arXiv subjects

Ingve Simonsen

Publications and source records attributed to Ingve Simonsen.

At least 19 recordsLinked to original sources

arXiv2025

Turbulent Dynamics in Active Solids

Turbulence is most commonly associated with high Reynolds number flow, however the framework of turbulent dynamics has been conceptually extended to many other fields, such as magnetohydrodynamic turbulence, elastic wave turbulence in solids, and more recently to low Reynolds number active turbulence in biological fluids. Here we report a form of solid turbulent dynamics in a self-propelled two-dimensional elastic sheet. We show numerically that the polar ordering dynamics in the active elastic solid model (AES) exhibit hallmark features of turbulent dynamics: power-law scaling of the energy spectrum and non-Gaussian statistics of velocity increments. However, there is no energy cascade, in line with previous findings for active turbulence in fluids. These results extend the concept of active turbulence to solid-state active matter, and can be important for understanding collective dynamics in biological active solids such as bacterial colonies and epithelial cell layers.

cond-mat.soft↗

arXiv2023

Eigenmodes of fractal drums: A numerical student experiment

``Can one hear the shape of a drum?'' was a question posed (and made famous) by mathematician Mark Kac in the mid-1960s. It addresses whether a deeper connection exists between the resonance modes (eigenmodes) of a drum and its shape. Here we propose a numerical experiment, suitable for advanced undergraduate physics students, on the calculation of the eigenmodes of a square Koch fractal drum, for which experimental results do exist. This exercise is designed to develop the students' understanding of the vibrations of fractal drums, their eigenmodes, and potentially their integrated density of states. The students calculate the lowest order eigenmodes of the fractal drum, visualize these modes, and study their symmetry properties. As an extension, the students may investigate the integrated density of states of the fractal drum and compare their findings to the Weyl-Berry conjecture.

physics.ed-ph↗

arXiv2023

Degree of polarization of light scattered from correlated surface and bulk disorders

Using a single-scattering theory, we derive the expression of the degree of polarization of the light scattered from a layer exhibiting both surface and volume scattering. The expression puts forward the intimate connection between the degree of polarization and the statistical correlation between surface and volume disorders. It also permits a quantitative analysis of depolarization for uncorrelated, partially correlated and perfectly correlated disorders. We show that measuring the degree of polarization could allow one to assess the surface-volume correlation function, and that, reciprocally, the degree of polarization could be engineered by an appropriate design of the correlation function.

physics.optics↗

arXiv2023

Haze and light diffraction of dielectric line-gratings

The optical characterization of dielectric periodic line-gratings for which the period of the grating is significantly larger than the probing wavelength is investigated experimentally, numerically, and analytically. The experimental diffraction efficiencies are analyzed in transmission with the help of a closed-form approximate solution within a single scattering picture. In particular, the angular width of significant scattering and the haze are analyzed for samples of increasing grating profile amplitude.

physics.optics↗

arXiv2022

Atom binary holography at a finite distance: Resolution, contrast and flux

In classical binary holography, a target pattern located at infinity is generated by the diffraction of a plane wave passing through a binary mask with holes of the same size, placed at specific positions of a rectangular grid. Fresnel binary atom holography was recently proposed as a means for achieving nanometer-resolution mask-based lithography with metastable atom beams. In practice, there will be fabrication imposed limits: the binary mask will have a minimum hole size, a minimum distance between the holes in the grid~(pitch), a maximum size, and the target pattern plane will always have a finite distance from the mask. In this paper, we show that, in praxis, for a given wavelength, mask, and target pattern sizes, there will be a cross-over value for the distance between the mask and the target pattern plane (the screen plane) which results in aliasing-free patterns. It is demonstrated how this insight can lead to the generation of better-resolved patterns of higher contrast and nanometer resolution can be achieved within experimental limitations. Since flux is one of the main factors influencing the quality of patterns fabricated by nano-lithography, we obtain an expression for the ``patterning flux'' (the flux that contributes to producing the target pattern, normalized by the flux that is incident onto the structured portion of the mask). Numerically we find that its ratio scales approximately like $x^{-2}$ where $x$ is the mask-screen distance over the cross-over distance. The method that we propose can be used with any beam that can be modeled as a scalar wave, including acoustic waves and other matter-wave beams such as helium ions or electrons.

