X-ray Waveguide Research Articles

Nano-optical theory of planar x-ray waveguides.

X-ray waveguides are routinely used at synchrotron light sources in imaging setups and as a platform for experiments with quantum emitters, providing nanometer-sized confinement - even x-ray optics on a chip has been showcased. X-ray waveguides are weakly guiding and experience significant material absorption, such that the established waveguide theory is not immediately applicable. Here, a general self-contained nano-optical theory of planar waveguides is derived, which is appropriate for hard x-ray energies. Solutions of the electromagnetic fields and its Green's functions are derived in detail. Asymptotic expansions into resonant and non-resonant modes are derived, which are particularly useful in the presence of strong material absorption. A method to reliably find the resonant modes of x-ray waveguide structures is presented. Based on the general theory, certain common experimental geometries, namely evanescent coupling in grazing-incidence, front-coupling in forward-incidence and radiation from buried emitters, are discussed in more detail. Complementing the analytic discussion, numerical tools are provided and applied to quantitatively extract the main figures of merit. The theory provides an analytic foundation for the interpretation of past and future experiments and, combined with the numerical tools, will facilitate the computer-aided design of x-ray waveguides.

Nanoscale Kirkendall shift in thin films studied using x-ray waveguide structures

Kirkendall effect has played an important role in developing the understanding of atomic diffusion and mass transport in solids. In thin films and multilayers, in which the microstructure may be far from thermal equilibrium, behavior of a system can be very different from that of the bulk. Therefore, there is a great need to understand the peculiarities of Kirkendall shift occurring at nanometer or sub-nanometer length scale in such systems. In the present work, Kirkendall shift in thin films has been measured with sub-nanometer accuracy, by making use of x-ray planar waveguide structures. Using this technique, we report an apparently counterintuitive result of Kirkendall shift associated with self-diffusion in nanocrystalline iron. The cavity of the waveguide consists of two layers of iron having different microstructures, separated by a thin marker layer of Ag. Thermal annealing results in shift of the Ag marker towards the Fe layer having a coarser grain structure. The effect is established unambiguously by studying two samples with the order of the two Fe layers reversed, and a third sample with the two Fe layers having the same microstructure. The result can be understood in terms of the difference in the microstructure of the two Fe layers; difference in the grain size and hence different concentration of the grain boundaries in the two layers results in a net mass transfer from one region to the other.

Transient nuclear inversion by x-ray free electron laser in a tapered x-ray waveguide

By restricting the spatial energy transmission of an electromagnetic wave, dielectric waveguides transmit light over long distances at sustained intensity. Waveguides have been used in the microwave and optical range to maintain strong signal intensities in connection with lasers, but guiding of intense short-wavelength radiation such as x-rays has proven more cumbersome. Here we investigate theoretically how tapered x-ray waveguides can focus and guide radiation from x-ray free electron lasers. Elliptical waveguides using a cladding material with high atomic number such as platinum can maintain an x-ray intensity up to three orders of magnitude larger than in free space. This feature can be used to significantly enhance resonant interactions of x-rays, for instance driving nuclear transitions up to transient nuclear population inversion. This could be the first breakthrough in nuclear state population control. Our results anticipate the important role of tapered x-ray waveguides in the emerging field of x-ray quantum optics with nuclear transitions.

X-Ray Structural Analysis of Single Adult Cardiomyocytes: Tomographic Imaging and Microdiffraction

We present a multiscale imaging approach to characterize the structure of isolated adult murine cardiomyocytes based on a combination of full-field three-dimensional coherent x-ray imaging and scanning x-ray diffraction. Using these modalities, we probe the structure from the molecular to the cellular scale. Holographic projection images on freeze-dried cells have been recorded using highly coherent and divergent x-ray waveguide radiation. Phase retrieval and tomographic reconstruction then yield the three-dimensional electron density distribution with a voxel size below 50 nm. In the reconstruction volume, myofibrils, sarcomeric organization, and mitochondria can be visualized and quantified within a single cell without sectioning. Next, we use microfocusing optics by compound refractive lenses to probe the diffraction signal of the actomyosin lattice. Comparison between recordings of chemically fixed and untreated, living cells indicate that the characteristic lattice distances shrink by ∼10% upon fixation.

