All-optical majority gate based on an injection-locked laser.

An all-optical computer has remained an elusive concept. To construct a practical computing primitive equivalent to an electronic Boolean logic, one should utilize nonlinearity that overcomes weaknesses that plague many optical processing schemes. An advantageous nonlinearity provides a complete set of logic operations and allows cascaded operations without changes in wavelength or in signal encoding format.

Using the fibre structure of paper to determine authenticity of the documents: analysis of transmitted light images of stamps and banknotes.

A novel method is presented for distinguishing postal stamp forgeries and counterfeit banknotes from genuine samples. The method is based on analyzing differences in paper fibre networks. The main tool is a curvelet-based algorithm for measuring overall fibre orientation distribution and quantifying anisotropy.

Cloaked electromagnetic, acoustic, and quantum amplifiers via transformation optics.

The advent of transformation optics and metamaterials has made possible devices producing extreme effects on wave propagation. Here we describe a class of invisible reservoirs and amplifiers for waves, which we refer to as Schrödinger hats. The unifying mathematical principle on which these are based admits such devices for any time harmonic waves modeled by either the Helmholtz or Schrödinger equation, e.

Cloaking a sensor via transformation optics.

Ideal transformation optics cloaking at positive frequency, besides rendering the cloaked region invisible to detection by scattering of incident waves, also shields the region from those same waves. In contrast, we demonstrate that approximate cloaking permits a strong coupling between the cloaked and uncloaked regions; careful choice of parameters allows this coupling to be amplified, leading to effective cloaks with degraded shielding. The sensor modes we describe are close to but distinct from interior resonances, which destroy cloaking.

Approximate quantum cloaking and almost-trapped states.

We describe potentials which act as approximate cloaks for matter waves. These potentials are derived from ideal cloaks for the conductivity and Helmholtz equations. At most energies E, if a potential is surrounded by an approximate cloak, then it becomes almost undetectable and unaltered by matter waves originating externally to the cloak.

Electrical impedance tomography problem with inaccurately known boundary and contact impedances.

In electrical impedance tomography (EIT) electric currents are injected into a body with unknown electromagnetic properties through a set of contact electrodes at the boundary of the body. The resulting voltages are measured on the same electrodes and the objective is to reconstruct the unknown conductivity function inside the body based on these data. All the traditional approaches to the reconstruction problem assume that the boundary of the body and the electrode-skin contact impedances are known a priori.

Electromagnetic wormholes and virtual magnetic monopoles from metamaterials.

We describe new configurations of electromagnetic (EM) material parameters, the electric permittivity epsilon and magnetic permeability micro, which allow one to construct devices that function as invisible tunnels. These allow EM wave propagation between the regions at the two ends of a tunnel, but the tunnels themselves and the regions they enclose are not detectable to lateral EM observations. Such devices act as wormholes with respect to Maxwell's equations and effectively change the topology of space vis-à-vis EM wave propagation.

Parallelized Bayesian inversion for three-dimensional dental X-ray imaging.

Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because of high radiation dose, low-resolution or the cost of the CT scanner equipment.

Wavelet-based reconstruction for limited-angle X-ray tomography.

The aim of X-ray tomography is to reconstruct an unknown physical body from a collection of projection images. When the projection images are only available from a limited angle of view, the reconstruction problem is a severely ill-posed inverse problem. Statistical inversion allows stable solution of the limited-angle tomography problem by complementing the measurement data by a priori information.

Anisotropic conductivities that cannot be detected by EIT.

We construct anisotropic conductivities in dimension 3 that give rise to the same voltage and current measurements at the boundary of a body as a homogeneous isotropic conductivity. These conductivities are non-zero, but degenerate close to a surface inside the body.