## Abstract

We present an innovative grating design based on conical diffraction which acts as an almost perfect and low-loss beamsplitter for extreme ultraviolet radiation. The scheme is based on a binary profile operated in grazing incidence along the grating bars under total external reflection. It is shown that periods of a few 10^{2} nm may permit an exclusive (±1)^{st} order diffraction with efficiencies up to ∼ 35% in each of them, whereas higher evanescent orders vanish. In contrast, destructive interference eliminates the 0^{th} order. For a sample made of SiO_{2} on silicon, measured data and simulated results from rigorous coupled wave analysis procedures are given.

© 2012 OSA

## 1. Introduction

Precise and efficient beamsplitters for the extreme ultraviolet wavelength range are of particular interest for interferometric applications in plasma diagnostics [1,2]. In the absence of refractive optical components due to strong absorption in that spectral range [3], specialized diffractive elements have been developed [4]. Used in grazing incidence, such lamellar structures provide reflected intensities of about 20% in the 0^{th} and (−1)^{st} order as well [5]. However, their equalization, essential for a high fringe visibility, is extremely sensitive on the grating design parameters like groove depth and duty cycle. Moreover, the shadowing effect, enhanced by grazing incidence, causes significant diffraction losses.

In this paper, we suggest an alternative approach which circumvents those problems by means of conical diffraction. In our arrangement, the propagation direction of the incident field is oriented perpendicular to the grating vector. In this way, exactly symmetrized (±1)^{st} order efficiencies near the theoretical limit are easily obtained. In Sect. 2, fundamentals of the conical mounting are reviewed. Design requirements for proper operation are discussed in Sect. 3 and applied to an optimized prototype made of SiO_{2} on silicon in Sect. 4. Simulation and measurement results for that sample are presented in Sect. 5 and 6, respectively. An outlook to further prospects of improvement is given in Sect. 7.

## 2. Basic features of conical diffraction

In most applications, one-dimensional transmission or reflection gratings are exclusively operated in the plane of incidence which is spanned by the wave vector *k⃗*_{inc} of the incident field and the normal *n⃗* to the grating surface. If this plane contains the grating vector *G⃗* too, all diffracted orders are spread within this plane. This well-known situation changes under oblique incidence, namely arbitrary angles between the plane of incidence and *G⃗*.

We apply the elegant, purely geometrical concept of the “direction cosine space” (DCS) [6] to describe arrangements of that type. Since the conical incidence is often associated with wide-angle, i.e. non-paraxial diffraction, its linearization appears to be convenient. Following Harvey and Vernold [6], this can be achieved using the “direction cosines” of the actual spatial coordinates *r⃗* = (*x*,*y*,*z*) in a cartesian system,

*α*-axis roughly parallel to

*G⃗*and the

*β*-axis along the grooves, precisely

*ψ*≡ ∢(

*G⃗*,

*e⃗*). The

_{β}*γ*-axis is oriented as the surface normal. A schematic illustration is given on the left of Fig. 1 for the special case of reflection and

*ψ*= 90°. The sum condition from Eq. (1) confines the problem to the unit sphere from which only the upper half is shown in Fig. 1. In that system, the incident ray is described by its coordinates

*θ*

_{0}and

*ϕ*

_{0}are defined as in Fig. 1. From the grating equation – for a period

*d*and wavelength

*λ*– and its additional constraint to reflection,

*m*

^{th}order with the unit sphere are found as (

*α*,

_{m}*β*) – where

_{m}*β*→

_{m}*β*

_{0}for

*ψ*= 90°. The spatial spectrum of apparent, “real” orders is limited by the inequality ${\alpha}_{m}^{2}+{\beta}_{m}^{2}\le 1$.

In grazing incidence with *ϕ*_{0} → 90°, the projected grating period *d* cos*ϕ*_{0} ≪ *d* enables the construction of an almost perfect beamsplitter for short wavelengths: We specify the general case from the left of Fig. 1 to symmetric incidence with *θ*_{0} = 0° and arrive at the configuration shown on the right. With *α _{i}* = 0 but an implemented tilt

*ψ*= 90° ±

*δψ*with |

*δψ*| ≲ 1°, we obtain from Eq. (3) and using [6]

*ϕ*

_{0}close to 90° restricts the set of possible orders to −1 ≤

*m*≤ +1 even for “macroscopic” periods, compared to the wavelength. In this way, the symmetric conical mounting on the right of Fig. 1 differs from more conventional (near) normal incidence arrangements in diffraction. Whereas the 0

^{th}order undergoes an elementary reflection within the plane of incidence from (0,

*β*) to (0,

_{i}*β*

_{0}), the (±1)

^{st}orders are mirrored at this point to (

*α*

_{±1},

*β*

_{±1}) – both in direction and intensity, if there is no tilt (

*δψ*= 0°).