X-ray tomography with multiple ultranarrow cone beams.

Hollow glass microcapillaries or x-ray waveguides very efficiently confine x-rays to submicron or nanospots, which can be used for point projection imaging. However, x-ray beams exiting from such devices have ultranarrow cones that are limited by the critical angle for the total external reflection to a few milliradians. Narrow cone beams result in small fields of view, and the application of multiple-reflection optics to cone beam tomography is challenging. In this work, we describe a new nonconventional tomographic geometry realized with multiple confocal ultranarrow cone beams. The geometry enables an increase in the effective radiation cone to over 10° without resolution reduction. The proposed tomographic scans can be performed without truncations of the field of view or limitations of the angular range and do not require sample translations, which are inherent to other multibeam x-ray techniques. Volumetric imaging is possible with a simultaneous iterative reconstruction technique or with a fast approximate noniterative two-step approach. A proof-of-principle experiment was performed in the multipoint projection geometry with polycapillary optics and a multi-pinhole mask inserted upstream of the optics. The geometry is suited for phase-contrast tomography with polychromatic laboratory and synchrotron sources.

Interface asymmetry in AlN/Ni and Ni/AlN interfaces: A study using resonant soft X-ray reflectivity

X-ray waveguides are layered structures consisting of a low Z material sandwiched between two high Z materials. The performance of such waveguide structures is influenced by quality of interfaces formed by low and high Z materials. Electric field intensity calculations for Ni/AlN/Ni waveguide structure suggest them as a promising candidate for such applications. We have optimized design parameters of this trilayer structure to trap wave field of 8 keV energy and studied interface properties of two interfaces viz. Ni-on-AlN and AlN-on-Ni by depositing different bilayer samples on Si substrate. AlN-on-Ni bilayer grown on Si substrate gives a good contrast for grazing incidence X-ray reflectivity (GIXRR) measurements using Cu Kα photons but Ni-on-AlN bilayer on Si substrate comes out as a single layer system in GIXRR measurement due to poor contrast between AlN and Si optical constants. To overcome this situation, we have applied resonant soft x-ray reflectivity near Ni L-edge region using soft x-ray reflectivity beamline at Indus-2 synchrotron source. It has been observed that an interlayer is formed in case of AlN-on-Ni interface due to diffusion of AlN or Al and N atoms separately into Ni layer, whereas in case of Ni-on-AlN interface, either AlN molecules or Al and N atoms diffuse into top Ni layer without formation of any interlayer.

Reconstruction of evolving nanostructures in ultrathin films with X-ray waveguide fluorescence holography

Controlled synthesis of nanostructure ultrathin films is critical for applications in nanoelectronics, photonics, and energy generation and storage. The paucity of structural probes that are sensitive to nanometer-thick films and also capable of in-operando conditions with high spatiotemporal resolutions limits the understanding of morphology and dynamics in ultrathin films. Similar to X-ray fluorescence holography for crystals, where holograms are formed through the interference between the reference and the object waves, we demonstrated that an ultrathin film, being an X-ray waveguide, can also generate fluorescence holograms as a result of the establishment of X-ray standing waves. Coupled with model-independent reconstruction algorithms based on rigorous dynamical scattering theories, the thin-film-based X-ray waveguide fluorescence holography becomes a unique in situ and time-resolved imaging probe capable of elucidating the real-time nanostructure kinetics with unprecedented resolutions. Combined with chemical sensitive spectroscopic analysis, the reconstruction can yield element-specific morphology of embedding nanostructures in ultrathin films.

Multi-scale X-ray phase-contrast tomography of murine heart tissue.