physics.optics↗

arXiv2022

Observation of the Boson Peak in a 2D Material

The boson peak is an excess in the phonon density of states relative to the Debye Model, which occurs at frequencies below the Debye limit. It is present in most amorphous materials and, as was recently shown, can sometimes be found also in crystals. Here we present first experimental evidence of the boson peak in a 2D material, namely 2D silica (SiO$_2$). The measurements were obtained by helium atom scattering. A dispersionless boson peak is seen at $6 \pm 0.5$ meV (1.5$ \pm$ 0.15 THz) and $-6 \pm 1.5$ meV ($-1.5 \pm 0.4$ THz), with reasonable evidence for a double excitation at $\pm 12 \pm 2.5$ meV ($2.9 \pm 0.6$ THz).

cond-mat.mtrl-sci↗

arXiv2021

Non-parametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data: Application to computer generated and experimental scattering data

An approach is introduced for the non-parametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data. Starting from expressions within the Kirchhoff approximation for the light scattered diffusely by a two-dimensional randomly rough surface, an analytic expression for the normalized surface height correlation function is obtained as an integral over the in-plane and co-polarized scattering data with the introduction of only a couple of additional approximations. The inversion approach consists of two main steps. In the first step the surface roughness is estimated. Next, this value is used to obtain the functional form of the surface height correlation function without initially assuming any particular form for this function (non-parametric inversion). The input data used in validating this inversion approach consist of in-plane and co-polarized scattering data obtained for different forms of the correlation function by either computer simulations or by experiments for two-dimensional randomly rough dielectric or metallic surfaces. Good agreement was obtained between the correlation function and surface roughness obtained during the reconstruction and the corresponding quantities assumed when generating the input scattering data; this was the case for both dielectric and metallic surfaces, for both p- and s-polarized light, and for different polar angles of incidence. The proposed inversion approach provides an accurate, efficient, robust and contact-less method based on in-plane and co-polarized scattering data for the non-parametric characterization of the statistical properties of isotropic two-dimensional randomly rough dielectric and metallic surface.

physics.optics↗

arXiv2020

Perfect depolarization in single scattering of light from uncorrelated surface and volume disorder

We demonstrate that single scattering of p-polarized waves from uncorrelated surface and volume disorder can lead to perfect depolarization. The degree of polarization is shown to vanish in specific scattering directions that can be characterized based on simple geometric arguments. Depolarization results from the different polarization response of each source of disorder, providing a clear physical interpretation of the depolarization mechanism.

physics.optics↗

arXiv2018

Experimental studies of the transmission of light through low coverage regular or random arrays of silica micropillars supported by a glass substrate

The transmission of light through low coverage regular and random arrays of glass supported silica micropillars of diameters 10 to 40 \micro\meter and height 10 \micro\meter is studied experimentally. Angle-resolved measurements of the transmitted intensity are performed at visible wavelengths by either a goniospectrophotometer or a multimodal imaging (Mueller) polarimetric microscope. It is demonstrated that for the regular arrays, the angle-resolved measurements are capable of resolving many of the densely packed diffraction orders that are expected for periodic structures of lattice constants 20 to 80 \micro\meter, but they also display features that are due to the scattering and guiding of light in individual micropillars or in the supporting glass slides. These latter features are also found in angle-resolved measurements on random arrays of micropillars of the same surface coverage. Finally we perform a comparison of direct measurements of haze in transmission for our patterned glass samples with what can be calculated from the angle-resolved transmitted intensity measurements. Good agreement between the two types of results are found which testifies to the accuracy of the angle-resolved measurements that we report.

physics.optics↗

arXiv2018

Physics of polarized light scattering from weakly rough dielectric surfaces: Yoneda and Brewster scattering phenomena