## 3. Design constraints for EUV beamsplitters

An optimized conception based on this idea turns out to be straightforward now. In the EUV and soft X-ray band, all known materials are characterized by strong absorption and a weak refractive power, i.e. their refractive index is commonly written as *n* = 1 − *δ* − *iβ*, with real coefficients 0 < *δ*,*β* ≪ 1 [3]. The peculiarity Re(*n*) = 1 − *δ* < 1 leads to total external reflection of an incident electromagnetic field with a critical incidence angle
${\varphi}_{\text{crit}}\approx \pi /2-\sqrt{2\delta}$ [7], more or less damped by the extinction *β*. Since numerous absorption edges preclude an efficient total external reflection in their vicinity throughout the soft X-ray and EUV spectrum, the grating composition and the wavelength of operation should be carefully selected. We choose silicon (Si) and its oxide SiO_{2} for the substrate and the grating bars, respectively, at a wavelength well beyond the Si_{L} edge near 12.4 nm. In Fig. 2, the s-polarized reflectivity under grazing incidence, evaluated by means of the Fresnel formulae and the Henke data [3], is shown for both materials in the spectral range of interest. Within 15 nm ≲ *λ* ≲ 40 nm, the superior performance of pure Si is obvious, compared to SiO_{2}. We discriminate between the substrate and the bars however, for reasons of technological simplicity (see Sect. 4) in the context of this “proof-of-concept” work. Furthermore, the limited precision in high-resolution nano-fabrication and constraints on the experimental setup for the measurements (see Sect. 6) suggest an accessible period of 400 nm, the spectral band from about 20 nm to 30 nm and a grazing angle of a few degrees; we set the initial test wavelength to *λ _{c}* = 25 nm and aim at an inclination near

*ϕ*

_{0}≈ 85°. Zero-roughness reflectivities of 91% for Si and 76% in case of SiO

_{2}are expected for those parameters. In average, an unsophisticated estimation predicts a summed efficiency in all propagating orders up to ∼ 80%, presumed a duty cycle of 50%.

We would like to build a true beamsplitter which implies the elimination of the 0^{th} order. In total external reflection, the required groove depth for that purpose can be roughly pre-selected by the geometrical condition for destructive interference from two rays reflected from the rectangular grating bars with a thickness Δ*t* and the substrate, respectively. Their optical path difference is given as Δ*s*_{opt} = 2Δ*t* cos*ϕ*_{0}. This length should be equal to an odd multiple of *λ*/2. For the values from above, we find the lowest thickness Δ*t*_{min} ∼ 70 nm in this approximation.

The actual field-matter interaction is nonetheless governed by the wave nature of light, as described by the Maxwell equations. In agreement with the specifications of the experimental setup at the synchrotron beamline as discussed in Sect. 6, we constrain to *s*-polarized incidence. Starting from that coarse estimation for Δ*t*_{min} and a duty cycle *f* = 50%, numerical rigorous coupled wave analysis (RCWA) techniques yield an optimized target thickness of ≈ 100 nm. As described in Sect. 4 and confirmed by the EUV measurements (Sect. 6), that goal is matched with an accuracy of a few nm for the fabricated film. We thus present the results here from an alternating iteration with respect to Δ*t* and *f*, in terms of a best-fit algorithm to the empirical data set, in particular the incidence angle *ϕ*_{0} = 84.77° for which the 0^{th} order intensity passes through its minimum. As it is shown on the left of Fig. 3, only the “lowest-order” interference reflection with a groove depth of 101 nm provides the highest (±1)^{st} order efficiency in each of them, accompanied by an almost vanishing 0^{th} order contribution. Towards multiples of this best thickness Δ*t*_{opt}, near 290 nm for instance, the contrast between the (±1)^{st} and the 0^{th} order decreases, due to stronger coupling losses within the grooves. On the right of Fig. 3, the duty cycle is varied for Δ*t*_{opt} within 0 ≤ *f* ≤ 1. Again, the highest contrast for a duty cycle of 54.8% is obtained with an efficiency of 35% in the (±1)^{st} order, whereas the 0^{th} order drops down to 3.4 × 10^{−4} % or less, depending on the numerical RCWA sample rate. It should be noted that an alternative design for *p*-polarized waves yields quite similar efficiencies in all orders, albeit for slightly shifted optimal values in groove depth and duty cycle. Typically, variations of a few nm in Δ*t* and ∼ 1% in *f* arise, respectively. Such an effect is evident from the different coupling strength between the incident and the diffracted waves for s- and p-polarization [8].

