Campuses:

<span class=strong>Reception and poster session</span>

Monday, October 2, 2006 - 3:40pm - 6:00pm
Lind 400
  • Error analysis of mixed finite element methods for

    wave propagation in double negative metamaterials


    In this paper, we develop both semi-discrete and fully-discrete
    mixed finite element methods for modeling wave propagation in three-dimensional
    double negative metamaterials. Optimal error estimates are proved for Nedelec
    spaces under the assumption of smooth solutions.
    To our best knowledge, this is the first error analysis obtained for Maxwell's
    equations when metamaterials are involved.
  • Novel metamaterial using Cubic high dielectric resonators
    Anand Gopinath (University of Minnesota, Twin Cities)Jaewon Kim (University of Minnesota, Twin Cities)
    Simulations have been performed on a novel
    metamaterial structure generated by periodic
    placement of identical high dielectric cubic
    resonators, in a low dielectric background. These
    resonators have degenerate modes, which implies
    that the TE and TM modes are resonant at the same
    frequency. Negative index behavior is deduced
    from these simulations near their resonant
    frequency. The periodic cubic structure with
    these high dielectric resonators results in a
    metamaterial, without any plasmonic metallic
    material, and should be low loss.
  • A homogenization-based study of the scattering resonances of a

    microstructured slab

    Haiping Shen (New York University)
    This poster studies the scattering resonance problem associated with a
    waveguide consisting of an infinite slab with 2-D microstructure embedded
    in a homogeneous material. The main goal is to understand how resonances
    are affected by the presence of the microstructure in the slab. Our method
    is similar to the prior work of S. Moskow, F. Santosa and M. Vogelius, as
    the investigation concentrates on the first order correction to the
    homogenized resonance. The outgoing radiation condition at infinity makes
    the problem non-selfadjoint. Furthermore, there are boundary layers on the
    edges of the slab, due to the presence of rapidly vaying coefficients in
    the highest order term of the underlying equation. Our main result is a
    formula for the first order correction. The formula indicates strong influence
    of the way microstructure hits the edges of the slab.
  • Homogenization theory of negative index materials in the optical

    range

    Gennady Shvets (The University of Texas at Austin)
    The challenge in engineering negative index materials in the optical
    frequency range involves designing sub-wavelength building blocks that
    exhibit both
    electric and magnetic activity. Achieving strong magnetic response is
    particularly challenging because magnetic moment of a structure scales as
    the square of the unit cell size. We address this challenge by employing
    higher order (multipole) electrostatic resonances that have a non-vaishing
    magnetic moment for a finite unite cell size. This approach provides a
    natural starting point for a perturbation theory that uses the ratio
    of the building block size to vacuum wavelength as the smallness
    parameter. Perturbative calculation yields the effective parameters of the
    metamaterial: effective epsilon and mu tensors. Those can be compared with
    the effective parameters extracted from fully electromagnetic simulations.
    Examples are given for two and three dimensional structures.
  • Nonlinear transmission in layered structures containing thin

    film of negative index material

    Natalia Litchinitser (University of Michigan)
    Co-authors: Ildar R. Gabitov, Andrei I. Maimistov, and Vladimir M. Shalaev.

    We investigate analytically and numerically nonlinear transmission in
    a bilayer structure consisting of a slab of positive index material
    with Kerr-type nonlinearity and a thin layer of negative index
    material (NIM). We find that a sub-wavelength layer of NIM
    significantly modifies the bistable nonlinear transmission
    characteristics of the considered bilayer structure and leads to
    nonreciprocal transmission with enhanced operational range,
    potentially enabling novel photonic devices such as optical diodes.
    The demonstrated high sensitivity of the nonlinear response of the
    structure to the material parameters of NIMs suggests that optical
    bistability in these structures has a strong potential for developing
    new tools for NIM characterization.
  • Radiation enhancement and radiation suppression by a left-handed

    metamaterial

    Allan Boardman (University of Salford)
    Joint work with K. Marinov
    (Photonics and Nonlinear Science Group, Joule Laboratory, Department of
    Physics, University of Salford, Salford M5 4WT, UK).

    It is shown that the perfect lens property of the left-handed metamaterials
    can be exploited to control the radiation efficiency of an electromagnetic
    radiation source (e.g. an antenna). In particular, the radiation
    characteristics of two identical sources, in the focal planes of the lens
    can be controlled depending on the relative phase difference between their
    feeding voltages. When the feeding voltages are pi-out-of-phase the
    resulting system behaves as a non-radiating configuration with a strong
    electromagnetic field confined in the space between the lens and the
    emitters and almost no electromagnetic radiation emitted. It is shown that
    such a system can be used as a very sensitive detector since any object
    disturbing the configuration of the electromagnetic fields inside the system
    stimulates radiation. Even objects of subwavelength dimensions are able to
    produce a substantial increase of the total power emitted by the system, and
    thus their presence can be revealed. The finite-difference time-domain
    (FDTD) numerical analysis performed allows a realistic system performance
    evaluation to be made. It is shown that if a pair of identical sources
    driven with in-phase feeding voltages are used in the same resonant
    configuration this results in an increase of the radiation resistance of
    each of the sources. The latter property can be useful for small antennas.
  • Optical hyperlens : Far-field imaging beyond the

    diffraction limit

    Zubin Jacob (Princeton University)
    Joint work with Leonid V. Alekseyev and Evgenii Narimanov.

