A sensitive EUV Schwarzschild microscope for plasma studies with sub-micrometer resolution

Strongly correlated dense plasmas may be created by exciting a solid with sub-picosecond, high-intensity laser pulses.¹ In the last decade, improvements in laser technology increased the potential repetition rate of such experiments to several shots per second.² With each laser-matter interaction requiring a fresh target, this calls for high repetition-rate target delivery such as micrometer-thin liquid or cryogenic jets. Recently, it has been demonstrated that cryogenic hydrogen jets³ allow for studies of electron-ion equilibration⁴ and the generation of pulsed proton beams.^5–7 

The reliable shot-to-shot characterization of jet thickness, pointing jitter, relative alignment with tiny laser foci and potentially the time-resolved probing of the hydrodynamic plasma expansion, calls for high-resolution single-shot imaging with sub-micrometer resolution. Static, time-integrating microscopy in the sub-μm regime has already demonstrated the advantage of extreme ultraviolet (EUV) radiation using transmissive⁸ and reflective optics.⁹ Single-shot sensitivity can be achieved using large aperture optics with reflective multilayer coatings that have a reflectivity R > 65% with a spectral bandwidth of a few percent. An all-reflective optical system with high spatial resolution and good aberration characteristics is a Schwarzschild objective (SO) that employs two concentric spherical mirrors.¹⁰ A generic schematic of a Schwarzschild objective is shown in Fig. 1.

Intense, prominent examples of short-pulse sources of EUV radiation are, amongst others, high-harmonic generation from gases¹¹ or surfaces¹² and high-gain free-electron lasers (FELs).¹³ The latter provide sub-picosecond pulses with laser-like properties and about 10¹² photons per pulse. Meanwhile, first high repetition rate studies of dense plasmas at the Free-electron LASer in Hamburg (FLASH) were performed using jets from liquid water¹⁴ and cryogenic hydrogen.^4,15

We have developed an experimental platform at FLASH for studying the dynamic properties of warm dense hydrogen,^16–18 which allows us to investigate conditions typically found in planetary and fusion science. The basis for these studies is a cryogenically cooled hydrogen jet that liquefies hydrogen gas through a cryostat (18 K) and a circular nozzle (2–10 μm diameter).³ The liquid hydrogen jet becomes solid due to evaporative cooling providing a cylindrically shaped target with a mass density of ∼0.08 g/cm³. The intense EUV radiation ionizes the solid hydrogen target so that a solid density plasma is created. Even if fully ionized, the free electrons would result in a plasma frequency which is one order of magnitude lower than the frequency of 13.5 nm EUV photons (photon energy of 92 eV). Accordingly, EUV radiation can propagate into the plasma volume, in contrast to optical radiation in the visible or near-infrared spectrum which launches density waves.¹⁹ With an absorption length of 9 μm for the 13.5 nm EUV radiation in our experiments, the EUV pulses are sufficiently absorbed and isochorically heat the cryogenic hydrogen target by photo ionization. We have recently shown that microscopic plasma properties can be investigated by EUV scattering: the elastic scattering cross section increases by more than a factor of two when solid density hydrogen dissociates and becomes ionized as a result of electron-ion heat transfer.⁴ These results impact the modeling of planetary systems and inertial confinement fusion via the measurements of the dynamics of plasma parameters. These measurements so far average over the nearly Gaussian intensity distribution of the laser focus. Accordingly, the lack of spatial resolution limits the accuracy to which the applied intensity can be determined. For the experimental platform at FLASH, where the focal spot size of 25–30 μm could limit the spatial resolution, an EUV imaging system with ∼1 μm spatial resolution would be able to resolve the scattered radiation from sites with defined irradiation intensity. Moreover, imaging the scattering objects and the structure of the hydrogen target for each laser pulse would allow a more detailed analysis, e.g., target characterization or the disentanglement of volume and surface scattering. The development of an EUV microscope for these experiments thus significantly improves the experimental capabilities for studying dense plasmas at EUV free-electron lasers.

