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Register a new userGrazing incidence interferometry for rough convex aspherics
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Grazing incidence interferometry has been applied to rough planar and cylindrical surfaces. As suitable beam splitters diffractive optical phase elements are quite common because these allow for the same test sensitivity for all surface points. But a rotational-symmetric convex aspheric has two curvatures which reduces the measurable region to a meridian through the vortex of the aspheric, which is in contrast to cylindrical surfaces having a one-dimensional curvature which allows the test of the whole surface in gracing incidence. The meridional limitation for rotational-symmetric aspherics nevertheless offers the possibility to measure single meridians in a one-step measurement. An extension to the complete surface can be obtained by rotating the aspheric around its vortex within the frame of the test interferometer.
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Electromagnetic waves at grazing incidence onto a planar medium are analogous to zero energy quantum particles incident onto a potential well. In this limit waves are typically completely reflected. Here we explore dielectric profiles supporting optical analogues of `half-bound states, allowing for zero reflection at grazing incidence. To obtain these profiles we use two different theoretical approaches: supersymmetric quantum mechanics, and direct inversion of the Helmholtz equation.
We here report coherent reflection of thermal He atom beams from various microscopically rough surfaces at grazing incidence. For a sufficiently small normal component $k_z$ of the incident wave-vector of the atom the reflection probability is found to be a function of $k_z$ only. This behavior is explained by quantum-reflection at the attractive branch of the Casimir-van der Waals interaction potential. For larger values of $k_z$ the overall reflection probability decreases rapidly and is found to also depend on the parallel component $k_x$ of the wave-vector. The material specific $k_x$ dependence for this classical reflection at the repulsive branch of the potential is explained qualitatively in terms of the averaging-out of the surface roughness under grazing incidence conditions.
Diffraction patterns produced by grazing scattering of fast atoms from insulator surfaces are used to examine the atom-surface interaction. The method is applied to He atoms colliding with a LiF(001) surface along axial crystallographic channels. The projectile-surface potential is obtained from an accurate DFT calculation, which includes polarization and surface relaxation. For the description of the collision process we employ the surface eikonal approximation, which takes into account quantum interference between different projectile paths. The dependence of projectile spectra on the parallel and perpendicular incident energies is experimentally and theoretically analyzed, determining the range of applicability of the proposed model.
We theoretically address grazing incidence fast atom diffraction (GIFAD) for H atoms impinging on a LiF(001) surface. Our model combines a description of the H-LiF(001) interaction obtained from Density Functional Theory calculations with a semi-quantum treatment of the dynamics. We analyze simulated diffraction patterns in terms of the incidence channel, the impact energy associated with the motion normal to the surface, and the relevance of Van der Waals (VdW) interactions. We then contrast our simulations with experimental patterns for different incidence conditions. Our most important finding is that, for normal energies lower than 0.5 eV and incidence along the <100> channel, the inclusion of Van der Waals interactions in our potential energy surface yields a greatly improved accord between simulations and experiments. This agreement strongly suggests a non-negligible role of Van der Waals interactions in H/LiF(001) GIFAD in the low-to-intermediate normal energy regime.
For the reliable fabrication of the current and next generation of nanostructures it is essential to be able to determine their material composition and dimensional parameters. Using the grazing incidence X-ray fluoresence technique, which is taking advantage of the X-ray standing wave field effect, nanostructures can be investigated with a high sensitivity with respect to the structural and elemental composition. This is demonstrated using lamellar gratings made of Si$_3$N$_4$. Rigorous field simulations obtained from a Maxwell solver based on the finite element method allow to determine the spatial distribution of elemental species and the geometrical shape with sub-nm resolution. The increasing complexity of nanostructures and demanded sensitivity for small changes quickly turn the curse of dimensionality for numerical simulation into a problem which can no longer be solved rationally even with massive parallelisation. New optimization schemes, e.g. machine learning, are required to satisfy the metrological requirements. We present reconstruction results obtained with a Bayesian optimization approach to reduce the computational effort.
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