Related papers: Modeling the interaction of an arbitrary light fie…
Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and…
We use geometrical optics and the caustic-touching theorem to study, in an exact way, the change in the topology of the image of an object obtained by reflections on an arbitrary smooth surface. Since the procedure that we use to compute…
The far field refractor problem with a discrete target is solved with a numerical scheme that uses and simplify ideas from Caffarelli, Kochengin and Oliker. A numerical implementation is carried out and examples are shown.
We discuss suitable classes of diffusion processes, for which functionals relevant to finance can be computed via Monte Carlo methods. In particular, we construct exact simulation schemes for processes from this class. However, should the…
Future NASA X-ray Observatories will shed light on a variety of high-energy astrophysical phenomena. Off-plane reflection gratings can be used to provide high throughput and spectral resolution in the 0.3--1.5 keV band, allowing for…
In light refraction between two transparent media, Snell's law describes the relationship between the incident angle and refraction angle. The refractive index is usually determined from Snell's law using the minimum deviation angle through…
Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics. A full exposition of Markov chains and their use…
We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…
The montecarlo method, which is quite commonly used to solve maximum entropy problems in statistical physics, can actually be used to solve inverse problems in a much wider context. The probability distribution which maximizes entropy can…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
An occulter is a large diffracting screen which may be flown in conjunction with a telescope to image extrasolar planets. The edge is shaped to minimize the diffracted light in a region beyond the occulter, and a telescope may be placed in…
The scattering equation formalism is a general framework for calculation of amplitudes in theories of massless particles. We provide a detailed introduction to the 4D scattering equation framework accessible to non-experts, outline current…
We develop a statistical-mechanical formulation for image restoration and error-correcting codes. These problems are shown to be equivalent to the Ising spin glass with ferromagnetic bias under random external fields. We prove that the…
A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld…
The high scintillation luminosity of n-type GaAs at 10K is surprising because (1) with a refractive index of about 3.5, escape is inhibited by total internal reflection and (2) narrow-beam experiments at 90K report infrared absorption…
An exact solution has been found for the problem of diffraction radiation appearing when a charged particle moves perpendicularly to a thin finite screen having arbitrary conductivity and frequency dispersion. Expressions describing the…
Lens design uses a calculation of the lens' surfaces that permit to obtain an image from a given object. A set of general rules and laws permits to calculate the essential points of the optical system such as distances, thickness, pupils,…
An adaptive algorithm for computing eigenmodes and propagation constants of optical fibers is proposed. The algorithm is built using a dual-weighted residual error estimator. The residuals are based on the eigensystem for leaky hybrid modes…
A general scattering problem of a plane electromagnetic wave on an infinite cylindrical rod is formulated and solved in a form of Bessel functions series expansion. The conductivity account via Ohm law directly in Maxwell equation leads to…
Conventional surface-relief gratings are inefficient at deflecting normally-incident light by large angles. This constrains their use in many applications and limits the overall efficiency of any optical instrument integrating gratings.…