Related papers: Mathematical retroreflectors
This work demonstrates the existence of both negative refraction and a negative refractive index in an optical uniaxial absorbent medium that can be characterized by ordinary and extraordinary refractive indices. Negative refraction occurs…
Atom reflection is studied in the presence of a non-Abelian vector potential proportional to a spin-1/2 operator. The potential is produced by a relatively simple laser configuration for atoms with a tripod level scheme. We show that the…
We introduce the notion of a Billiard Array. This is an equilateral triangular array of one-dimensional subspaces of a vector space $V$, subject to several conditions that specify which sums are direct. We show that the Billiard Arrays on…
A black mirror is an accelerated boundary that produces particles in an exact correspondence to an evaporating black hole. We investigate the spectral dynamics of the particle creation during the formation process.
In this paper, we discuss a mathematical model for inverse freeform design of an optical system with two reflectors in which light transfers from a point source to a point target. In this model, the angular light intensity emitted from the…
For every quadrilateral sufficiently close to a rectangle, we shall show that it possess a periodic billiard path. This is an REU work done at ICERM in Summer 2012.
Recently, Zhang et al. (Phys. Rev. Lett. 91, 157404 (2003)) have demonstrated that an amphoteric refraction, i. e. both positive and negative refraction, may prevail at the interface of two uniaxial anisotropic crystals when their optical…
The utilization of time reversal symmetry in designing and implementing (quantum) optical experiments has become more and more frequent over the past years. We review the basic idea underlying time reversal methods, illustrate it with…
We consider right prisms with horizontal quadrilateral bases and tops, and vertical rectangular sides. We look for examples where all the edges, face diagonals and space diagonals are integers. We find examples when the base is an isosceles…
Time-reversal symmetry is important to optics. In linear optics, a time-reversed process to laser emission enables total absorption of coherent light fields into an optical cavity of loss by time-reversing the original gain medium. In…
One highly desirable function of a diffraction grating is its ability to deflect incident light into a specific diffraction order with near-perfect efficiency. While such asymmetry can be achieved in a variety of ways, e.g., by using a…
We describe and present the first observational evidence that light propagating near a rotating black hole is twisted in phase and carries orbital angular momentum. The novel use of this physical observable as an additional tool for the…
We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption…
The relatively hot temperature of the human body causes people to turn into long-wave infrared light sources. Since this emitted light has a larger wavelength than visible light, many surfaces in typical scenes act as infrared mirrors with…
Traditional lens design is a numerical and forward process based on ray tracing and aberration theory. This method has limitations because the initial configuration of the lens has to be specified and the aberrations of the lenses have to…
Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according to the law of reflection. A billiard trajectory is then…
Plane mirror can make one object into two for observers on the object's side. Yet, there seems no way to achieve the same effect for observers from all directions. In this letter, we will design a new class of gradient index lenses from…
We present a learning-based approach to relight a single image of Lambertian and low-frequency specular objects. Our method enables inserting objects from photographs into new scenes and relighting them under the new environment lighting,…
Gravitational lensing deflects light. A single lens deflector can only shear images, but cannot induce rotations. Multiple lens planes can induce rotations. Such rotations can be observed in quadruply imaged sources, and can be used to…
The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…