Related papers: Diffuse Reflection Radius in a Simple Polygon
A simple $n$-gon is a polygon with $n$ edges with each vertex belonging to exactly two edges and every other point belonging to at most one edge. Brass asked the following question: For $n \geq 5$ odd, what is the maximum perimeter of a…
In this paper we show that for each $n$, there exists a simple graph whose reliability polynomial has at least $n$ inflection points.
Undoing the image formation process and therefore decomposing appearance into its intrinsic properties is a challenging task due to the under-constraint nature of this inverse problem. While significant progress has been made on inferring…
In this paper we study reflection of holes in direct-band semiconductors from the linear potential barrier. It is shown that light-heavy hole transformation matrix is universal. It depends only on a dimensionless product of the light hole…
We consider the problem of assigning radii to a given set of points in the plane, such that the resulting set of circles is connected, and the sum of radii is minimized. We show that the problem is polynomially solvable if a connectivity…
Let $X_1,X_2, \ldots $ be independent random uniform points in a bounded domain $A \subset \mathbb{R}^d$ with smooth boundary. Define the coverage threshold $R_n$ to be the smallest $r$ such that $A$ is covered by the balls of radius $r$…
We consider the process of low-power light scattering by optical solitons in a slab waveguide with homogeneous and inhomogeneous refractive index core. We observe resonant reflection (Fano resonance) as well as resonant transmission of…
I derive a temporally propagated uni-directional optical pulse equation valid in the few cycle limit. Temporal propagation is advantageous because it naturally preserves causality, unlike the competing spatially propagated models. The exact…
This paper presents two approaches to the precise design of maximally flat antireflection coatings reducing the reflectance of the substrate to near zero in a certain region around the central frequency. The first ideal case concerns…
It is proved that every convex body in the plane has a point such that the union of the body and its image under reflection in the point is convex. If the body is not centrally symmetric, then it has, in fact, three affinely independent…
The mechanisms leading to a seemingly superluminal propagation of light in dispersive media are examined. The anomalous dispersion near an absorption line, involved in the first experiments displaying negative group velocity propagation, is…
Surface plasmon scattering by 1D indentations and protrusions is examined, mainly in the optical regime. The width of the defects is fixed, while its height is varied. Both individual and arrays of defects are considered. Protrusions mainly…
Image-based lighting is a widely used technique to reproduce shading under real-world lighting conditions, especially in real-time rendering applications. A particularly challenging scenario involves materials exhibiting a sparkling or…
We show in random matrix theory, microwave measurements, and computer simulations that the mean free path of a random medium and the strength and position of an embedded reflector can be determined from radiation scattered by the system.…
Recently it has been proposed that a planar slab of material, for which both the permittivity and permeability have the values of -1, could bring not only the propagating fields associated with a source to a focus, but could also refocus…
A programming library was developed, based on Stratton-Chu diffraction integrals for calculating reflected optical fields. Dipole-type focusing schemes with tunable number of beams and mirror placements were studied, considering the…
We consider the reflection of light, from a stationary source, off of a uniformly moving flat mirror, and derive the relativistic reflection law using well-known properties of conic sections. The effective surface of reflection (ESR) is…
We provide a mechanism to imprint local temporal correlations in photon streams which have the same character as spatial correlations in liquids. Usual single-photon emitters correspond, in this picture, to a (temporal) gas while…
This work models the propagation of an optical pulse in a 4-level atomic system in the electromagnetic induced transparency regime. By demonstrating that linear and nonlinear optical properties can be externally controlled and tailored by a…
Single-image relighting is a challenging task that involves reasoning about the complex interplay between geometry, materials, and lighting. Many prior methods either support only specific categories of images, such as portraits, or require…