Graph Sparsification by Edge-Connectivity and Random Spanning Trees

We present new approaches to constructing graph sparsifiers --- weighted subgraphs for which every cut has the same value as the original graph, up to a factor of $(1 \pm \epsilon)$. Our first approach independently samples each edge $uv$ with probability inversely proportional to the edge-connectivity between $u$ and $v$. The fact that this approach produces a sparsifier resolves a question posed by Bencz\'ur and Karger (2002). Concurrent work of Hariharan and Panigrahi also resolves this question. Our second approach constructs a sparsifier by forming the union of several uniformly random spanning trees. Both of our approaches produce sparsifiers with $O(n \log^2(n)/\epsilon^2)$ edges. Our proofs are based on extensions of Karger's contraction algorithm, which may be of independent interest

Optical Torque from Enhanced Scattering by Multipolar Plasmonic Resonance

We present a theoretical study of the optical angular momentum transfer from a circularly polarized plane wave to thin metal nanoparticles of different rotational symmetries. While absorption has been regarded as the predominant mechanism of torque generation on the nanoscale, we demonstrate numerically how the contribution from scattering can be enhanced by using multipolar plasmon resonance. The multipolar modes in non-circular particles can convert the angular momentum carried by the scattered field, thereby producing scattering-dominant optical torque, while a circularly symmetric particle cannot. Our results show that the optical torque induced by resonant scattering can contribute to 80% of the total optical torque in gold particles. This scattering-dominant torque generation is extremely mode-specific, and deserves to be distinguished from the absorption-dominant mechanism. Our findings might have applications in optical manipulation on the nanoscale as well as new designs in plasmonics and metamaterials.Comment: main article 20 pages, 4 figures; supplementary material 6 pages, 2 figure

Transformation Optics scheme for two-dimensional materials

Two dimensional optical materials, such as graphene can be characterized by a surface conductivity. So far, the transformation optics schemes have focused on three dimensional properties such as permittivity $\epsilon$ and permeability $\mu$. In this paper, we use a scheme for transforming surface currents to highlight that the surface conductivity transforms in a way different from $\epsilon$ and $\mu$. We use this surface conductivity transformation to demonstrate an example problem of reducing scattering of plasmon mode from sharp protrusions in graphene

Electron-photon scattering mediated by localized plasmons: A quantitative analysis by eigen-response theory

We show that the scattering interaction between a high energy electron and a photon can be strongly enhanced by different types of localized plasmons in a non-trivial way. The scattering interaction is predicted by an eigen-response theory, numerically verified by finite-difference-time-domain simulation, and experimentally verified by cathodoluminescence spectroscopy. We find that the scattering interaction associated with dark plasmons can be as strong as that of bright plasmons. Such a strong interaction may offer new opportunities to improve single-plasmon detection and high-resolution characterization techniques for high quality plasmonic materials.Comment: 4 pages, 4 figures (excluding Supporting Information

Photon Emission Rate Engineering using Graphene Nanodisc Cavities

In this work, we present a systematic study of the plasmon modes in a system of vertically stacked pair of graphene discs. Quasistatic approximation is used to model the eigenmodes of the system. Eigen-response theory is employed to explain the spatial dependence of the coupling between the plasmon modes and a quantum emitter. These results show a good match between the semi-analytical calculation and full-wave simulations. Secondly, we have shown that it is possible to engineer the decay rates of a quantum emitter placed inside and near this cavity, using Fermi level tuning, via gate voltages and variation of emitter location and polarization. We highlighted that by coupling to the bright plasmon mode, the radiative efficiency of the emitter can be enhanced compared to the single graphene disc case, whereas the dark plasmon mode suppresses the radiative efficiency

Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system

Hexagonal boron nitride (hBN) is a natural hyperbolic material which can also accommodate highly dispersive surface phonon-polariton modes. In this paper, we examine theoretically the mid-infrared optical properties of graphene-hBN heterostructures derived from their coupled plasmon-phonon modes. We found that the graphene plasmon couples differently with the phonons of the two Reststrahlen bands, owing to their different hyperbolicity. This also leads to distinctively different interaction between an external quantum emitter and the plasmon-phonon modes in the two bands, leading to substantial modification of its spectrum. The coupling to graphene plasmons allows for additional gate tunability in the Purcell factor, and narrow dips in its emission spectra

Excitation and Imaging of Resonant Optical Modes of Au Triangular Nano-Antennas Using Cathodoluminescence Spectroscopy

Cathodoluminescence (CL) imaging spectroscopy is an important technique to understand resonant behavior of optical nanoantennas. We report high-resolution CL spectroscopy of triangular gold nanoantennas designed with near-vacuum effective index and very small metal-substrate interface. This design helped in addressing issues related to background luminescence and shifting of dipole modes beyond visible spectrum. Spatial and spectral investigations of various plasmonic modes are reported. Out-of-plane dipole modes excited with vertically illuminated electron beam showed high-contrast tip illumination in panchromatic imaging. By tilting the nanostructures during fabrication, in-plane dipole modes of antennas were excited. Finite-difference time-domain simulations for electron and optical excitations of different modes showed excellent agreement with experimental results. Our approach of efficiently exciting antenna modes by using low index substrates is confirmed both with experiments and numerical simulations. This should provide further insights into better understanding of optical antennas for various applications.Comment: To be published in JVST B (accepted, Sep 2010) (15 pages, 6 figures, originally presented at EIPBN 2010

Chiral plasmon in gapped Dirac systems

We study the electromagnetic response and surface electromagnetic modes in a generic gapped Dirac material under pumping with circularly polarized light. The valley imbalance due to pumping leads to a net Berry curvature, giving rise to a finite transverse conductivity. We discuss the appearance of nonreciprocal chiral edge modes, their hybridization and waveguiding in a nanoribbon geometry, and giant polarization rotation in nanoribbon arrays