Here we present an EUV microscope based on a Schwarzschild objective. We demonstrate its high spatial resolution and detection efficiency by observing single-shot scattering from a weakly scattering cryogenic hydrogen jet at the FLASH FEL.

In the Schwarzschild geometry, the degrees of freedom for the radius of curvature of the two spherical mirrors, and therefore also the distances, are determined by the magnification M. Larger mirrors increase the numerical aperture and shrink the Airy disc. However, aberrations from the outer parts of the mirror will compromise the resolution. This could be compensated, for example, by an aspherical surface of the small mirror. We based our design on an optimized, compact design which was initially published by Artioukov and Krymski in 1999¹⁰ and was frequently used thereafter.^20,21 We found that this design is a good compromise in terms of optics size, resolution, and aberration mitigation.

We performed a detailed design study using the raytracing software ZEMAX. Simulations confirmed that the initial parameters lead to optimum aberration correction. A tolerance analysis has also shown that the performance of the SO is relatively robust regarding misalignment and manufacturing tolerances. The optimization with ZEMAX has shown that the magnification can be controlled over a large parameter range with excellent aberration characteristics using the same optical elements. The parameters of the optical elements of the SO are summarized in Table I. Before different options in terms of resolution and magnification are presented, we discuss general design criteria of the EUV microscope with respect to the experiment.

The requirements in terms of magnification are driven by the experiment and the detector: In the case of the hydrogen jet, a spatial resolution of ≤1 μm is needed in order to resolve the jet diameter of 2–10 μm and to discriminate between different intensity regimes across the FEL focus with a spot size of 25–30 μm full-width at half-maximum (FWHM). Since the smallest pixel pitch of commercially available direct-detection EUV CCDs is 13.5 μm, the required magnification of the microscope should be larger than >13.5× to allow for imaging 1 μm structures with a standard EUV CCD.

The SO design described in Ref. 10 has a magnification M of 21.27 which would allow us to resolve sub μm structures with the CCD. For this setup, simulations using ZEMAX yield an Airy disk diameter in the detector plane of 1.84 μm and an aberrated geometric point spread function (PSF) of 2 μm. This is in agreement with previously published analytic results¹⁰ and corresponds to a spatial resolution of 2 μm/M ∼ 100 nm. However, the achievable resolution is limited by the CCD pixel size which can be calculated to 13.5 μm/M ∼ 0.6 μm for this configuration.

For different magnification settings, the distances between the CCD detector and the two spherical mirrors must be adapted. Table II lists magnifications for mirror distances which are varied in 100 μm steps. The corresponding parameters have been optimized using ZEMAX. At a magnification of ∼89, the Airy spot and the pixel size of 13.5 μm coincide and therefore the highest spatial resolution of ∼150 nm can be achieved. However, the field of view recorded by the CCD camera will be very small and the CCD has to be placed 2.4 m away from the objective. Such a high spatial resolution is also not needed for our experiments. We therefore found a compromise by increasing the magnification slightly to M = 35 as compared to Ref. 10. The aberrations within the resulting 150 μm field-of-view (FoV) of the jet-FEL interaction are still <0.3 μm and do not compromise the imaging quality of the presented EUV microscope. Outside the FoV, the image is strongly distorted.

Both mirrors are coated with a high-reflectivity molybdenum (Mo) and silicon (Si) multilayer for a center wavelength of 13.5 nm. The spectral bandwidth amounts to ∼0.5 nm FWHM but is narrowed to about 0.2 nm due to the two subsequent reflections. The coating is optimized for incidence angles between 1°–8° and has a reflectivity of R ∼ 0.68. This yields a throughput of 46% of the optical system. The angle variation over the mirror aperture still allows for a homogeneous coating, no gradient in the multilayer spacing is required. We also note that the changes of the incidence angle for the different magnification settings as presented in Table II are small compared to the angular coverage of the reflection curve, i.e., one multilayer coating can be used for all presented magnification settings.