Since all higher diffraction orders with |*m*| ≥ 2 are found as being evanescent, the losses in our simulated beamsplitter are minimized and mainly caused by absorption on the grating surface. Moreover, we neglect here the surface roughness which would lead to diffusely scattered photons. As it will be discussed in Sect. 4, this assumption is justified with an excellent accuracy. In summary, Fig. 4 gives an overview on the geometrical parameters and the diffraction characteristics. The total sample dimensions of 4.0 mm × 15 mm account for the special features of the experimental setup at the synchrotron facility, where the device is measured afterwards (Sect. 6). In particular, its length enables the full exploitation of the available beam intensity, whereas potential stitching errors from the e-beam writer can be still neglected at this size.

## 4. Fabrication

The tight thickness tolerance close to 100 nm from above suggests an atomic layer deposition (ALD) of the SiO_{2} film. We use an optical grade, polished 4” silicon wafer in 〈100〉 orientation. Heated to 400 K, the substrate is subsequently coated in an O_{2} plasma enhanced ALD procedure with a growth rate of 0.86 Å per cycle. Ellipsometric measurements show a final central layer thickness of 92 nm, whereat a thickness homogeneity of 0.9% is assured. Afterwards the 50 nm chromium metal hard mask is deposited by magnetron sputtering. In order to define the grating structure with a period of 400 nm and an implemented variation in the duty cycle 0.49 ≲ *f* ≲ 0.59 in steps of ≈ 2.6 × 10^{−2}, we use conventional electron beam lithography (Vistec SB350 OS) with the chemical amplified resist FEP 171, as illustrated in Fig. 5. After exposure and developing, reactive ion etching (RIE) is performed on the chromium in a parallel plate reactor (SI 591, Sentech Instruments Berlin) by a chlorine-oxygen plasma. Because of the etch chemistry and – in consequence – the isotropic part of the etching process, there is a significant loss in the grating bar width which has been taken into account in the initial design. The chromium serves as a mask for the following etch step in SiO_{2} by reactive ion beam etching (RIBE) and CF_{4}. This is done in a self-made tool with a 150 mm ion source (“Kaufmann-type”). The SiO_{2} etching process stops quite well on the silicon substrate, an important condition for an efficient grating performance. In Fig. 6, a sequence of SEM pictures illustrates each fabrication stage. Finally, the chromium mask is removed. This is done by wet etching to prevent damage on the silicon substrate, since the silicon etch rate would be comparable to that of chromium in the chlorine-oxygen dry etching tool.

Though not initially intended, the natural formation of an extremely thin “native” SiO_{2} layer with a typical thickness of about 1 nm on a blank Si surface in air is a well-known phenomenon [9] and inevitable in practice, for typical exposure times of several hours. An intermediate layer of that thickness is thus assumed to coat the bottom of the grooves and incorporated in all RCWA simulations presented in this work. Analogous numerical evaluations performed on bare Si indicate no significant effect on the 0^{th} order and an acceptable diffraction loss of up to ≈ 2% in the (±1)^{st} ones. That moderate diminishment can be understood from the relatively large penetration depth Δ*z _{p}* = 5 nm of the electromagnetic field in SiO

_{2}[10]. From the duty cycle series, an optimized specimen with

*f*= 0.547 ± 0.017 is identified, which is close the modeled value of 0.548 within an error range of ±1% as described in Sect. 3. Its intrinsic uncertainty of almost ±7 nm has its origin in the line edge roughness caused by non-perfect etching. Compared to an ideal structure, both the 0

^{th}and the (±1)

^{st}order efficiencies are thus expected to degrade as it will be shown in Sect. 6. Moreover, scattering losses would arise in case of significant surface imperfections, i.e. an inevitable roughness of the SiO

_{2}grating bars on the nm scale. However, scanned by an atomic force microscope (AFM), their thickness is determined to 98 ± 0.6 nm, as visualized in Fig. 7 – a few nm more than in the central wafer region, but in good agreement with the value Δ

*t*

_{opt}= 101 nm indirectly deduced from 0

^{th}order diffraction (Sect. 6). The estimated RMS level should nearly maintain the optical performance, as calculated from the Fresnel formulae. Indeed, the reflectivity of SiO

_{2}degrades from 76.0% to 75.8%, whereas that of pure Si would only be reduced from 91.5% to 91.4% [11].