The optical Yoneda and Brewster scattering phenomena are studied theoretically based on pertubative solutions of the reduced Rayleigh equations. The Yoneda phenomenon is characterized as an enhancement of the intensity of the diffuse light scattered by a randomly rough interface between two dielectric media when the light is observed in the optically denser medium. The intensity enhancement occurs above a critical angle of scattering which is independent of the angle of incidence of the excitation. The Brewster scattering phenomenon is characterized by a zero scattered intensity either in the reflected or transmitted light for an angle of scattering which depends on the angle of incidence. We also describe a generalization of the Brewster scattering phenomenon for outgoing evanescent waves and circularly-polarized waves. The physical mechanisms responsible for these phenomena are described in terms of simple notions such as scalar waves, oscillating and rotating dipoles and geometrical arguments, and are valid in a regime of weakly rough interfaces.

physics.optics↗

arXiv2018

Nanometer resolution mask lithography with matter waves: Near-field binary holography

Mask-based pattern generation is a crucial step in microchip production. The next-generation extreme-ultraviolet- (EUV) lithography instruments with a wavelength of \SI{13.5}{\nano\meter} is currently under development. In principle, this should allow patterning down to a resolution of a few nanometers in a single exposure. However, there are many technical challenges, including those due to the very high energy of the photons. Lithography with metastable atoms has been suggested as a cost-effective, less-complex alternative to EUV lithography. The great advantage of atom lithography is that the kinetic energy of an atom is much smaller than that of a photon for a given wavelength. However, up till now no method has been available for making masks for atom lithography that can produce arbitrary, high resolution patterns. Here we present a solution to this problem. First, traditional binary holography is extended to near-field binary holography, based on Fresnel diffraction. By this technique, we demonstrate that it is possible to make masks that can generate arbitrary patterns in a plane in the near field (from the mask) with a resolution down to the nanometer range using a state of the art metastable helium source. We compare the flux of this source to that of an established EUV source (ASML, NXE:3100) and show that patterns can potentially be produced at comparable speeds. Finally, we present an extension of the grid-based holography method for a grid of hexagonally shaped subcells. Our method can be used with any beam that can be modeled as a scalar wave, including other matter-wave beams such as helium ions, electrons or acoustic waves.

physics.app-ph↗

arXiv2018

Features in the diffraction of a scalar plane wave from doubly-periodic Dirichlet and Neumann surfaces

The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of the diffracted Bragg beams. From the results of these calculations the diffraction efficiencies of several of the lowest order diffracted beams are calculated as functions of the polar and azimuthal angles of incidence. The angular dependencies of the diffraction efficiencies display features that can be identified as Rayleigh anomalies for both types of surfaces. In the case of a Neumann surface additional features are present that can be attributed to the existence of surface waves on such surfaces. Some of the results obtained through the use of the Rayleigh equation are validated by comparing them with results of a rigorous Green's function numerical calculation.

physics.optics↗

arXiv2017

The scattering of a scalar beam from isotropic and anisotropic two-dimensional randomly rough Dirichlet or Neumann surfaces: The full angular intensity distributions

By the use of Green's second integral identity we determine the field scattered from a two-dimensional randomly rough isotropic or anisotropic Dirichlet or Neumann surface when it is illuminated by a scalar Gaussian beam. The integral equations for the scattering amplitudes are solved nonperturbatively by a rigorous computer simulation approach. The results of these calculations are used to calculate the full angular distribution of the mean differential reflection coefficient. For isotropic surfaces, the results of the present calculations for in-plane scattering are compared with those of earlier studies of this problem. The reflectivities of Dirichlet and Neumann surfaces are calculated as functions of the polar angle of incidence, and the reflectiveties for the two kinds of surfaces of similar roughness parameters are found to be different. For an increasing level of surface anisotropy, we study how the angular intensity distributions of the scattered waves are affected by this level. We find that even small to moderate levels of surface anisotropy can significantly alter the symmetry, shape, and amplitude of the scattered intensity distributions when Gaussian beams are incident on the anisotropic surfaces from different azimuthal angles of incidence.

physics.optics↗

arXiv2017

Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces and its application to the retrieval of self-affine parameters

Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces is studied for the purpose of using the intensity scattered from them to obtain the Hurst exponent and topothesy that characterize the self-affine roughness. By the use of the Kirchhoff approximation a closed form mathematical expression for the angular dependence of the mean differential reflection coefficient is derived under the assumption that the surface is illuminated by a plane incident wave. It is shown that this quantity can be expressed in terms of the isotropic, bivariate ($\alpha$-stable) L\'evy distribution of a stability parameter that is two times the Hurst exponent of the underlying surface. Features of the expression for the mean differential reflection coefficient are discussed, and its predictions compare favorably over large regions of parameter space to results obtained from rigorous computer simulations based on equations of scattering theory. It is demonstrated how the Hurst exponent and the topothesy of the self-affine surface can be inferred from scattering data it produces. Finally several possible scattering configurations are discussed that allow for an efficient extraction of these self-affine parameters.

physics.class-ph↗

arXiv2017

Replacement of ensemble averaging by the use of a broadband source in scattering of light from a one-dimensional randomly rough interface between two dielectric media

By the use of phase perturbation theory we show that if a single realization of a one-dimensional randomly rough interface between two dielectric media is illuminated at normal incidence from either medium by a broadband Gaussian beam, it produces a scattered field whose differential reflection coefficient closely matches the result produced by averaging the differential reflection coefficient produced by a monochromatic incident beam over the ensemble of realizations of the interface profile function.

physics.optics↗

arXiv2017

Selective enhancement of Sel\'enyi rings induced by the cross-correlation between the interfaces of a two-dimensional randomly rough dielectric film

By the use of both perturbative and non-perturbative solutions of the reduced Rayleigh equation, we present a detailed study of the scattering of light from two-dimensional weakly rough dielectric films. It is shown that for several rough film configurations, Sel\'enyi interference rings exist in the diffusely scattered light. For film systems supported by dielectric substrates where only one of the two interfaces of the film is weakly rough and the other planar, Sel\'enyi interference rings are observed at angular positions that can be determined from simple phase arguments. For such single-rough-interface films, we find and explain by a single scattering model that the contrast in the interference patterns is better when the top interface of the film (the interface facing the incident light) is rough than when the bottom interface is rough. When both film interfaces are rough, Sel\'enyi interference rings exist but a potential cross-correlation of the two rough interfaces of the film can be used to selectively enhance some of the interference rings while others are attenuated and might even disappear. This feature may in principle be used in determining the correlation properties of interfaces of films that otherwise would be difficult to access.

physics.optics↗

arXiv2017

On the optimal design of grid-based binary holograms for matter wave lithography

Grid based binary holography (GBH) is an attractive method for patterning with light or matter waves. It is an approximate technique in which different holographic masks can be used to produce similar patterns. Here we present an optimal design method for GBH masks that allows for freely selecting the fraction of open holes in the mask from below 10% to above 90%. Open-fraction is an important design parameter when making masks for use in lithography systems. The method also includes a rescaling feature that potentially enables a better contrast of the generated patterns. Through simulations we investigate the contrast and robustness of the patterns formed by masks generated by the proposed optimal design method. It is demonstrated that high contrast patterns are achievable for a wide range of open-fractions. We conclude that reaching a desired open-fraction is a trade-off with the contrast of the pattern generated by the mask.

physics.optics↗

arXiv2017

Neutral Helium Atom Diffraction from a Micron Scale Periodic Structure: Photonic Crystal Membrane Characterization

Surface scattering of neutral helium beams created by supersonic expansion is an established technique for measuring structural and dynamical properties of surfaces on the atomic scale. Helium beams have also been used in Fraunhofer and Fresnel diffraction experiments. Due to the short wavelength of the atom beams of typically 0.1nm or less, Fraunhofer diffraction experiments in transmission have so far been limited to grating structures with a period (pitch) of up to 200nm. However, larger periods are of interest for several applications, for example for the characterization of photonic crystal membrane structures, where the period is typically in the micron/high sub-micron range. Here we present helium atom diffraction measurements of a photonic crystal membrane structure with a two dimensional square lattice of 100x100 circular holes. The nominal period and hole radius were 490nm and 100nm respectively. To our knowledge this is the largest period that has ever been measured with helium diffraction. The helium diffraction measurements are interpreted using a model based on the helium beam characteristics. It is demonstrated how to successfully extract values from the experimental data for the average period of the grating, the hole diameter and the width of the virtual source used to model the helium beam.

physics.class-ph↗