Related papers: Surprises in aperiodic diffraction
Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…
A path integral formulation is developed to study the spectrum of radiation from a perfectly reflecting (conducting) surface. It allows us to study arbitrary deformations in space and time. The spectrum is calculated to second order in the…
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…
Light propagation in a medium made of densely packed dielectric spheres is investigated by using a rigorous diffraction theory. It is shown that a substantial suppression of the local density of states occurs in spectral domains where the…
In this paper the author studies the problem of the homogenization of a diffusion perturbed by a periodic reflection invariant vector field. The vector field is assumed to have fixed direction but varying amplitude. The existence of a…
The use of coherent wave phenomena to enhance device performance is a cornerstone of modern optics. In juxtaposition to (locally) periodic metasurfaces, their disordered counterparts exhibit an interplay of destructive and constructive…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
Among the many families of nonperiodic tilings known so far, SCD tilings are still a bit mysterious. Here, we determine the diffraction spectra of point sets derived from SCD tilings and show that they have no absolutely continuous part,…
Through the study of the power spectra of a monochromatic light beam reflected by metallic mirrors, fluctuations in their reflectance is observed. The power spectra were obtained down to a factor $10^{-6}$ below the Standard Quantum Limit,…
We present a full quantum mechanical three dimensional theory describing an electromagnetic field interacting with an ensemble of identical atoms. The theory is constructed such that it describes recent experiments on light-matter quantum…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
The optical theorem relates the total scattering cross-section of a given structure with its forward scattering, but does not impose any restrictions on other directions. Strong backward-forward asymmetry in scattering could be achieved by…
A new approach to the phenomenon of large numbers coincidence leads to unexpected results. No matter how strange it might sound, the exact value of cosmological parameters and their analytical expression through fundamental constants have…
Our visual perception of our surroundings is ultimately limited by the diffraction limit, which stipulates that optical information smaller than roughly half the illumination wavelength is not retrievable. Over the past decades, many…
We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
The concept of quantum superposition is reconsidered and discussed from the viewpoint of Bohmian mechanics, the hydrodynamic formulation of quantum mechanics, in order to elucidate some physical consequences that go beyond the simple…
We study the backward scatterings of plane waves by reciprocal scatterers and reveal that $n$-fold ($n\geq3$) rotation symmetry is sufficient to secure invariant backscattering for arbitrarily-polarized incident plane waves. It is further…
Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry, and partly from…