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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…
We introduce a new type of lens that focuses a plane wave into a spherical one, where light comes from all directions. Our method also suggests the design of ideal optical tweezers or, in the reverse direction, photo-detection of nearly all…
We develop a relativistic treatment of interference between light reflected from a falling cube retroreflector in the vertical arm of an interferometer, and light in a reference beam in the horizontal arm. Coordinates that are nearly…
Motivated by recent Event Horizon Telescope findings, we investigate constrained optics of rotating black holes in Einstein-Maxwell-scalar gravity theory. Precisely, we mainly study the parameter effects on two relevant optical concepts…
Sensing and manipulating targets hidden under scattering media are universal problems that take place in applications ranging from deep-tissue optical imaging to laser surgery. A major issue in these applications is the shallow light…
Photometric stereo (PS) techniques nowadays remain constrained to an ideal laboratory setup where modeling and calibration of lighting is amenable. To eliminate such restrictions, we propose an efficient principled variational approach to…
The hemispherical Mueller matrix map for light reflected from a plane-parallel planetary atmosphere is shown to obey several symmetry properties that provide a straightforward method to check their physical realizability. The mirror…
Soibelman's theory of quantized function algebra A_q(SL_n) provides a representation theoretical scheme to construct a solution of the Zamolodchikov tetrahedron equation. We extend this idea originally due to Kapranov and Voevodsky to…
The purpose of this paper is to study the reflections of a convex body. In particular, we are interested in orthogonal reflections of its sections that can be extended to reflections of the whole body. For this reason, we need to study the…
A unique perspective approach based on an analogy method is presented to solve the ray equation in a model of a continuous inhomogeneous medium, which has a spherically symmetric distribution. Basically, in the standard undergraduate…
Motivated by a recent experiment [J. Eschner {\it et al.}, Nature {\bf 413}, 495 (2001)], we now present a theoretical study on the fluorescence of an atom in front of a mirror. On the assumption that the presence of the distant mirror and…
We consider mirrors of the spherical shape, that can expand or contract. Due to the excitation of the vacuum around, some spherical waves radiated from vibrating mirrors are encountered. Using experience from well-known literature on…
A light ray in space is characterized by two vectors: (i) a transverse spatial-vector associated with the point where the ray intersects a given spherical cap; (ii) an angular-frequency vector which defines the ray direction of propagation.…
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…
We introduce a model to design reflectors that take into account the inverse square law for radiation. We prove existence of solutions, both in the near and far field cases, when the input and output energies are prescribed.
In this paper we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D nonlinear Schrodinger equation as the underlying mathematical model and we use an implicit-explicit type…
Studying the albedos of the planets and moons of the Solar System dates back at least a century. Of particular interest is the relationship between the albedo measured at superior conjunction, known as the ``geometric albedo", and the…
A numerical scheme is presented to solve the one source near field refractor problem to arbitrary precision and it is proved that the scheme terminates in a finite number of iterations. The convergence of the algorithm depends upon proving…
Retrolensing is a gravitational lensing effect in which light emitted by a background source is deflected by a black hole and redirected toward the observer after undergoing nearly complete loops around the black hole. In this context, we…
We investigate the shadow of an exact black hole solution of Einstein's equations recently proposed by Cardoso et al., to describe a supermassive black hole immersed in a dark matter halo. We analyze and discuss the light rings and the…