Superfluid to Mott insulator transition in one, two, and three dimensions

No Heading We have created one-, two-, and three-dimensional quantum gases and study the superfluid to Mott insulator transition. Measurements of the transition using Bragg spectroscopy show that the excitation spectra of the low-dimensional superfluids differ significantly from the three-dimensional case.PACS numbers: 05.30.Jp, 03.75.Kk, 03.75.Lm, 73.43.Nq     

Determining spatial modes of lasers with spatial coherence measurements

We explain a technique that extracts both the structure and the modal weights of spatial modes of lasers by analyzing the spatial coherence of the beam. This is the first time, to our knowledge, that an experimental method is being used to measure arbitrary forms of the spatial modes. We applied this method to an edge-emitting Fabry-Perot semiconductor laser with a stripe width of 5 mum and extracted fundamental and first-order lateral modes with relative power weights of 96.2% and 3.8%. There was a single transverse mode.     

Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination

Two-beam interferogram intensity modulation decoding using spatial carrier phase shifting interferometry is discussed. Single frame recording, simplicity of experimental equipment, and uncomplicated data processing are the main advantages of the method. A comprehensive analysis of the influence of systematic errors (spatial carrier miscalibration, nonuniform average intensity profile, and nonlinear recording) on the modulation distribution determination using automatic fringe pattern analysis techniques is presented. The results of searching for the optimum calculation algorithm are described. Extensive numerical simulations are compared with laboratory findings obtained when testing vibrating silicon microelements under various experimental conditions.     

Using light scattering to measure the temporal coherence of optical sources

We demonstrate a simple and robust method for characterizing the temporal coherence of statistically stationary optical sources by using dynamic light scattering. Measurement of the contrast of the fluctuating speckle pattern produced by two counterpropagating beams incident on a scattering medium is used to evaluate their mutual coherence. Important features of this method are high statistical accuracy, the ability to compensate for imperfect spatial coherence, and the possibility of characterizing milliwatt-level optical beams with a wide range of spectral widths. As an example, the squared magnitude of the field autocorrelation function for light emitted by a broadband argon-ion laser is obtained.     

Diffraction of transmission light through triangular apertures in array of retro-reflective microprisms

An array of microprisms was described by a model of multiperiod blazed gratings consisting of triangular apertures. The origins of hexagram-shaped diffraction patterns were interpreted based on multiple-beam interference and diffraction array theorem. The relation between zonal/line ghost fringes and imperfectly fabricated array structures was analyzed. Geometrical performance (e.g., the dihedral angle of the microprism) was tested by measuring the features of diffraction patterns of samples from three retroreflective sheeting manufacturers.     

Quantity is only one of the qualities

As our fields have become more sophisticated, complex, and specialized, we deal with ever larger masses of data, and our quantitative results have become more detailed and esoteric, and difficult to interpret. Because our methods are predominantly quantitative, we tend to overlook or underemphasize the qualitative judgments that enter at every stage of our work, and to forget that quantity is only one of the qualities. As in our world today, where we face a flood of factoids and quantitative data stripped of context, and struggle to evaluate it, to give it meaning, and make it into information, so ought we qualitatively to acknowledge and contextualize our research results, not only to make them more relevant, meaningful, and useful to the larger world, but to give our work greater impact and value.     

Measurement of the spatial coherence of superluminescent diodes

Abstract

In recent years, superluminescent diodes (SLDs) have gained increasing importance as light sources for partial coherence interferometry and optical coherence tomography. The requirements of SLDs are high spatial coherence, low temporal coherence, and, for some applications, high power. Since there might be a trade-off between these properties we built an instrument for measuring the spatial coherence of SLDs. This instrument consists of a hybrid bulk optic-fibre optic Mach-Zehnder interferometer. The special advantages of the instrument are the ability to measure the spatial coherence between arbitrary points within the light beam and to observe directly the measurement points within the beam which facilitates the alignment. We used this instrument to evaluate the spatial coherence of several commercially available SLDs. As expected, a single mode fibre pigtailed SLD shows the best spatial coherence. If free-space emitting SLDs are considered, those with a more complicated chip structure have a somewhat poorer spatial coherence, however, their temporal coherence is considerably better than that of a SLD which is only antireflection coated.     