The spatial organization of cardiac muscle tissue exhibits a complex structure on multiple length scales, from the sarcomeric unit to the whole organ. Here we demonstrate a multi-scale three-dimensional imaging (3d) approach with three levels of magnification, based on synchrotron X-ray phase contrast tomography. Whole mouse hearts are scanned in an undulator beam, which is first focused and then broadened by divergence. Regions-of-interest of the hearts are scanned in parallel beam as well as a biopsy by magnified cone beam geometry using a X-ray waveguide optic. Data is analyzed in terms of orientation, anisotropy and the sarcomeric periodicity via a local Fourier transformation.

Nanoscale x-ray holotomography of human brain tissue with phase retrieval based on multienergy recordings.

.X-ray cone-beam holotomography of unstained tissue from the human central nervous system reveals details down to subcellular length scales. This visualization of variations in the electron density of the sample is based on phase-contrast techniques using intensities formed by self-interference of the beam between object and detector. Phase retrieval inverts diffraction and overcomes the phase problem by constraints such as several measurements at different Fresnel numbers for a single projection. Therefore, the object-to-detector distance (defocus) can be varied. However, for cone-beam geometry, changing defocus changes magnification, which can be problematic in view of image processing and resolution. Alternatively, the photon energy can be altered (multi-E). Far from absorption edges, multi-E data yield the wavelength-independent electron density. We present the multi-E holotomography at the Göttingen Instrument for Nano-Imaging with X-Rays (GINIX) setup of the P10 beamline at Deutsches Elektronen-Synchrotron. The instrument is based on a combined optics of elliptical mirrors and an x-ray waveguide positioned in the focal plane for further coherence, spatial filtering, and high numerical aperture. Previous results showed the suitability of this instrument for nanoscale tomography of unstained brain tissue. We demonstrate that upon energy variation, the focal spot is stable enough for imaging. To this end, a double-crystal monochromator and automated alignment routines are required. Three tomograms of human brain tissue were recorded and jointly analyzed using phase retrieval based on the contrast transfer function formalism generalized to multiple photon energies. Variations of the electron density of the sample are successfully reconstructed.

Ion-Beam and X-Ray Methods of Elemental Diagnostics of Thin Film Coatings

We show how the combined use of the methods of Rutherford backscattering of ions and X-ray fluorescence analysis under conditions of total external reflection of the flow of exciting hard X-ray radiation and registration of the X-ray radiation output during ion excitation allows to effectively diagnose the elemental composition of thin-film coatings and films of dry residues of liquids. These methods and the features of their experimental application are briefly described. Examples of the complex methodological analysis of real objects are given. The possibility of increasing the efficiency of the methods of X-ray fluorescence analysis of materials due to the inclusion in the X-ray optical schemes of experimental measurements of flat X-ray waveguide resonators is indicated.

The Total-Reflection X-Ray Fluorescence Yield Formed by a Waveguide Resonator under Conditions of Ion Beam Excitation

The features of methods for total-reflection X-ray fluorescence analysis with proton-induced X‑ray fluorescence emission are described. A setup for obtaining X-ray fluorescence spectra under the conditions of proton-beam excitation has been developed using these methods. The setup is based on a specially designed planar X-ray waveguide resonator. The features of the new experimental diagnostic method in the unique research facility (UNU no. 45) of the Sokol-3 analytical ion-beam complex are discussed; some attention has been paid to the description of the capabilities of this facility.

Focus characterization of the NanoMAX Kirkpatrick-Baez mirror system.

The focusing and coherence properties of the NanoMAX Kirkpatrick-Baez mirror system at the fourth-generation MAX IV synchrotron in Lund have been characterized. The direct measurement of nano-focused X-ray beams is possible by scanning of an X-ray waveguide, serving basically as an ultra-thin slit. In quasi-coherent operation, beam sizes of down to 56 nm (FWHM, horizontal direction) can be achieved. Comparing measured Airy-like fringe patterns with simulations, the degree of coherence |μ| has been quantified as a function of the secondary source aperture (SSA); the coherence is larger than 50% for SSA sizes below 11 µm at hard X-ray energies of 14 keV. For an SSA size of 5 µm, the degree of coherence has been determined to be 87%.

