Related papers: On the Bragg Diffraction Spectra of a Meyer Set
The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centred on lattice sites or via a Fourier sum. Here, we argue that representing instead the $\mathit{logarithm}$ of the density…
We study Bragg scattering at 1D atomic lattices. Cold atoms are confined by optical dipole forces at the antinodes of a standing wave generated inside a laser-driven cavity. The atoms arrange themselves into an array of lens-shaped layers…
We construct an electron optical system to investigate Bragg diffraction (the crystal lattice plane, $10^{-2}$-$10^{-3}$ rad) with the objective lens turned off by adjusting the current in the intermediate lenses. A crossover was located on…
Bragg peaks in point set diffraction show up as eigenvalues of a dynamical system. Topological Bragg peaks arrise from topological eigenvalues and determine the torus parametrisation of the point set. We will discuss how qualitative…
A theoretical study of the coherent light scattering from disordered photonic crystal is presented. In addition to the conventional enhancement of the reflected light intensity into the backscattering direction, the so called coherent…
By the m-spectrum of a real number q>1 we mean the set Y^m(q) of values p(q) where p runs over the height m polynomials with integer coefficients. These sets have been extensively investigated during the last fifty years because of their…
We study points in cut-and-project sets which are visible from the origin, continuing a direction of inquiry initiated in [6,14] where the asymptotic density of visible points was investigated. We establish an error bound for the density of…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual Fourier-space formulations of atomicity. The new algorithm implements atomicity constraints in real-space, as well as…
The translation action of $\RR^{d}$ on a translation bounded measure $\omega$ leads to an interesting class of dynamical systems, with a rather rich spectral theory. In general, the diffraction spectrum of $\omega$, which is the carrier of…
Unique intensity features arising from dynamical diffraction arise in coherent x-ray nanobeam diffraction patterns of crystals having thicknesses larger than the x-ray extinction depth or exhibiting combinations of nanoscale and mesoscale…
Two systems are homometric if they are indistinguishable by diffraction. We first make a distinction between Bragg and diffuse scattering homometry, and show that in the last case, coherent diffraction can allow the diffraction diagrams to…
Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…
Properties of a Bose-Einstein condensate were studied by stimulated, two-photon Bragg scattering. The high momentum and energy resolution of this method allowed a spectroscopic measurement of the mean-field energy and of the intrinsic…
For the oblique helicoidal structure of the chiral twist-bend nematic-forming mixture of CB7CB/CB6OCB/5CB doped by light-sensitive chiral compound based on azo-fragment, two consequent states of Bragg reflection of the light in the visible…
We show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems build from locally finite measures on locally compact Abelian groups. This generalizes all earlier results of this type. Our…
We introduce a new class of $\mathcal{PT}$-symmetric complex crystals which are almost transparent and one-way reflectionless over a broad frequency range around the Bragg frequency, i.e. unidirectionally invisible, regardless of the…
When an X-ray area detector based on a single crystalline material, for instance, a state of the art hybrid pixel detector, is illuminated from a point source by monochromatic radiation, a pattern of lines appears which overlays the…
The static diffraction intensity distribution from large material system conceived as perfectly homogeneous system made inhomogeneous, though substitution of groups of atoms, small particles, by other groups of atoms, is explicitly…