Efficient Analysis of Metasurfaces in Terms of Spectral-Domain GSTC Integral Equations

We present a spectral-domain (SD) technique for the efficient analysis of metasurfaces. The metasurface is modeled by generalized sheet transition conditions (GSTCs) as a zero-thickness sheet creating a discontinuity in the electromagnetic field. The SD expression of these GSTCs for a specified incident field leads to a system of four surface integral equations for the reflected and transmitted fields, which are solved using the method of moments in the spectral domain. Compared to the finite-difference and finite-element techniques that require meshing the entire computational domain, the proposed technique reduces the problem to the surface of the metasurface, hence eliminating one dimension and providing substantial benefits in terms of memory and speed. A monochromatic generalized-refractive metasurface and a polychromatic focusing metasurface are presented as illustrative examples

Generalized Inpainting Method for Hyperspectral Image Acquisition

A recently designed hyperspectral imaging device enables multiplexed acquisition of an entire data volume in a single snapshot thanks to monolithically-integrated spectral filters. Such an agile imaging technique comes at the cost of a reduced spatial resolution and the need for a demosaicing procedure on its interleaved data. In this work, we address both issues and propose an approach inspired by recent developments in compressed sensing and analysis sparse models. We formulate our superresolution and demosaicing task as a 3-D generalized inpainting problem. Interestingly, the target spatial resolution can be adjusted for mitigating the compression level of our sensing. The reconstruction procedure uses a fast greedy method called Pseudo-inverse IHT. We also show on simulations that a random arrangement of the spectral filters on the sensor is preferable to regular mosaic layout as it improves the quality of the reconstruction. The efficiency of our technique is demonstrated through numerical experiments on both synthetic and real data as acquired by the snapshot imager.Comment: Keywords: Hyperspectral, inpainting, iterative hard thresholding, sparse models, CMOS, Fabry-P\'ero

Spectroscopic Evidence for Multiple Order Parameter Components in the Heavy Fermion Superconductor CeCoIn_5

Point-contact spectroscopy was performed on single crystals of the heavy-fermion superconductor CeCoIn_5 between 150 mK and 2.5 K. A pulsed measurement technique ensured minimal Joule heating over a wide voltage range. The spectra show Andreev-reflection characteristics with multiple structures which depend on junction impedance. Spectral analysis using the generalized Blonder-Tinkham-Klapwijk formalism for d-wave pairing revealed two coexisting order parameter components, with amplitudes Delta_1 = 0.95 +/- 0.15 meV and Delta_2 = 2.4 +/- 0.3 meV, which evolve differently with temperature. Our observations indicate a highly unconventional pairing mechanism, possibly involving multiple bands.Comment: 4 pages, 3 figure

Generalized Fourier transform and its application to the volume integral equation for elastic wave propagation in a half space

AbstractIn the present study, a generalized Fourier transform for time harmonic elastic wave propagation in a half space is developed. The generalized Fourier transform is obtained from the spectral representation of the operator derived from the elastic wave equation. By means of the generalized Fourier transform, a volume integral equation method for the analysis of scattered elastic waves is presented. The proposed method is based on the Krylov subspace iteration technique. During the iterative process, the discrete generalized Fourier transform is used, where the derivation of a huge and dense matrix from the volume integral equation is not necessary

Theory of coherent active convolved illumination for superresolution enhancement

Recently an optical amplification process called the plasmon injection scheme was introduced as an effective solution to overcoming losses in metamaterials. Implementations with near-field imaging applications have indicated substantial performance enhancements even in the presence of noise. This powerful and versatile compensation technique, which has since been renamed to a more generalized active convolved illumination, offers new possibilities of improving the performance of many previously conceived metamaterial-based devices and conventional imaging systems. In this work, we present the first comprehensive mathematical breakdown of active convolved illumination for coherent imaging. Our analysis highlights the distinctive features of active convolved illumination, such as selective spectral amplification and correlations, and provides a rigorous understanding of the loss compensation process. These features are achieved by an auxiliary source coherently superimposed with the object field. The auxiliary source is designed to have three important properties. First, it is correlated with the object field. Second, it is defined over a finite spectral bandwidth. Third, it is amplified over that selected bandwidth. We derive the variance for the image spectrum and show that utilizing the auxiliary source with the above properties can significantly improve the spectral signal-to-noise ratio and resolution limit. Besides enhanced superresolution imaging, the theory can be potentially generalized to the compensation of information or photon loss in a wide variety of coherent and incoherent linear systems including those, for example, in atmospheric imaging, time-domain spectroscopy, ${\cal PT}$ symmetric non-Hermitian photonics, and even quantum computing.Comment: revised, more details and references adde

Shortlisting by Incomplete Descriptions: The Power of Combination.

In this paper we make use of a particular technique of data analysis to empirically study the effect of joint attributes presentation in a multi-step process of choice, in which consumers first use a simple method for shortlisting, then proceed with a closer inspection of a restrict number of alternatives. Shortlisting is based on an incomplete description of the attributes of an alternative. We focus, in particular, on the presentation couples of attributes. The mathematical framework we used is the generalized spectral analysis. We tested this method on data collected through an ad hoc survey. Thanks to this powerful machinery we were able to identify the attraction single attributes have, from the effect of their combination. The use of generalized spectral analysis to decompose data on preferences is totally new. The decomposition allows us to underline two effects: the first and second order effect. The first order effect measures the average attraction that a single feature has when it is coupled with a second one. The second order effect detects the positive (or negative) power of combination of two coupled attributes. We present here a particular case, the choice of a car, among the ones we studied, to show how the method can be used, and its power. A particular emphasis will be given to gender differences in the evaluation of car attributes in the choice process.

Shortlisting by Incomplete Descriptions: The Power of Combination.

In this paper we make use of a particular technique of data analysis to empirically study the effect of joint attributes presentation in a multi-step process of choice, in which consumers first use a simple method for shortlisting, then proceed with a closer inspection of a restrict number of alternatives. Shortlisting is based on an incomplete description of the attributes of an alternative. We focus, in particular, on the presentation couples of attributes.x10The mathematical framework we used is the generalized spectral analysis. We tested this method on data collected through an ad hoc survey. Thanks to this powerful machinery we were able to identify the attraction single attributes have, from the effect of their combination.x10The use of generalized spectral analysis to decompose data on preferences is totally new. The decomposition allows us to underline two effects: the first and second order effect.x10The first order effect measures the average attraction that a single feature has when it is coupled with a second one. The second order effect detects the positive (or negative) power of combination of two coupled attributes. We present here a particular case, the choice of a car, among the ones we studied, to show how the method can be used, and its power. A particular emphasis will be given to gender differences in the evaluation of car attributes in the choice process.

Guruswami-Sinop Rounding without Higher Level Lasserre

Guruswami and Sinop give a O(1/delta) approximation guarantee for the non-uniform Sparsest Cut problem by solving O(r)-level Lasserre semidefinite constraints, provided that the generalized eigenvalues of the Laplacians of the cost and demand graphs satisfy a certain spectral condition, namely, the (r+1)-th generalized eigenvalue is at least OPT/(1-delta). Their key idea is a rounding technique that first maps a vector-valued solution to [0,1] using appropriately scaled projections onto Lasserre vectors. In this paper, we show that similar projections and analysis can be obtained using only l_2^2 triangle inequality constraints. This results in a O(r/delta^2) approximation guarantee for the non-uniform Sparsest Cut problem by adding only l_2^2 triangle inequality constraints to the usual semidefinite program, provided that the same spectral condition, the (r+1)-th generalized eigenvalue is at least OPT/(1-delta), holds