Wave scattering theory applied to inversion and design
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- Institutt for fysikk 
The scattering of waves from objects can be used as a tool for both characterization and manipulation. The way waves interact and scatter from objects can give us information about their structure and composition. Additionally, the interaction itself can be used to form and change the incident beam. Physical waves come in many forms, be it acoustic waves or electromagnetic waves. Even atoms can be treated as waves through the de Broglie formalism with short, sub-Ångström wavelengths. In this work, several methods for inverting experimental wave scattering results are investigated. The main emphasis has been on waves in the sub-Ångström regime, corresponding to the energy of so-called thermal atom beams. Models for beam shaping and holographic systems are also discussed, with the goal of using them for atom lithography. Helium atom scattering is a surface sensitive characterization technique that can be used for both elastic and inelastic measurements, measuring either geometric properties or dynamical properties of the surface. We present results of elastic helium atom diffraction experiments and compare them to simulations to uncover the geometry of a photonic crystal membrane and characterize the atom source used. The observed behavior of the atom source is consistent with results from other more direct measurements. Inelastic helium scattering is used to measure the surface phonons of a 2D silica film. Through analysis of the experimental results, we were able to extract the bending rigidity of the film, which showed elastic properties comparable to those of macroscopic silica. This is only the second time the bending rigidity of a 2D material has been measured experimentally, and the first time for a material with more than one layer of atoms. The fact that we can show that the material behaves as would be expected from classical mechanics is an important result that sheds new light on the Yakobson’s paradox. A model for obtaining the morphological parameters of a plasmonic photonic crystal from ellipsometric measurements is also presented and compared with SEM and AFM measurements. The method is based on the reduced Rayleigh equation, which makes it computationally efficient, while providing accurate results. Any non-flat surface can be described as rough. Many natural and manufactured surfaces show no periodic structure and can be described as randomly rough. Randomly rough surfaces are typically described by their statistical properties. In this work, we present a numerical method for obtaining the full angular intensity distribution of a scalar beam scattered from a two-dimensional surface. The method is used to investigate the scattering behavior of both isotropic and anisotropic randomly rough surfaces. Both Dirichlet and Neumann boundary conditions are considered in the scattering problem. This rigorous numerical method is time- consuming and may not be well suited for inverting experimental data. An analytical method based on the Kirchhoff approximation for finding the scalar wave scattering from self-affine surfaces is presented. This analytical method is applied to parameter retrieval and compares well with results from the rigorous numerical simulations. The very short wavelength of atoms can not only be used as a high-resolution probe for characterizing a surface, it can also be used to create high-resolution lithography patterns. We discuss a method of forming arbitrary intensity patterns with atoms called grid-based binary holograms. We present a study of the behavior of grid-based binary holograms, with focus on the open fraction of the masks. Simulation results of high-resolution patterns are shown for both a plane incident wave, as well as for an incident wave based on a virtual source model. It is shown that patterns with nanometer resolution could in principle be generated with present day atom sources, and it is demonstrated for the first time that atom lithography could be a realistic and much cheaper alternative to the extreme ultra violet photonic light source for next generation ultra-high-resolution lithography. A novel extension of grid-based holography for hexagonal substrates is also presented.