Another important design consideration is the efficiency of the optical system since we would like to obtain microscopy images with a single FEL pulse. Owing to fluctuations of the hydrogen jet target and the EUV source, single-exposure imaging (requiring 10³–10⁴ photons per image) is crucial for successful experiments. The detection efficiency η of the presented design, defined as the number of detected photon per isotropically emitted source photon, can be estimated by

where A₁ is the surface area of the large concave mirror at distance d₁ from the source point, A₂ is the area of the small convex mirror mount at distance d₂ which will partly obscure the large mirror, R ∼ 0.68 is the reflectivity of a single multilayer mirror, and η_QE(λ) is the quantum efficiency of the detector (Princeton Instruments PIXIS-XO: 2KBTM back thinned CCD).

For the hydrogen jet experiment, we assume 10¹² FLASH photons per pulse in the focus, an incoherently scattered fraction of ∼10⁻⁵ into the full solid angle and hence 10⁷ scattered photons. Applying the above-estimated η, this will yield images containing ≤10⁴ photons per single exposure. If the imaged object covers ∼100 pixels, each pixel would contain on average ∼100 photons.

We assess the influence of misalignment on the spatial resolution using ZEMAX simulations. If the mirrors were laterally misaligned by Δx ≤ ±15 μm with respect to each other, the calculated PSF on the optical axis is 400 nm. If the centers of curvature of the two mirrors were separated by ΔZ ≤ ±500 μm along the optical axis and the image is refocused by adjusting the distance of the microscope to the target, a PSF of ≤1 μm can be maintained. Another issue is the misalignment in the angle of the spherical mirrors. Assuming an angular misalignment or tolerance of the mirror substrate of >5 arc min, this would result in an aberrated PSF in the detector plane of 6.7 μm, i.e., half a pixel pitch.

From the analysis of alignment requirements, we decided to develop a simple mechanical system for mounting the optics. Fine-precision machining of the mount components should be sufficient in order to fulfill the rather relaxed requirements in terms of resolution and alignment precision. We decided to build a mechanically robust EUV microscope system that can be added to an experimental platform in a flexible way without elaborate alignment procedures. We therefore constructed a mount system with a minimum amount of motions. This also limits the coupling of vibrations of the mount system to the optical components. Some photographs of the vacuum housing and the EUV microscope are shown in Figs. 2(a)–2(c).

The distance between the CCD detector and the mirror assembly determines the magnification, and the length of the vacuum tube is adapted accordingly. In order to obtain sharp images on the detector, at least one of the distances source-SO, concave-convex mirror, and SO-detector plane has to be adjustable during the experiment. We used bellows with manual position control to both steer the image to the center of the CCD detector and to adjust the distance between source and the objective. In order to separate the (potentially cooled) CCD detector from the source in the interaction vacuum chamber, we installed a gate valve between the SO and the CCD. This allows us to vent the interaction chamber while keeping the detector cooled under vacuum conditions. Since the SO also focuses optical light from the source point, we can insert a 200 nm thin zirconium (Zr) foil using a vacuum manipulator to block optical light. The transmission of 13.5 nm photons through the foil is 50%.

The EUV microscope was mounted to the experimental platform at FLASH. EUV pulses with a wavelength of 13.5 nm, a pulse duration of 60 fs, and a pulse energy of ∼150 μJ were focused to the center of the vacuum chamber where test targets and the hydrogen jet can be inserted. The EUV microscope is vertically oriented so that the EUV pulses are scattered approximately 90° into the EUV microscope. Fiducial grids were used for calibrating the EUV microscope. The plane of the metallic grids were oriented with an angle of ∼30° to the focal plane to allow for EUV illumination with the FLASH facility. We aligned the EUV microscope manually so that a sharp image was achieved. The results are shown in Fig. 3. A magnification of M = 32.7 was found, which means that a 13.5 μm pixel pitch corresponds to 0.41 μm in the object plane. This is very close to the design value and implies that the spherical mirrors are a few micrometers closer than anticipated. This is well within the tolerances of the machining precision. A FoV of 100–150 μm was demonstrated using the alignment grids.

