Search Results
Real-time spatial characterization of micrometer-sized X-ray free-electron laser beams focused by bendable mirrors
A real-time and accurate characterization of the X-ray beam size is essential to enable a large variety of different experiments at free-electron laser facilities. Typically, ablative imprints are employed to determine shape and size of μm-focused X-ray beams. The high accuracy of this state-of-the-art method comes at the expense of the time required to perform an ex-situ image analysis. In contrast, diffraction at a curved grating with suitably varying period and orientation forms a magnified image of the X-ray beam, which can be recorded by a 2D pixelated detector providing beam size and pointing jitter in real time. In this manuscript, we compare results obtained with both techniques, address their advantages and limitations, and demonstrate their excellent agreement. We present an extensive characterization of the FEL beam focused to ≈1 μm by two Kirkpatrick-Baez (KB) mirrors, along with optical metrology slope profiles demonstrating their exceptionally high quality. This work provides a systematic and comprehensive study of the accuracy provided by curved gratings in real-time imaging of X-ray beams at a free-electron laser facility. It is applied here to soft X-rays and can be extended to the hard X-ray range. Furthermore, curved gratings, in combination with a suitable detector, can provide spatial properties of μm-focused X-ray beams at MHz repetition rate.
Modeling of line roughness and its impact on the diffraction intensities and the reconstructed critical dimensions in scatterometry
We investigate the impact of line edge and line width roughness (LER, LWR) on the measured diffraction intensities in angular resolved extreme ultraviolet (EUV) scatterometry for a periodic line-space structure designed for EUV lithography. LER and LWR with typical amplitudes of a few nanometers were previously neglected in the course of the profile reconstruction. The 2D rigorous numerical simulations of the diffraction process for periodic structures are carried out with the finite element method (FEM) providing a numerical solution of the two-dimensional Helmholtz equation. To model roughness, multiple calculations are performed for domains with large periods, containing many pairs of line and space with stochastically chosen line and space widths. A systematic decrease of the mean efficiencies for higher diffraction orders along with increasing variances is observed and established for different degrees of roughness. ...
Transient magnetic gratings on the nanometer scale
Laser-driven non-local electron dynamics in ultrathin magnetic samples on a sub-10 nm length scale is a key process in ultrafast magnetism. However, the experimental access has been challenging due to the nanoscopic and femtosecond nature of such transport processes. Here, we present a scattering-based experiment relying on a laser-induced electro- and magneto-optical grating in a Co/Pd ferromagnetic multilayer as a new technique to investigate non-local magnetization dynamics on nanometer length and femtosecond timescales. We induce a spatially modulated excitation pattern using tailored Al near-field masks with varying periodicities on a nanometer length scale and measure the first four diffraction orders in an x-ray scattering experiment with magnetic circular dichroism contrast at the free-electron laser facility FERMI, Trieste. The design of the periodic excitation mask leads to a strongly enhanced and characteristic transient scattering response allowing for sub-wavelength in-plane sensitivity for magnetic structures. In conjunction with scattering simulations, the experiment allows us to infer that a potential ultrafast lateral expansion of the initially excited regions of the magnetic film mediated by hot-electron transport and spin transport remains confined to below three nanometers.
Direct and inverse elastic scattering problems for diffraction gratings
This paper is concerned with the direct and inverse scattering of time-harmonic plane elastic waves by unbounded periodic structures (diffraction gratings). We present a variational approach to the forward scattering problems with Lipschitz grating profiles and give a survey of recent uniqueness and existence results. We also report on recent global uniqueness results within the class of piecewise linear grating profiles for the corresponding inverse elastic scattering problems. Moreover, a discrete Galerkin method is presented to efficiently approximate solutions of direct scattering problems via an integral equation approach. Finally, an optimization method for solving the inverse problem of recovering a 2D periodic structure from scattered elastic waves measured above the structure is discussed.
On a fast integral equation method for diffraction gratings
The integral equation method for the simulation of the diffraction by optical gratings is an efficient numerical tool if profile gratings determined by simple cross-section curves are considered. This method in its recent version is capable to tackle profile curves with corners, gratings with thin coated layers, and diffraction scenarios with unfavorably large ratios period over wavelength. We discuss special implementational issues including the efficient evaluation of the quasi-periodic Green kernels, the quadrature algorithm, and the iterative solution of the arising systems of linear equations. Finally, as application we present the simulation of coated echelle gratings which demonstrates the efficency of our approach.
Inverse scattering of elastic waves by periodic structures : uniqueness under the third or fourth kind boundary conditions
The inverse scattering of a time-harmonic elastic wave by a two-dimensional periodic structure in R 2 is investigated. The grating profile is assumed to be a graph given by a piecewise linear function on which the third or fourth kind boundary conditions are satisfied. Via an equivalent variational formulation, existence of quasi-periodic solutions for general Lipschitz grating profiles is proved by applying the Fredholm alternative. However, uniqueness of solution to the direct problem does not hold in general. For the inverse problem, we determine and classify all the unidentifiable grating profiles corresponding to a given incident elastic field, relying on the reflection principle for the Navier equation and the rotational invariance of propagating directions of the total field. Moreover, global uniqueness for the inverse problem is established with a minimal number of incident pressure or shear waves, including the resonance case where a Rayleigh frequency is allowed. The gratings that are unidentifiable by one incident elastic wave provide non-uniqueness examples for appropriately chosen wave number and incident angles