Kossel interferences of proton-induced X-ray emission lines to study thin film waveguides

PIXE combined in Kossel geometry was developed as a non-destructive structural characterization method of nanometer thin films deposited on Si. The method is applied to study Pt/Fe/Pt and Ta/Cr/Pt thin films designed as X-ray planar waveguides. The intensities of characteristic X-ray emissions versus the detection angle (grazing exit), called Kossel curves, were measured by an energy dispersive X-ray camera. It is found that an interfacial compound is formed in Pt/Fe/Pt waveguide, whereas oxidation and mixing occur in the Ta/Cr/Pt system. It was not possible to obtain the description of the successive layers when considering only grazing incidence x-ray reflectivity. When PIXE-Kossel experiments are considered, supplementary constraints have to be fulfilled when fitting the values of the stack parameters (number, composition, thickness, roughness and density of the layers) which restrict the possible descriptions of waveguides. Thus PIXE-Kossel is suitable to characterize stacks of nanometer thin films designed as an x-ray waveguide.

A beamline-compatible STED microscope for combined visible-light and X-ray studies of biological matter.

A dedicated stimulated emission depletion (STED) microscope had been designed and implemented into the Göttingen Instrument for Nano-Imaging with X-rays (GINIX) at the synchrotron beamline P10 of the PETRA III storage ring (DESY, Hamburg). The microscope was installed on the same optical table used for X-ray holography and scanning small-angle X-ray scattering (SAXS). Scanning SAXS was implemented with the Kirkpatrick-Baez (KB) nano-focusing optics of GINIX, while X-ray holography used a combined KB and X-ray waveguide optical system for full-field projection recordings at a defocus position of the object. The STED optical axis was aligned (anti-)parallel to the focused synchrotron beam and was laterally displaced from the KB focus. This close proximity between the STED and the X-ray probe enabled in situ combined recordings on the same biological cell, tissue or any other biomolecular sample, using the same environment and mounting. Here, the instrumentation and experimental details of this correlative microscopy approach are described, as first published in our preceding work [Bernhardt et al. (2018), Nat. Commun. 9, 3641], and the capabilities of correlative STED microscopy, X-ray holography and scanning SAXS are illustrated by presenting additional datasets on cardiac tissue cells with labeled actin cytoskeleton.

Time-resolved x-ray phase-contrast tomography of sedimenting micro-spheres

We have implemented a time-dependent (dynamic) x-ray tomography of sedimenting micro-spheres suspended in water. To achieve phase contrast at high magnification we use the divergent and highly coherent beam emitted from an x-ray waveguide. Holograms are recorded with 5 ms acquisition time while the sample is rotated at 1 Hz, over a run of 40 s. We show that under these conditions, more than 20 000 individual particle trajectories can be tracked. The analysis of the trajectories shows apparent super-diffusive behavior due to collective flow patterns, as also further evidenced by plotting the temporal averaged spatial distribution of particle densities and velocities.

Towards x-ray waveguide formation upon ion irradiation of a Co thin film on Si(111)

We have obtained the essential features of x-ray waveguide formation in an ion-irradiated cobalt thin film on Si substrate. Ion irradiation was carried out with 1 MeV Si+ ions at a fluence of 5 × 1016 ions cm−2. X-ray reflectivity (XRR) experiment shows characteristic dips in the total external reflection region indicating formation of resonant electromagnetic modes—an essential requirement for x-ray waveguides. XRR analysis further reveals formation of a low electron-density layer sandwiched between higher electron-density layers. These are two key requirements for an x-ray waveguide. Computation of x-ray intensity within the irradiated sample shows about 15 times flux enhancement of the electric field within the low electron-density guiding layer.

