Experimental violation of Bell's inequality in spatial-parity space

We report the first experimental violation of Bell's inequality in the spatial domain using the Einstein-Podolsky-Rosen state. Two-photon states generated via optical spontaneous parametric down-conversion are shown to be entangled in the parity of their one-dimensional transverse spatial profile. Superpositions of Bell states are prepared by manipulation of the optical pump's transverse spatial parity-a classical parameter. The Bell-operator measurements are made possible by devising simple optical arrangements that perform rotations in the one-dimensional spatial-parity space of each photon of an entangled pair and projective measurements onto a basis of even-odd functions. A Bell-operator value of 2.389+/-0.016 is recorded, a violation of the inequality by more than 24 standard deviations.     

Complete modal decomposition for optical waveguides

Virtually all electromagnetic waveguiding structures support a multiplicity of modes. Nevertheless, to date, an experimental method for unique decomposition of the fields in terms of the component eigenmodes has not been realized. The fundamental problem is that all current attempts of modal decomposition do not yield phase information. Here we introduce a noninterferometric approach to achieve modal decomposition of the fields at the output of a general waveguiding structure. The technique utilizes a mapping of the two-dimensional field distribution onto the one-dimensional space of waveguide eigenmodes, together with a phase-retrieval algorithm to extract the amplitudes and phases of all the guided vectorial modes. Experimental validation is provided by using this approach to examine the interactions of 16 modes in a hollow-core photonic-band gap fiber.     

Three-dimensional polarization control in microscopy

We propose an approach to optical microscopy that enables full control over the three-dimensional polarization vector at the focal spot of a high-numerical-aperture lens. The input field to the lens is linearly polarized and no polarization optics are needed. This technique utilizes the azimuthal spatial degree of freedom of the input field. We find that only a small set of low-order azimuthal spatial harmonics contributes to the focused field on axis, and a simple transformation exists between the linear vector space of these harmonics and the three-dimensional polarization-vector space. Controlling the relative complex weights of these azimuthal harmonics produces any desired three-dimensional state of polarization.     

Multimaterial preform coextrusion for robust chalcogenide optical fibers and tapers

The development of robust infrared fibers is crucial for harnessing the capabilities of new mid-infrared lasers. We present a novel approach to the fabrication of chalcogenide glass fiber preforms: one-step multimaterial extrusion. The preform consists of a glass core and cladding surrounded by a built-in, thermally compatible, polymer jacket for mechanical support. Using this approach we extrude several preform structures and draw them into robust composite fibers. Furthermore, the polymer cladding allows us to produce robust tapers with submicrometer core diameter.     

Models for capacitated lot-sizing problem with backlogging,setup carryover and crossover

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.     

Stability and convergence of the spectral Lagrange-Galerkin method for mixed periodic/non-periodic convection-dominated diffusion problems

We present a convergence analysis of the spectral Lagrange-Galerkinmethod for mixed periodic/non-periodic convection-diffusionproblems. The scheme is unconditionally stable, independentof the diffusion coefficient, even in the case when numericalquadrature is used. The theoretical predictions are illustratedby a series of numerical experiments. For the periodic case,our results present a significant improvement on those givenby Süli & Ware (1991) SIAM J. Numer.Anal.28, 423-445).     

Entangled-photon imaging of a pure phase object

We demonstrate experimentally and theoretically that a coherent image of a pure phase object [implemented by a microelectromechanical system (MEMS) micromirror array] may be obtained by use of a spatially incoherent illumination beam. This is accomplished by employing a two-beam source of entangled photons generated by spontaneous parametric down-conversion. One of the beams probes the phase object while the other is scanned. Though each of the beams is, in and of itself, spatially incoherent, the pair of beams exhibits higher-order interbeam coherence.