## 5. Simulations

The two-dimensional intensity pattern obtained in conical diffraction impedes the direct experimental characterization of special sample features using synchrotron light. We thus start with an investigation of those properties by means of RCWA calculations, again. Slightly different coupling strengths of the *E⃗*- and *H⃗*-field are well known from the literature [8] for planar gratings of that type. The polarization is accordingly expected to affect the diffraction efficiencies at least in minor magnitude. We quantify this amplitude as follows: In agreement with Fig. 4, the orientation of the incident *E⃗*-field is defined by the angle *ϑ* with respect to the s-polarized direction (*E*_{⊥}). As it is confirmed afterwards by the numerical evaluation, the total diffracted power into the *m*^{th} order can be written as

*ϑ*< 2

*π*. Towards the symmetry angle

*ϑ*̃

*, that excess goes down to zero, wherefore the maximum is found for*

_{m}*ϑ*̃

*±*

_{m}*π*/2. The results of the simulation for the propagating orders, combined with the model just described, are shown in Fig. 8. For simplicity, the RCWA data are calculated only in the half plane

*A*

_{⊥}≥ 0 here and mirrored for

*A*

_{⊥}< 0. Given the binary profile, the symmetry of the (±1)

^{st}orders with respect to the plane of incidence is obvious, where the symmetry angle is found as

*ϑ*̃

_{±1}= ±58.5°. Since the excess amplitude turns out to be quite small, ${\tilde{P}}_{\pm 1}\sim {10}^{-2}{P}_{\pm 1}^{\xb0}$, the beamsplitter may be used in practice for arbitrary polarizations with an almost constant efficiency. In contrast, the 0

^{th}order shows the oppositional behavior; the amplitude

*P̃*

_{0}exceeds the global minimum ${P}_{0}^{\xb0}\lesssim {10}^{-3}\%$ for

*ϑ*̃

_{0}= 0° by two magnitudes.

Those polarization characteristics might be of interest in sophisticated interferometric applications – in most cases however, the two-dimensional alignment of the grating to the beam around the both remaining axes affects its performance even more. If fixed with respect to the *y*-axis, i.e. for *s*-polarization again, the experimental setup permits as well the variation of the incidence angle *ϕ*_{0} and its orthogonal counterpart *ψ*. Fig. 9 visualizes the results of RCWA simulations. The modest misalignment around the *x*-axis is apparently not critical for the (±1)^{st} order, tolerances up to ±0.5° would degrade their brightness by a few percent at most. A nearly singular behavior is observed instead for the central 0^{th} order. As it is shown in the mid of Fig. 9, this sharp minimum runs through two magnitudes within the narrow band of ±0.1°. On the other hand, accidental tilts around the *z*-axis evoke an asymmetric distribution between the (−1)^{st} and the (+1)^{st} order, as depicted on the left and right of Fig. 9. Now the wide-range minimum would suppress the 0^{th} order within about ±0.1°. Depending on the concrete setup, enlarged non-diffracted – as for misadjusted incidence angles *ϕ*_{0} – or unbalanced orders for operation – as for tilted gratings around *e⃗ _{z}* – can reduce the visibility of an EUV interferometer [5]. Its design should thus match the technical feasible error budget in angular coordinates.