For generating warm dense hydrogen plasmas, we used the cryogenic jet with a diameter of 5 μm. It was irradiated by individual FLASH pulses and images were recorded with a repetition rate of 10 Hz using the EUV microscope. Figure 4 shows a typical image of the initial hydrogen ice jet, illuminated in a ∼50 μm wide region by a nearly Gaussian shaped EUV focus of 25 μm. Most importantly, our experiment shows that quantitative single-pulse scattering data can be recorded using the EUV microscope. This novel experimental capability will allow scattering experiments with improved data analysis and high statistical significance. For example, we can record the intensity distribution of the FLASH focus on-target and subsequently analyze scattering from selected intensity intervals. Moreover, we can image the longitudinal structure of the jet target: We find that the jet structure varies from shot-to-shot and deviates from the assumed cylindrical shape. Apparently, ice fragments and crystallization formation strongly influence the geometry of the target which has to be accounted for in the analysis of the experiments.

We observe small ice fragments in many of our images. An example, which shows a very small hydrogen ice fragment is shown in Fig. 5. The imaged ice fragment has a size of ∼2 pixels (FWHM) or ∼0.8 μm. Accordingly, the small ice fragment can be used to estimate the upper limit for the spatial resolution. This example demonstrates that we can achieve sub-micrometer EUV imaging of hydrogen targets with a single FLASH pulse. We have ruled out that the observed structures originate from the intensity distribution within the FEL focus by illuminating samples with homogeneous density and smooth surface. In an EUV-pump EUV-probe experiment, the amount of scattered radiation will rise by more than a factor of two,⁴ as compared to the single exposure reported here.

We have demonstrated an EUV microscope for scattering experiments at the FLASH free-electron laser using a Schwarzschild objective. The design of the EUV microscope allows us to perform sub-micrometer resolved imaging of solid-density hydrogen targets. We were able to acquire images with single pulse exposure using FLASH pulses with a wavelength of 13.5 nm and a pulse energy of 150 μJ. The EUV microscope has a robust mechanical design and can easily be integrated to the experimental platform. These novel imaging capabilities will allow improved experimental studies of EUV heated hydrogen plasmas. For example, single pulse imaging data facilitates intensity-resolved scattering experiments. Moreover, imaging the hydrogen jet with single exposure has revealed the complex geometry of the target that needs to be taken into account in the analysis of the experiments. Further, it might open interesting scientific questions in the formation and crystallization of hydrogen.

More generally, the ability to characterize the micrometer-sized laser-target interaction with sub-picosecond time resolution in the EUV has a wide application range. For example, 68 eV extreme ultraviolet (XUV) plasma emission was employed to infer the plasma temperature,²² but this study was limited to a spatial resolution of ∼10 μm. It becomes possible to perform these studies with sub-μm resolution, yielding information on electron transport and filamentation. Alternatively, choosing the monochromatic reflectivity of the multilayer to match a specific emission line will enable us to resolve transport processes such as ionization fronts or heat flux in mass limited targets, in particular with anisotropic targets such as liquid jets, droplets, and nano-wires.

This work was partially supported by the German Ministry for Education and Research (BMBF) via a Priority Program (Nos. FSP 301 and 302). C. Rödel acknowledges support from the Volkswagen Foundation. The work of T.D. was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. The SLAC HED group is supported by Fusion Energy Sciences under FWP100182. C.F.G. acknowledges support from the European Cluster of Advanced Laser Light Sources (EUCALL) project which has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 654220.