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It was argued recently that there exists an unexpected phenomenon, the reflection of incoming particles on the event horizon of black holes (Kuchiev(2003)). This means that a particle approaching the black hole can bounce back into the…
We derive certain constraints on the reflection matrix for reflection from a plane, nonmagnetic, optically anisotropic surface using a reciprocity theorem stated long ago by van de Hulst in the context of scattering of polarized light. The…
This paper considers some open questions related to the inverse problem of pure point diffraction, in particular, what types of objects may diffract, and which of these may exhibit the same diffraction. Some diverse objects with the same…
Shape from shading is a classical inverse problem in computer vision. This shape reconstruction problem is inherently ill-defined; it depends on the assumed light source direction. We introduce a novel mathematical formulation for…
We study immersed surfaces in $\mathbb{R}^3$ which are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary, and when the boundary…
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…
In this work are reviewed several aspects of gravitational lensing produced by astrophysical bodies that strongly curve the spacetime in their vicinity. When an object with a photon sphere (e.g. a black hole) is interposed between a source…
We consider the effect on the propagation of light of inhomogeneities with sizes of order 10 Mpc or larger. The Universe is approximated through a variation of the Swiss-cheese model. The spherical inhomogeneities are void-like, with…
This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source…
In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from a final observation. We first drive the…
We derive from first principles the momentum exchange between a photon and a quantum mirror upon reflection, by considering the boundary conditions imposed by the mirror surface on the photon wave equation. We show that the system generally…
We investigate the finite source size effect in the context of the wave optics in the gravitational lensing. The magnification of an extended source is presented in an analytic manner for the singular isothermal sphere lens model as well as…
A particular mix of integral equations and discretization techniques is suggested for the solution of a planar Helmholtz transmission problem with relevance to the study of surface plasmon waves. The transmission problem describes the…
The edge diffraction of a homogeneously polarized light beam is studied theoretically based on the paraxial optics and Fresnel-Kirchhoff approximation, and the dependence of the diffracted beam pattern of the incident beam polarization is…
This paper is concerned with the Boltzmann equation with specular reflection boundary condition. We construct a unique global solution and obtain its large time asymptotic behavior in the case that the initial data is close enough to a…
We study scattering of polarized light by a rotating (Kerr) black hole of the mass M and the angular momentum J. In order to keep trace of the polarization dependence of photon trajectories one can use the following dimensionless parameter:…
An algorithm is developed and tested for the problem posed by photometric observations of the bulge of the Milky Way. The latter subtends a non-trivial solid angle on the sky, and we show that this permits inversion of the projected…
We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…
A random-matrix theory is presented for the reflection of light by a disordered medium backed by a phase-conjugating mirror. Two regimes are distinguished, depending on the relative magnitude of the inverse dwell time of a photon in the…
The standard theory of weak gravitational lensing relies on the infinitesimal light beam approximation. In this context, images are distorted by convergence and shear, the respective sources of which unphysically depend on the resolution of…