Besides its interferometric application, the conical grazing incidence device also works as an ordinary spectroscopic instrument within a certain range of wavelengths [12], wherever the somewhat complicated off-plane detection is acceptable. In comparison to state-of-the-art blazed reflection [13] or transmission gratings [14] used in classical orientation with an incidence along the grating vector, it may provide a similar or even higher net efficiency in the (±1)^{st} order without any background photons from higher orders and a strongly suppressed 0^{th} order contribution which can both degrade the achievable signal-to-noise ratio. Fig. 10 shows the simulated efficiencies which propagate within 21 nm ≤ *λ* ≤ 29 nm. The great advantage of the grazing incidence condition relies on the projected or “effective” period *d* cos*ϕ*_{0} ≪ *d*, enabling the simple construction of high-throughput gratings with eliminated higher orders by means of standard e-beam lithography techniques. Nevertheless, the price that has to be paid for this comfort is an enlarged grating area. In particular, the lateral dimension Δ*x* along the grating vector should measure at least 4 × 10^{−3} m for our sample to receive a resolving power *λ*/Δ*λ* ∼ 10^{4} as desired for future plasma diagnostics in astronomy, for instance. The longitudinal dimension is determined by the beam diameter, Δ*y* = ∅_{beam}/ cos*ϕ*_{0}. Based on the technical constraints at the EUV synchrotron beamline, i.e. for sufficient brightness of the diffracted light, we set this minimum length to Δ*y* = 1.5 × 10^{−2} m, as it was already shown in Fig. 4.

## 6. Measurement technique and results

The measurements are performed using synchrotron radiation in the reflectometer [15] at the EUV radiometry beamline [16] in the laboratory of PTB at the storage ring BESSY II [17]. Highly monochromatic (*λ*/Δ*λ* ∼ 10^{3}) radiation of the constant wavelength *λ* = 25 nm, linearly polarized in s-orientation with a degree of polarization of 99.3%, is collimated to better than 0.5 mrad in both directions and has a cross section of (1.6 × 1.1)mm^{2} in *x*- and *z*-direction, respectively. Fig. 11 shows the respective edge scans of the intensity profile in both directions. For an incidence angle of *ϕ*_{0} = 85°, the beam is spread to about 12 mm in vertical direction in projection on the grating surface plane. The diffraction pattern is recorded using the photodiode detector of the EUV reflectometer which moves at a circle with a radius of 550 mm around the *x*-axis (see Fig. 4) with an accuracy of ±0.01°. An additional drive moves the detector parallel to the *x*-axis, perpendicular to the plane of reflection. This allows to move the detector to the out-of-plane diffraction orders in the conical diffraction geometry. Besides the rotation around the *x*-axis, the sample can also be rotated around its normal, the *z*-axis. Fig. 12 illustrates the effect of small angular variations *δψ* of this type in the direction cosine space.

We start with an investigation of the 0^{th} order efficiency as a function of the duty cycle. For this purpose, a series of different duty cycles was fabricated (see Sect. 4). The measurement is a relative measurement by comparing the radiant power in the incoming beam and the diffracted or reflected beam. Both measurements are done using the same photodiode detector with a sensitive area of at least (5.5 × 5.5) mm^{2}, significantly larger than the photon beam size as given above. Therefore, the measured ratio of the photodiode signals directly equals the ratio of the incident and diffracted radiant power, i.e. the diffraction efficiency, because the detector sensitivity cancels in this ratio. Table 1 gives an overview for empirical duty cycles 49% ≲ *f*_{exp} ≲ 59%. For each sample, the angle of incidence *ϕ*_{0} is varied from 83.8° to 86.2° in steps of 0.04°. Subsequent to those scans, the incidence angle for minimized 0^{th} order reflectance *P*_{0} at each duty cycle is used to fit the measured results with an RCWA model. The simulated thickness Δ*t*_{sim}, continuously increasing with *f*_{exp}, indicates an almost constant aspect ratio 𝒜 = 0.47 ± 0.01 of the grating bars for this set of samples. The 0^{th} order yields a distinct global minimum of 0.12% for the specimen with the almost optimal duty cycle *f*_{exp} = 54.7%. Analogous RCWA calculations yield an even lower value. The experimentally obtained result for *P*_{0} is therefore not yet perfect albeit likely deep enough for real applications even if that non-diffracted light contaminates the signal from the (±1)^{st} order.

To examine the suitability of conical grazing incidence gratings as beamsplitters, the sample with *f*_{exp} = 54.7% from above is adjusted to the corresponding angle of incidence for minimized 0^{th} order reflection again. The position and intensity of the (±1)^{st} order is now measured via angular and lateral movements of the photodiode around and along the *x*-axis, respectively. For each measurement, the EUV spot is carefully centered to the detector. For various tilt angles −0.2° ≤ *δψ* ≤ + 0.2°, the results are shown in Fig. 13. In general, the diffraction from a tilted grating [6] is described by Eq. (4), i.e.