Raman spectroscopy of polyconjugated molecules and materials: confinement effect in one and two dimensions

The effect of the confinement of pi electrons in one- and two-dimensional domains is illustrated with several examples ranging from linear polyene chains to planar molecules with honeycomb structure. Theoretical computations and specific Raman experiments on molecular materials demonstrate that a molecular approach provides a unified key to the interpretation of the Raman response both of linear polyconjugated polymers (polyacetylene) and of nanostructured graphitic materials.     

Dispersion and pollution of the FEM solution for the Helmholtz equation in one,two and three dimensions

For high wave numbers, the Helmholtz equation suffers the so‐called ‘pollution effect’. This effect is directly related to the dispersion. A method to measure the dispersion on any numerical method related to the classical Galerkin FEM is presented. This method does not require to compute the numerical solution of the problem and is extremely fast. Numerical results on the classical Galerkin FEM (p‐method) is compared to modified methods presented in the literature. A study of the influence of the topology triangles is also carried out. The efficiency of the different methods is compared. The numerical results in two of the mesh and for square elements show that the high order elements control the dispersion well. The most effective modified method is the QSFEM [1,2] but it is also very complicated in the general setting. The residual‐free bubble [3,4] is effective in one dimension but not in higher dimensions. The least‐square method [1,5] approach lowers the dispersion but relatively little. The results for triangular meshes show that the best topology is the ‘criss‐cross’ pattern. Copyright © 1999 John Wiley & Sons, Ltd.     

Measuring characteristic length scales of eigenfunctions of Sturm–Liouville equations in one and two dimensions

The spatial resolution of eigenfunctions of Sturm–Liouville equations in one-dimension is frequently measured by examining the minimum distance between their roots. For example, it is well known that the roots of polynomials on finite domains cluster like O(1/N ²) near the boundaries. This technique works well in one dimension, and in higher dimensions that are tensor products of one-dimensional eigenfunctions. However, for non-tensor-product eigenfunctions, finding good interpolation points is much more complicated than finding the roots of eigenfunctions. In fact, in some cases, even quasi-optimal interpolation points are unknown. In this work an alternative measure, ℓ, is proposed for estimating the characteristic length scale of eigenfunctions of Sturm–Liouville equations that does not rely on knowledge of the roots. It is first shown that ℓ is a reasonable measure for evaluating the eigenfunctions since in one dimension it recovers known results. Then results are presented in higher dimensions. It is shown that for tensor products of one-dimensional eigenfunctions in the square the results reduce trivially to the one-dimensional result. For the non-tensor product Proriol polynomials, there are quasi-optimal interpolation points (Fekete points). Comparing the minimum distance between Fekete points to ℓ shows that ℓ is a reasonably good measure of the characteristic length scale in two dimensions as well. The measure is finally applied to the non-tensor product generalized eigenfunctions in the triangle proposed by Taylor MA, Wingate BA [(2006) J Engng Math, accepted] where optimal interpolation points are unknown. While some of the eigenfunctions have larger characteristic length scales than the Proriol polynomials, others show little improvement.     

Cylindrical ion trap array with mass selection by variation in trap dimensions

A mass spectrometer array is described in which each array element is a cylindrical ion trap (CIT) within which an approximately quadrupolar, time-varying, field is established. The individual traps are of different sizes, so that when the array is operated with a fixed rf potential, ions of different masses (or mass ranges) are stored in each trap. By choosing the dimensions of each CIT element in the array, a multiple ion monitoring experiment can be performed. For example, in a two-element array with elements having internal radii of 5 and 4 mm, the smaller trap selects for m/z 91 and the larger for m/z 57, corresponding to characteristic aromatic and aliphatic hydrocarbon ions. Ion storage using both rf/dc (apex) isolation and the stored waveform inverse Fourier transform method is demonstrated.The array reduces the complexity of the electronics needed to operate the ion trap, which should make it suitable for use in a miniature mass spectrometer system.     

Radiometric theory of spatial coherence in free-space propagation

The radiometric theory of spatial coherence is presented with special attention to the validity of the approximations on which it is based. A new definition of the transverse coherence area is introduced and shown to be in general agreement with earlier definitions. In free-space propagation the product of the transverse coherence area and the intensity is shown to be constant along rectilinear rays, and, for radiation from uniform Lambert sources, a well-known paraxial formula for the transverse coherence area is extended to the extraparaxial domain. A decrease of the spatial coherence in free-space propagation takes place in regions with an increase of the intensity. For imaging systems this occurs in a finite part of image space whenever a real image of a diffusely radiating, extended object is formed at a finite distance.     

