Related papers: Diffraction of limit periodic point sets
The spatially periodic 2D patterns at output mirror of solid state microchip laser with high Fresnel number (100-1000) are discussed in view of numerical modeling with split-step FFT code comprising nonlinear gain, relaxation of inversion…
We discuss several examples of point processes (all taken from Hough, Krishnapur, Peres, Vir\'ag (2009)) for which the autocorrelation and diffraction measures can be calculated explicitly. These include certain classes of determinantal and…
The diffraction trace formula ({\em Phys. Rev. Lett.} {\bf 73}, 2304 (1994)) and spectral determinant are tested on the open three disk scattering system. The system contains a generic and exponentially growing number of diffraction…
Cut and project sets are obtained by projecting an irrational slice through a lattice to a lower dimensional subspace. Under standard conditions, the resulting pattern has no translational periods even though it retains some regularity of…
We review both theoretical and experimental advances in the recently emerged physics of modulated photonic lattices. Artificial periodic dielectric media, such as photonic crystals and photonic lattices, provide a powerful tool for the…
The acoustic properties of a porous sheet of medium resistivity backed by a rigid plate in which are embedded a periodic set of circular inclusions is investigated. Such a structure behaves like a multi-component diffraction gratings.…
Interference and diffraction of two-identical-particles are considered in the context of open quantum systems. This theoretical study is carried out within two approaches, the effective time-dependent Hamiltonian due to Caldirola-Kanai (CK)…
Optical modes of a multilayered photonic structure with the twisted nematic liquid crystal as a defect layer have been investigated. The electroconvective flow in the nematic makes a spatially periodic structure in the form of abnormal…
We address periodic-image errors arising from the use of periodic boundary conditions to describe systems that do not exhibit full three-dimensional periodicity. The difference between the periodic potential, as straightforwardly obtained…
Results of research of resonant phenomena in planar periodic structures consisted of dielectric elements are presented. A problem of plane wave diffraction by a structure which a periodic cell is composed of two dielectric bars with…
Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
We address the propagation of light beams in longitudinally modulated PT-symmetric lattices, built as arrays of couplers with periodically varying separation between their channels, and show a number of possibilities for efficient…
The reflecting features (reflected spectrum and phase) on the surface of pure-material plate depend on refractive index, extinction coefficient, incident angle, polarization direction and so on. The features, however, do not depend on a cut…
Friedel's law guarantees an inversion-symmetric diffraction pattern for thin, light materials where a kinematic approximation or a single-scattering model holds. Typically, breaking Friedel symmetry is ascribed to multiple scattering events…
Periodically time-varying media, known as photonic time crystals (PTCs), provide a promising platform for observing unconventional wave phenomena. We analyze the scattering of electromagnetic waves from spatially finite PTCs using the…
We report numerical experiments of optical wave propagation in composites of high refractive index dielectric rods at frequencies where their first electric and magnetic Mie resonances are excited. The arrays of these particles have been…
Topological phase transitions, which have fascinated generations of physicists, are always demarcated by gap closures. In this work, we propose very simple 2D photonic crystal lattices with gap closure points, i.e. band degeneracies…
Diffraction is a fundamental property of light propagation. Owing to this phenomenon,light diffracts out in all directions when it passes through a subwavelength slit.This imposes a fundamental limit on the transverse size of a light beam…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…