Related papers: On the Bragg Diffraction Spectra of a Meyer Set

We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures…

The understanding of how the arrangement of defects in photonic crystals impacts its photonic properties is cru-cial for the design of functional materials based thereon. By preparing photonic crystals with random missing scatterers we…

The paper shows that silicon-based 2D photonic crystal can be a promising material for acoustooptical devices. Isotropic and anisotropic Bragg diffraction of light in photonic crystal is considered. The computational method for calculation…

Antiferromagnetism of ultracold fermions in an optical lattice can be detected by Bragg diffraction of light, in analogy to the diffraction of neutrons from solid state materials. A finite sublattice magnetization will lead to a Bragg peak…

It is well known that almost every dilation of a sequence of real numbers, that diverges to $\infty$, is dense modulo~1. This paper studies the exceptional set of points -- those for which the dilation is not dense. Specifically, we…

The Bragg glass phase is a nearly perfect crystal with glassy features predicted to occur in vortex lattices and charge density wave systems in the presence of disorder. Detecting it has been challenging despite its sharp theoretical…

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…

Light propagation in a photonic crystal infiltrated with polarizable molecules is considered. We demonstrate that the interplay between the spatial dispersion caused by Bragg diffraction and polaritonic frequency dispersion gives rise to…

We prove that crystalline points are dense in the spectrum of the completed Hecke algebra on unitary Shimura varieties.

The aim of this paper is to show the usefulness of Meyer wavelets for the classical problem of density estimation and for density deconvolution from noisy observations. By using such wavelets, the computation of the empirical wavelet…

The problem of changing the energy of a neutron when it passes through an accelerating crystal under conditions close to the Bragg condition is considered. It is shown that, similar to the case of the passage of long-wavelength neutrons…

The use of retro-reflection in light-pulse atom interferometry under microgravity conditions naturally leads to a double-diffraction scheme. The two pairs of counterpropagating beams induce simultaneously transitions with opposite momentum…

In contrast to relativistically induced transparency in electron--ion plasmas, where nonlinear electromagnetic waves render initially opaque plasmas transparent, we show using kinetic simulations that such waves can instead make initially…

We show that a translation bounded measure has pure point diffraction if and only if it is mean almost periodic. We then go on and show that a translation bounded measure solves what we call the phase problem if and only if it is…

Solids with spatially varying photonic structure offer gaps to light of a wider range of frequencies than do simple photonic systems. We solve numerically the field distribution in a solid cholesteric with a linearly varying inverse pitch…

The notion of Bregman divergence and sufficiency will be defined on general convex state spaces. It is demonstrated that only spectral sets can have a Bregman divergence that satisfies a sufficiency condition. Positive elements with trace 1…

The problem of neutron scattering by the single magnetic atom is theoretically considered in the second order perturbation theory. It is demonstrated that elastic scattering of unpolarized neutron by magnetic atom is skewed, i.e. contains…

The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the…

Letting $T$ denote an ergodic transformation of the unit interval and letting $f \colon [0,1)\to \mathbb{R}$ denote an observable, we construct the $f$-weighted return time measure $\mu_y$ for a reference point $y\in[0,1)$ as the weighted…

Electron diffraction through a thin patterned silicon membrane can be used to create complex spatial modulations in electron distributions by varying the intensity of different reflections using parameters such as crystallographic…