparable geometries utilizing periodic multilayer mirrors (e.g., [23]), we expect a similar contrast ratio in the range of 5% as shown in Figure A4.

For the given bandwidth of 0.52 eV and a corresponding Fourier limited pulse duration in the range of 3 fs, the calculated $GDD\approx -0.157$ fs² is negligible. The main pulse distortions arise from amplitude effects by the adjustable angle of incidence (AOI). For large AOI, a strongly reduced bandwidth and distorted spectral shape from the silicon edge at 100 eV are the dominant effects for temporal distortion.

The small footprint allows for easy integration into current HHG setups and provides a fixed focal position minimizing the mismatch between the sagittal and tangential focus caused by the tilted spherical mirror.

We demonstrated that the wavefront error at the focus position is sufficiently small to provide near Fourier transform-limited pulses, even if the focal intensity distribution is affected by astigmatism.

An ideal proof-of-principle experiment for a final evaluation of the bandwidth and performance of the presented setup is a time-resolved photoionization experiment in krypton to determine the temporal performance as well as the overall contrast of the setup, studying the Kr $M_{4,5}{N}_1{M}_{2,3}$ Auger decay with a sufficient resolution to excite the 3D spin components ($E_{3d3/2}=95\mathrm{eV}$ and $E_{3d5/2}=93.8\mathrm{eV}$), independently tuning the monochromator, as well as extracting the XUV bandwidth from the 4p photoelectron emission following the experimental work in [24,25,26].

This demonstrates that the XUV multilayer mirror monochromator provides the general capability of a pulse-preserving tunability of $8\mathrm{eV}$ bandwidth, supporting near Fourier transform-limited pulses down into the attosecond regime.