Related papers: Diffraction of limit periodic point sets
We show if a metric measure space admits a differentiable structure then porous sets have measure zero and hence the measure is pointwise doubling. We then give a construction to show if we only require an approximate differentiable…
In the present paper we present ways to modulate the periodic transmission peaks arising in disordered one dimensional photonic structures with hundreds of layers. Disordered structures in which the optical length nd (n is the refractive…
We demonstrate a smart laser-diffraction analysis technique for particle mixture identification. We retrieve information about the size, geometry, and ratio concentration of two-component heterogeneous particle mixtures with an efficiency…
The periodic points of a morphism of good reduction for a smooth projective curve with good reduction over the p-adics form a discrete set. This is used to give an interpretation of the morphic height in terms of asymptotic properties of…
We provide a class of examples of interacting particle systems on $\mathbb{Z}^d$, for $d\in\{1,2\}$, that admit a unique translation-invariant stationary measure, which is not the long-time limit of all translation-invariant starting…
Optical limiters are designed to transmit low intensity light, while blocking the light with excessively high intensity. A typical passive limiter absorbs excessive electromagnetic energy, which can cause its overheating and destruction. We…
The refraction of light by dispersion-free dielectric media can be modeled using well-localized macroscopic wave packets, enabling a description in terms of pseudo-particles. This approach is often used in thought experiments to illustrate…
In this paper, we show by experiment that by covering a thin flat nonlinear lens on the sources, the sub-diffraction-limit observation can be achieved by measuring either the near-field distribution or the far-field radiation of the sources…
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…
Short planar glow discharges coupled to a resistive layer exhibit a wealth of spontaneous spatio-temporal patterns. Several authors have suggested effective reaction-diffusion-models to explore similarities with other pattern forming…
We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of…
Hyperbolic metamaterials are materials in which at least one principal dielectric constant is negative. We describe the refractive index surface, and the resulting refraction effects, for a biaxial hyperbolic metamaterial, with principal…
We introduce darning of compact sets (darning and gluing of finite unions of compact sets), which are not thin at any of their points, in a potential-theoretic framework which may be described, analytically, in terms of harmonic…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
We generalize the notion of the Franhoufer diffraction from a single slit and a circular aperture to the case of partially temporal coherent and quasimonochromatic light. The problem is studied analytically and the effect of coherence…
We study light propagation in nanoscale periodic structures composed of dielectric and metal in the visible range. We demonstrate that diffraction can be tailored both in magnitude and in sign by varying the geometric features of the…
We prove that a positive-definite measure in $\mathbb{R}^n$ with uniformly discrete support and discrete closed spectrum, is representable as a finite linear combination of Dirac combs, translated and modulated. This extends our recent…
Certain alternative properties of physical systems are describable by supports of arguments of response functions (e.g. light cone, borders of media) and expressed by projectors; corresponding equations of restraints lead to dispersion…
This article considers the problem of diffraction by a wedge consisting of two semi-infinite periodic arrays of point scatterers. The solution is obtained in terms of two coupled systems, each of which is solved using the discrete…
The diffraction spectra of the Hat and Spectre monotile tilings, which are known to be pure point, are derived and computed explicitly. This is done via model set representatives of self-similar members in the topological conjugacy classes…