Ионно-пучковые и рентгеновские методы элементной диагностики тонкопленочных покрытий

Abstract We show how the combined use of the methods of Rutherford backscattering of ions and X-ray fluorescence analysis under conditions of total external reflection of the flow of exciting hard X-ray radiation and registration of the X-ray radiation output during ion excitation allows to effectively diagnose the elemental composition of thin-film coatings and films of dry residues of liquids. These methods and the features of their experimental application are briefly described. Examples of the complex methodological analysis of real objects are given. The possibility of increasing the efficiency of the methods of X-ray fluorescence analysis of materials due to the inclusion in the X-ray optical schemes of experimental measurements of flat X-ray waveguide resonators is indicated.

Three-dimensional virtual histology of human cerebellum by X-ray phase-contrast tomography

To quantitatively evaluate brain tissue and its corresponding function, knowledge of the 3D cellular distribution is essential. The gold standard to obtain this information is histology, a destructive and labor-intensive technique where the specimen is sliced and examined under a light microscope, providing 3D information at nonisotropic resolution. To overcome the limitations of conventional histology, we use phase-contrast X-ray tomography with optimized optics, reconstruction, and image analysis, both at a dedicated synchrotron radiation endstation, which we have equipped with X-ray waveguide optics for coherence and wavefront filtering, and at a compact laboratory source. As a proof-of-concept demonstration we probe the 3D cytoarchitecture in millimeter-sized punches of unstained human cerebellum embedded in paraffin and show that isotropic subcellular resolution can be reached at both setups throughout the specimen. To enable a quantitative analysis of the reconstructed data, we demonstrate automatic cell segmentation and localization of over 1 million neurons within the cerebellar cortex. This allows for the analysis of the spatial organization and correlation of cells in all dimensions by borrowing concepts from condensed-matter physics, indicating a strong short-range order and local clustering of the cells in the granular layer. By quantification of 3D neuronal "packing," we can hence shed light on how the human cerebellum accommodates 80% of the total neurons in the brain in only 10% of its volume. In addition, we show that the distribution of neighboring neurons in the granular layer is anisotropic with respect to the Purkinje cell dendrites.

Peculiarities in the Formation of X-Ray Fluxes by Waveguide–Resonators of Different Construction

The phenomenon of total external reflection (TER) of quasi-monochromatic X-ray radiation fluxes on a material interface and the effect of waveguide–resonator propagation of these fluxes in nanosize extended slit clearance, as well as a device operating on the basis of this effect—a planar X-ray waveguide–resonator—are briefly described. Experimental data on the formation of an X-ray flux by a composite X-ray waveguide–resonator are presented, and a model describing the decrease in the angular divergence of the formed flux without a decrease in the integral intensity is proposed. The model is based on the conception of partial angular tunneling of the radiation flux in the gap between two consequently mounted and mutually adjusted waveguide–resonators; the tunneling is implemented due to the interaction between interference fields of standing X-ray waves excited by the radiation transported by the slit clearance of these waveguide–resonators.

Diffractive X-ray Waveguiding Reveals Orthogonal Crystalline Stratification in Conjugated Polymer Thin Films

The depth dependence of crystalline structure within thin films is critical for many technological applications, but has been impossible to measure directly using common techniques. In this work, by monitoring diffraction peak intensity and location and utilizing the highly angle-dependent waveguiding effects of X-rays near grazing incidence we quantitatively measure the thickness, roughness and orientation of stratified crystalline layers within thin films of a high-performance semiconducting polymer. In particular, this diffractive X-ray waveguiding reveals a self-organized 5-nm-thick crystalline surface layer with crystalline orientation orthogonal to the underlying 65-nm-thick layer. While demonstrated for an organic semiconductor film, this approach is applicable to any thin film material system where stratified crystalline structure and orientation can influence important interfacial processes such as charge injection and field-effect transport.