Related papers: Mathematical retroreflectors
Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems, and is embodied in the time-reversal mirror. A time-reversal mirror…
A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: 1) Property $C$ and applications, 2) Stable inversion of fixed-energy 3D scattering data and its error estimate, 3)…
We present an abstract method in the setting of compact metric spaces which is applied to solve a number of problems in geometric optics. In particular, we solve the one source near field refraction problem. That is, we construct surfaces…
The effect of anti-mirror reflection from a bounded plane optical waveguide used earlier for observation of slow light in a Bragg waveguide is considered. A theory of the effect is proposed that allowed us to interpret the observed spectral…
We consider light ray reflections in $n$-dimensional semi-infinite tube, for $n\geq 3$, made of Lambertian material. The source of light is placed far away from the exit, and the light ray is assumed to reflect so that the distribution of…
This paper is devoted to investigating the physically interesting optical and electromagnetic properties, phenomena and effects of wave propagation in the negative refractive index materials, which is often referred to as the {\it…
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 palindromic composition of $n$ is a composition of $n$ which can be read the same way forwards and backwards. In this paper we define an anti-palindromic composition of $n$ to be a composition of $n$ which has no mirror symmetry amongst…
A reflexive cycle is any reflexive digraph whose underlying undirected graph is a cycle. Call a relational structure Slupecki if its surjective polymorphisms are all essentially unary. We prove that all reflexive cycles of girth at least 4…
People have been familiar with the phenomenon of wave refraction for several centuries. Recently, a novel type of refraction, i.e., negative refraction, where both incident and refractory lines locate on the same side of the normal line,…
We demonstrate experimentally and numerically that metamaterials based on bilayer cross wires give giant optical activity, circular dichroism, and negative refractive index. The presented chiral design offers a much simpler geometry and…
We present an efficient method for the design of anomalous reflectors for acoustic waves. The approach is based on the fact that the anomalous reflector is actually a diffraction grating in which the amplitude of all the modes is negligible…
Mathematical diffraction theory is concerned with the analysis of the diffraction measure of a translation bounded complex measure $\omega$. It emerges as the Fourier transform of the autocorrelation measure of $\omega$. The mathematically…
We consider a billiard in the plane with periodic configuration of convex scatterers. This system is recurrent, in the sense that almost every orbit comes back arbitrarily close to the initial point. In this paper we study the time needed…
Recently it was proved that every billiard trajectory inside a $C^3$ convex cone has a finite number of reflections. Here, by a $C^3$ convex cone, we mean a cone whose section with some hyperplane is a strictly convex closed $C^3$…
Curved refractive objects are common in the human environment, and have a complex visual appearance that can cause robotic vision algorithms to fail. Light-field cameras allow us to address this challenge by capturing the view-dependent…
The array of micro-prisms was described by model of multi-period blazed gratings consisting of triangular apertures. The origins of hexagram-shaped diffraction patterns were interpreted based on multiple-beam interference and diffraction…
We generate a set of "relativistic" predictions for the relationship between viewing angle and apparent frequency, for each of three different non-transverse shift equations. We find that a detector aimed transversely (in the lab frame) at…
Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…