Hybrid numerical method for solution of the radiative transfer equation in one, two, or three dimensions

A hybrid method is presented by which Monte Carlo (MC) techniques are combined with an iterative relaxation algorithm to solve the radiative transfer equation in arbitrary one-, two-, or three-dimensional optical environments. The optical environments are first divided into contiguous subregions, or elements. MC techniques are employed to determine the optical response function of each type of element. The elements are combined, and relaxation techniques are used to determine simultaneously the radiance field on the boundary and throughout the interior of the modeled environment. One-dimensional results compare well with a standard radiative transfer model. The light field beneath and adjacent to a long barge is modeled in two dimensions and displayed. Ramifications for underwater video imaging are discussed. The hybrid model is currently capable of providing estimates of the underwater light field needed to expedite inspection of ship hulls and port facilities.     

Defect characterization using an ultrasonic array to measure the scattering coefficient matrix

Ultrasonic nondestructive evaluation is used for detection, characterization, and sizing of defects. The accurate sizing of defects that are of similar or less size than the ultrasonic wavelength is of particular importance in assessing structural integrity. In this paper, we demonstrate how measurement of the scattering coefficient matrix of a cracklike defect can be used to obtain its size, shape, and orientation. The scattering coefficient matrix describes the far field amplitude of scattered signals from a scatterer as a function of incident and scattering angles. A finite element (FE) modeling procedure is described that predicts the scattering coefficient matrix of various cracklike defects. Experimental results are presented using a commercial 64-element, 5 MHz array on 2 aluminum test samples that contain several machined slots and through thickness circular holes. To minimize the interference from the reflections of neighboring defects, a subarray approach is used to focus ultrasound on each target defect in turn and extract its scattering coefficient matrices. A circular hole and a fine slot can be clearly distinguished by their different scattering coefficient matrices over a specific range of incident angles and scattering angles. The orientation angles of slots directly below the array are deduced from the measured scattering coefficient matrix to an accuracy of a few degrees, and their lengths are determined with an error of 10%.     

Partial spatial coherence effects in digital holographic microscopy with a laser source

We investigate a digital holographic microscope that permits us to modify the spatial coherence state of the sample illumination by changing the spot size of a laser beam on a rotating ground glass. Out-of-focus planes are refocused by digital holographic reconstruction with numerical implementation of the Kirchhoff-Fresnel integral. The partial coherence nature of the illumination reduces the coherent artifact noise with respect to fully coherent illumination. The investigated configuration allows the spatial coherence state to be changed without modifying the illumination level of the sample. The effect of the coherence state on the digital holographic reconstruction is theoretically and experimentally evaluated. We also show how multiple reflection interferences are limited by the use of reduced spatial coherent illumination.     

A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions

Developments in dynamical systems theory provide new support for the macroscale modelling of pdes and other microscale systems such as lattice Boltzmann, Monte Carlo or molecular dynamics simulators. By systematically resolving subgrid microscale dynamics the dynamical systems approach constructs accurate closures of macroscale discretisations of the microscale system. Here we specifically explore reaction–diffusion problems in two spatial dimensions as a prototype of generic systems in multiple dimensions. Our approach unifies into one the discrete modelling of systems governed by known pdes and the ‘equation-free’ macroscale modelling of microscale simulators efficiently executing only on small patches of the spatial domain. Centre manifold theory ensures that a closed model exists on the macroscale grid, is emergent, and is systematically approximated. Dividing space into either overlapping finite elements or spatially separated small patches, the specially crafted inter-element/patch coupling also ensures that the constructed discretisations are consistent with the microscale system/pde to as high an order as desired. Computer algebra handles the considerable algebraic details, as seen in the specific application to the Ginzburg–Landau pde. However, higher-order models in multiple dimensions require a mixed numerical and algebraic approach that is also developed. The modelling here may be straightforwardly adapted to a wide class of reaction–diffusion pdes and lattice equations in multiple space dimensions. When applied to patches of microscopic simulations our coupling conditions promise efficient macroscale simulation.