Related papers: Invisibility and Inverse Problems
The aim of this chapter is to make a review of the recent results using the Enclosure Method on inverse obstacle problems governed by the wave equation and the Maxwell system in time domain. We also describe some of unsolved problems…
We show that in one dimension the transfer matrix M of any scattering potential v coincides with the S-matrix of an associated time-dependent non-Hermitian 2 x 2 matrix Hamiltonian H(\tau). If v is real-valued, H(\tau) is pseudo-Hermitian…
The invariance under co-ordinate transformations of a set of partial differential equations can lead to the possibility of invisibility cloaking, whereby an anomaly in the interior of a body is shielded from an external observer. The form…
The $PT$-symmetric optical grating with index profile $e^{i\beta z}$ has been shown to have the interesting property of being essentially invisible for light incident from one side, while possessing greatly enhanced reflection at a…
An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…
Two novel classes of spherical invisibility cloaks based on nonlinear transformation have been studied. The cloaking characteristics are presented by segmenting the nonlinear transformation based spherical cloak into concentric isotropic…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
This paper presents a brief survey of the evolution of knowledge about diffraction gratings. After recalling some basic facts, historically and physically, we introduce the concept of Wood anomalies. Next, we present some recent works in…
Science opportunities and recommendations concerning optical/infrared polarimetry for the upcoming decade in the field of extragalactic astrophysics. Community-based White Paper to Astro2010 in response to the call for such papers.
Integrating conventional optics into compact nanostructured surfaces is the goal of flat optics. Despite the enormous progress of this technology, there are still critical challenges for real world applications due to a limited efficiency…
In elasticity, the design of a cloaking for an inclusion or a void to leave a vibrational field unperturbed by its presence, so to achieve its invisibility, is a thoroughly analyzed, but still unchallenged, mechanical problem. The 'cloaking…
Ultrasound modulated bioluminescence tomography (UMBLT) is an imaging method which can be formulated as a hybrid inverse source problem. In the regime where light propagation is modeled by a radiative transfer equation, previous approaches…
We describe the gauge-theoretic approach to transformations in integrable geometry through discussion of two classical examples: surfaces of constant negative Gauss curvature and isothermic surfaces. These are purely expository notes…
This tutorial paper describes the problem of image reconstruction from interferometric data with a particular focus on the specific problems encountered at optical (visible/IR) wavelengths. The challenging issues in image reconstruction…
In these lectures I give an overview of gravitational lensing, concentrating on theoretical aspects, including derivations of some of the important results. Topics covered include the determination of surface mass densities of intervening…
A survey on the generalizations of Heisenberg uncertainty relation and a general scheme for their entangled extensions to several states and observables is presented. The scheme is illustrated on the examples of one and two states and…
Comment on Phys. Rev. Lett. 86, 2086 (2001)
Transformation optics constructions have allowed the design of cloaking devices that steer electromagnetic, acoustic and quantum waves around a region without penetrating it, so that this region is hidden from external observations. The…
This PhD dissertation is concerned with integral geometric inverse problems. The geodesic ray transform is an operator that encodes the line integrals of a function along geodesics. The dissertation establishes many conditions when such…