*ψ*≈ 90°, i.e. for small variations

*δψ*≈ 0°, the set of equations from (6) may be – in 1

^{st}order of the Taylor expansion – written as

*θ*and thus the horizontal position of the diffracted spot along the

_{m}*x*-axis is almost not affected under the assumption |

*δψ*| ≲ 1°, both the vertical positions and the diffraction efficiencies

*P*

_{±1}follow approximately linear functions of the tilt

*δψ*. This fact permits a simplified and precise alignment of the grating in an interferometric configuration.

*V*using the conical beamsplitter would thus differ from the maximum

*V*= 1 by only 4.6 × 10

^{−8}.

From Fig. 3, the maximal values for *P*_{±1} do not coincide exactly with the minima for *P*_{0}, with respect to the groove depth Δ*t* and duty cycle *f* as well. That feature is confirmed indeed by RCWA calculations, based on the duty cycle series data for *ϕ*_{0} and Δ*t*_{sim} from Tab. 1 again. The corresponding (±1)^{st} order efficiencies are listed in Tab. 2 with their “ ± ” uncertainty as it follows from the standard deviation in *f*. The extremum in *P*_{±1} is no longer reached for *f*_{exp} = 54.7% but rather near the lowest duty cycle of 48.9%. Presumed the constant aspect ratio from above, the global, differentiable maximum in *P*_{±1} (*f*,*ϕ*_{0}) is located actually in the vicinity of an incidence angle *ϕ*_{0} ≈ 84.92°, where the variation of *P*_{±1} with *f* and *ϕ*_{0} vanishes, i.e. ∇⃗*P*_{±1} (*f*,*ϕ*_{0}) = 0. In Fig. 14, that region – from which only about one half is plotted – is found in the upper left corner. However, the gain of less than 2% in *P*_{±1} from *f*_{exp} = 54.7% towards 48.9% is probably negligible in practice, and an appropriate beamsplitter design should maximize the power ratio *P*_{±1}/*P*_{0} instead. As it is shown in Tab. 2 too, an ultimate ratio far beyond 10^{4} can be obtained, depending on the 0^{th} order suppression. For the measured sample in comparison, we obtain an experimental power ratio of 2.75 × 10^{2} at *f*_{exp} = 54.7% especially.

Due to the field-grating interaction length of 12 mm, the lowest 0^{th} order level should strongly correlate with profile imperfections in fact, in particular the statistical standard error of the duty cycle, i.e. the line edge roughness. However, its effect on absorption and stray light losses is not yet known in detail and demands for further analysis. Fig. 15 illustrates the measured results for the values from above (Tab. 1), together with numerical predictions for the calculated thickness data Δ*t*_{sim}. In each case, an interpolation up to the 3^{rd} order ensures the straightened appearance of the contour plots and the minimum, drawn in red, roughly follows a linear dependence
${\varphi}_{0}^{\text{min}}\left(f\right)$ across the (*f* − *ϕ*_{0}) plane. Despite of deviations especially for *f* ≲ 0.50 and *f* ≳ 0.58 and a less pronounced minimum around *f* ≈ 0.54 than expected from the RCWA model, an acceptable agreement is observed.

## 7. Conclusion

We introduce an alternative design for EUV beamsplitters, based on conical diffraction. Despite their technological simplicity, the optical performance exceeds that of well-known “classical” lamellar devices with an incidence along the grating vector. As predicted by RCWA simulations and confirmed by measurements on a fabricated sample, equalized efficiencies beyond 30% are obtained in the (±1)^{st} order, providing an extraordinary high interference contrast in corresponding setups. Moreover, any diffraction losses from higher orders or background contributions from the 0^{th} order are absent. Potential improvements might target the useable (±1)^{st} order output and an even better suppression of the non-diffracted light. Further research steps should thus include the look for alternative materials aside from Si and SiO_{2} with higher reflectivity and advanced fabrication procedures for high-precision etching of binary profiles.

## Acknowledgments

This work was part of the projects “Zentrum für Innovationskompetenz ultra optics” and “Photonische Nanomaterialien”, funded by the German Federal Ministry of Education and Research (BMBF) with the fund numbers 03Z1HN32 and 03IS2101A, respectively. We thank the team of the EUV beamline, Annett Barboutis, Martin Biel, Christian Buchholz, Jana Puls, and Christian Stadelhoff, for performing the measurements. The authors would also like to thank Frank Fuchs, Hans-Jörg Fuchs, Robert Hähle, Manuela Holz, Maria Oliva, Werner Rockstroh, Adriana Szeghalmi and Uwe Zeitner for their support and fruitful discussions.

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