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

Coherently tunable third-order nonlinearity in a nanojunction

A possibility of tuning the phase of the third-order Kerr-type nonlinear susceptibility in a system consisting of two interacting metal nanospheres and a nonlinearly polarizable molecule is investigated theoretically and numerically. It is shown that by varying the relative inter-sphere separation, it is possible to tune the phase of the effective nonlinear susceptibility \chi^{(3)}(\omega;\omega,\omega,-\omega)$in the whole range from 0 to$2\pi$.Comment: 10 pages 5 figure

Rethinking Criminal Law and Family Status

In our recent book, Privilege or Punish: Criminal Justice and the Challenge of Family Ties (OUP 2009), we examined and critiqued a number of ways in which the criminal justice system uses family status to distribute benefits or burdens to defendants. In their review essays, Professors Alafair Burke, Alice Ristroph & Melissa Murray identify a series of concerns with the framework we offer policymakers to analyze these family ties benefits or burdens. We think it worthwhile not only to clarify where those challenges rest on misunderstandings or confusions about the central features of our views, but also to show the deficiencies of the proposed alternatives. While we appreciate and admire the efforts of our critics to advance this important conversation, we hope this Essay will illuminate why the normative framework of Privilege or Punish remains a more helpful structure to policymakers assessing how family status should intersect with the criminal law within a liberal democracy such as our own

Reciprocity relation for the vector radiative transport equation and its application to diffuse optical tomography with polarized light

We derive a reciprocity relation for vector radiative transport equation (vRTE) that describes propagation of polarized light in multiple-scattering media. We then show how this result, together with translational invariance of a plane-parallel sample, can be used to compute efficiently the sensitivity kernel of diffuse optical tomography (DOT) by Monte Carlo simulations. Numerical examples of polarization-selective sensitivity kernels thus computed are given.Comment: 5 pages, 3 figure

Comment on "Optical Response of Strongly Coupled Nanopraticles in Dimer Arrays" (Phys. Rev. B 71(4), 045404, 2005)

I have re-calculated the extinction spectra of aggregates of two silver nanospheres shown in Figs.~2 and 3 of Ref.~8. I have used the approximate method of images according to Ref.~8 and an exact numerical technique. I have found that the three sets of data (those I have obtained by the method of images, the numerical results, and the results published in Ref.~8) do not coincide. In this Comment, I discuss the reasons for these discrepancies and the general applicability of the method of images to the quasi-static electromagnetic problem of two interacting nanospheres.Comment: 4 pages, 4 figures, submitted to Phys. Rev.

Multiple Projection Optical Diffusion Tomography with Plane Wave Illumination

We describe a new data collection scheme for optical diffusion tomography in which plane wave illumination is combined with multiple projections in the slab imaging geometry. Multiple projection measurements are performed by rotating the slab around the sample. The advantage of the proposed method is that the measured data can be much more easily fitted into the dynamic range of most commonly used detectors. At the same time, multiple projections improve image quality by mutually interchanging the depth and transverse directions, and the scanned (detection) and integrated (illumination) surfaces. Inversion methods are derived for image reconstructions with extremely large data sets. Numerical simulations are performed for fixed and rotated slabs

Comments on the nonpharmaceutical interventions in New York City and Chicago during the 1918 flu pandemic

This commentary was originally published in CIDRAP News and it is here reported almost verbatim to allow divulgation through open access. The Editorial summarizes John Barry's concerns about the value of accurate historical reporting and its implications in public policy determination. This short abstract was written by the Editor-in-Chief of the Journal of Translational Medicine to introduce the Editorial

Local anisotropy and giant enhancement of local electromagnetic fields in fractal aggregates of metal nanoparticles

We have shown within the quasistatic approximation that the giant fluctuations of local electromagnetic field in random fractal aggregates of silver nanospheres are strongly correlated with a local anisotropy factor S which is defined in this paper. The latter is a purely geometrical parameter which characterizes the deviation of local environment of a given nanosphere in an aggregate from spherical symmetry. Therefore, it is possible to predict the sites with anomalously large local fields in an aggregate without explicitly solving the electromagnetic problem. We have also demonstrated that the average (over nanospheres) value of S does not depend noticeably on the fractal dimension D, except when D approaches the trivial limit D=3. In this case, as one can expect, the average local environment becomes spherically symmetrical and S approaches zero. This corresponds to the well-known fact that in trivial aggregates fluctuations of local electromagnetic fields are much weaker than in fractal aggregates. Thus, we find that, within the quasistatics, the large-scale geometry does not have a significant impact on local electromagnetic responses in nanoaggregates in a wide range of fractal dimensions. However, this prediction is expected to be not correct in aggregates which are sufficiently large for the intermediate- and radiation-zone interaction of individual nanospheres to become important.Comment: 9 pages 9 figures. No revisions from previous version; only figure layout is change

Inversion formulas for the broken-ray Radon transform

We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the filtered backprojection formula of the conventional Radon transform. The advantages of the broken ray transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium simultaneously and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is typically discarded.Comment: To be submitted to Inverse Problem