Divergence of Dipole Sums and the Nature of Non-Lorentzian Exponentially Narrow Resonances in One-Dimensional Periodic Arrays of Nanospheres

Origin and properties of non-Lorentzian spectral lines in linear chains of nanospheres are discussed. The lines are shown to be super-exponentially narrow with the characteristic width proportional to exp[-C(h/a)^3] where C is a numerical constant, h the spacing between the nanospheres in the chain and a the sphere radius. The fine structure of these spectral lines is also investigated.Comment: 9 pages, 4 figure

Experimental demonstration of an analytic method for image reconstruction in optical tomography with large data sets

We report the first experimental test of an analytic image reconstruction algorithm for optical tomography with large data sets. Using a continuous-wave optical tomography system with 10^8 source-detector pairs, we demonstrate the reconstruction of an absorption image of a phantom consisting of a highly-scattering medium with absorbing inhomogeneities.Comment: 3 pages, 3 figure

Criminal Justice and the Challenge of Family Ties

This Article asks two basic questions: When does, and when should, the state use the criminal justice apparatus to accommodate family ties, responsibilities, and interests? We address these questions by first revealing a variety of laws that together form a string of family ties subsidies and benefits pervading the criminal justice system. Notwithstanding our recognition of the important role family plays in securing the conditions for human flourishing, we then explain the basis for erecting a Spartan presumption against these family ties subsidies and benefits within the criminal justice system. We delineate the scope and rationale for the presumption and under what circumstances it might be overcome. When the presumption is overcome, we urge distributing the benefit on terms that are neutral to family status, if possible, with a focus instead on functions served by established relationships of care-giving responsibility

Theoretical and numerical analysis of current-driven electromagnetic homogenization and the problem of effective medium parameters for finite samples

Reflection and refraction of electromagnetic waves by artificial periodic composites (metamaterials) can be accurately modeled by an effective medium theory only if the boundary of the medium is explicitly taken into account and the two effective parameters of the medium -- the index of refraction and the impedance -- are correctly determined. Theories that consider infinite periodic composites do not satisfy the above condition. As a result, they cannot model reflection and transmission by finite samples with the desired accuracy and are not useful for design of metamaterial-based devices. As an instructive case in point, we consider the "current-driven" homogenization theory, which has recently gained popularity. We apply this theory to the case of one-dimensional periodic medium wherein both exact and homogenization results can be obtained analytically in closed form. We show that, beyond the well-understood zero-cell limit, the current-driven homogenization result is inconsistent with the exact reflection and transmission characteristics of the slab.Comment: Accepted in this form to PRB. Title shortened. Some misprints in the formulas corrected, particularly in the appendice

Anderson Localization of Polar Eigenmodes in Random Planar Composites

Anderson localization of classical waves in disordered media is a fundamental physical phenomenon that has attracted attention in the past three decades. More recently, localization of polar excitations in nanostructured metal-dielectric films (also known as random planar composite) has been subject of intense studies. Potential applications of planar composites include local near-field microscopy and spectroscopy. A number of previous studies have relied on the quasistatic approximation and a direct analogy with localization of electrons in disordered solids. Here I consider the localization problem without the quasistatic approximation. I show that localization of polar excitations is characterized by algebraic rather than by exponential spatial confinement. This result is also valid in two and three dimensions. I also show that the previously used localization criterion based on the gyration radius of eigenmodes is inconsistent with both exponential and algebraic localization. An alternative criterion based on the dipole participation number is proposed. Numerical demonstration of a localization-delocalization transition is given. Finally, it is shown that, contrary to the previous belief, localized modes can be effectively coupled to running waves.Comment: 22 pages, 7 figures. Paper was revised and a more precise definition of the participation number given, data for figures recalculated accordingly. Accepted to J. Phys.: Cond. Mat

Solution of the inverse scattering problem by T-matrix completion. II. Simulations

This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of scalar waves. The underlying mathematical model is the scalar wave equation and the object function that is reconstructed is the medium susceptibility. The simulations are relevant to ultrasound tomographic imaging and seismic tomography. It is shown that DCTMC is a viable method for solving strongly nonlinear inverse problems with large data sets. It provides not only the overall shape of the object but the quantitative contrast, which can correspond, for instance, to the variable speed of sound in the imaged medium.Comment: This is Part II of a paper series. Part I contains theory and is available at arXiv:1401.3319 [math-ph]. Accepted in this form to Phys. Rev.

On the Convergence of the Born Series in Optical Tomography with Diffuse Light

We provide a simple sufficient condition for convergence of Born series in the forward problem of optical diffusion tomography. The condition does not depend on the shape or spatial extent of the inhomogeneity but only on its amplitude.Comment: 23 pages, 7 figures, submitted to Inverse Problem

Working Paper: Measuring Job Creation in Private Sector Development

The Donor Committee for Enterprise Development (DCED) Standard offers a best practice by outlining the key elements for practically and credibly estimating the results of Private Sector Development programmes, in a process which can be managed by programmes internally. It involves a few common impact indicators to ensure that donors will be able to add up their results across country programmes. The Standard is being piloted on a multi-agency basis; the DCED invites new programmes to join in adopting the approach