Related papers: Diffraction from visible lattice points and k-th p…
Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in general spatial dimension $D\geq 1$ when the density of states…
We study open point sets in Euclidean spaces $\mathbb{R}^d$ without a pair of points an integral distance apart. By a result of Furstenberg, Katznelson, and Weiss such sets must be of Lebesgue upper density zero. We are interested in how…
The structure of a two-dimensional honeycomb optical lattice potential with small inversion asymmetry is characterized using coherent diffraction of $^{87}$Rb atoms. We demonstrate that even a small potential asymmetry, with peak-to-peak…
The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…
We report an experimental observation of quantum Airy disk diffraction pattern using an entangled two-photon source. In contrast to the previous quantum lithography experiments where the subwavelength diffraction patterns were observed in…
We show how the existence of various free vector lattices and free vector lattice algebras can be derived from a theorem on equational classes in universal algebra. A discussion about free $f$-algebras over non-empty sets is given, where…
Light transmission through 2D subwavelength hole arrays in perfect-conductor films is shown to be complete (100%) at some resonant wavelengths even for arbitrarily narrow holes. Conversely, the reflection on a 2D planar array of…
When subjected to monochromatic incident light a nanoparticle will emit light which then interferes with the incident beam. With sufficient contrast and sufficiently close to the particle this interference pattern may be recorded with a…
Coherent Diffraction Imaging (CDI), a technique where an object is reconstructed from a single (2D or 3D) diffraction pattern, recovers the lost diffraction phases without a priori knowledge of the extent (support) of the object, which…
Fix an integer $n\ge 2$. To each non-zero point $\mathbf{u}$ in $\mathbb{R}^n$, one attaches several numbers called exponents of Diophantine approximation. However, as Khintchine first observed, these numbers are not independent of each…
Algebraic integers in totally imaginary quartic number fields are not discrete in the complex plane under a fixed embedding, which makes it impossible to visualize all integers in the plane, unlike the quadratic imaginary algebraic…
It is shown that a detailed sub microscopic consideration denies the wave-particle duality for both material particles and field particles, such as photons. In the case of particles, their \psi-wave function is interpreted as the particle's…
We answer in the negative a question by Gruenbaum who asked if there exists a finite basis of affine invariant points. We give a positive answer to another question by Gruenbaum about the "size" of the set of all affine invariant points.…
Absolute negative refraction regions for both polarizations of electromagnetic wave in two-dimensional photonic crystal have been found through both the analysis and the exact numerical simulation. Especially, absolute all-angle negative…
When used with coherent light, optical imaging systems, even diffraction-limited, are inherently unable to reproduce both the amplitude and the phase of a two-dimensional field distribution because their impulse response function varies…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
The electronic response of a telescope under direct illumination by a point-like light source is based on photon counting. With the data obtained using the SNDICE light source and the Megacam camera on the CFHT telescope, we show that the…
Starting from fundamental multiple scattering theory it is shown that negative refraction indices are feasible for matter waves passing a well-defined ensemble of scatterers. A simple approach to this topic is presented and explicit…
In this paper we describe the spectrum of values of weak uniform Diophantine exponents of lattices in arbitrary dimension.
The phenomenon of wave packet diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wave packet quantum scattering off an attractive or…