    We propose an approach to far-field optical imaging
    beyond the
    diffraction limit. The proposed system allows image
    magnification,
    is robust with respect to material losses and can be fabricated
    by
    adapting existing metamaterial technologies in a cylindrical
    geometry.

  • Maximization of the quality factor of an optical resonator
    Fadil Santosa (University of Minnesota, Twin Cities)
    We consider resonance phenomena for the scalar wave equation in an
    inhomogeneous medium. Resonance is a solution to the wave equation
    which is spatially localized while its time dependence is harmonic
    except for decay due to radiation. The decay rate, which is inversely
    proportional to the qualify factor, depends on the material properties
    of the medium. In this work, the problem of designing a resonator
    which has high quality factor (low loss) is considered. The design
    variable is the index of refraction of the medium.

    Finding resonance in a linear wave equation with radiation boundary
    condition involves solving a nonlinear eigenvalue problem. The
    magnitude of the ratio between real and imaginary part of the
    eigenvalue is proportional to the quality factor Q. The optimization
    we perform is finding a structure which possesses an eigenvalue with
    largest possible Q. We present a numerical approach for solving
    this problem and describe results obtained by our method.
  • Observation of increased transmission in sol-gel nanocomposites
    Peter Palffy-Muhoray (Kent State University)
    Nanocomposites made of Ag nanowires imbedded in a sol-gel host have been
    morphologically and optically investigated. Sonication during solidification
    significantly improved nanowire dispersal. The data from the nanocomposites
    were compared to the data from pure sol-gels in order to determine the
    effects of the nanowires. Reflectometry data at 1064 nm show that the
    presence of ~5% nanowires (by volume) results in a decrease from 1.17 to
    ≈1.1 in the real part of the index of refraction accompanied by an increase
    in the imaginary part. Transmission loss in the pure sol-gel is mainly due
    to scattering from inhomogeneities, and the inclusion of nanowires (or the
    process of doing so) results in a reduction of optical loss at VIS-NUV
    wavelengths in several samples.
  • Negative nanophotonics: controlling diffraction limit and group velocity

    in anisotropy-based NIMs

    Viktor Podolskiy (Oregon State University)
    We explore the perspectives of a new type of materials with negative index
    of refraction - non-magnetic NIMs. In contrast to conventional NIMs, based
    either on magnetism or on periodicity, our design is non-magnetic and relies
    on the effective-medium response of anisotropic meta-materials in waveguide
    geometries. Being highly-tolerable to fabrication defects, anisotropic
    systems allow a versatile control over the magnitude and sign of effective
    refractive index and open new ways to efficiently couple the radiation from
    micro-scale optical fibers to nm-sized waveguides followed by
    sub-diffraction light manipulation inside sub-critical waveguiding
    structures. Specific applications include photonic funnels, capable of
    transferring over 25% of radiation from conventional telecom fiber to the
    spots smaller than 1/30-th of a wavelength, and NIM-based lenses with a
    far-field resolution of the order of 1/10-th of a wavelength. We also
    investigate the perspectives of active nanoscale NIMs and demonstrate that
    material gain can not only eliminate problems associated with absorption,
    but is also a powerful tool to control the group velocity from negative to
    slow positive values.
  • A boundary integral method and adaptive treecode for the linear

    Poisson-Boltzmann equation

    Peijun Li (University of Michigan)
    Joint work with Robert Krasny.

    A boundary integral method (BIM) is developed for computing the
    electrostatic potential of biomolecules governed by the linear
    Poisson--Boltzmann equation (PBE). Compared with finite difference
    method and finite element method, the BIM provides a rigorous
    treatment on issues of the singular charges, the solute-solvent
    interfaces, and the infinite domain associated with the PBE.
    However, the BIM involves singular kernels. Their accurate
    integration is an important issues. Rather than investing in the
    development of complicated quadratures, we employ simple
    regularization techniques to evaluate surface integrals with
    regularized kernels. Furthermore, the high computational cost
    incurred in the conventional BIM is reduced by using an adaptive
    treecode algorithm based on Taylor approximation in Cartesian
    coordinates, and necessary Taylor coefficients are computed by
    recurrence relations. Numerical experiments are included to show the
    efficiency and accuracy of the proposed method.
  • Nanoparticle susceptibilities and the bianisotropic

    formalism

    Jeremy Neal (Kent State University)
    Since the spatial extent of nanoparticles is not negligible compared to
    the wavelength of light, non-local effects may be expected in the
    electric and magnetic response of nanoparticles at optical frequencies.
    It has been suggested that such spatially non-local response may be
    taken into account via the bianisotropic formalism for the constitutive
    equations. We have calculated the susceptibilities of pairs of
    nanowires as a function of orientation relative to the incident fields
    using the discrete dipole approximation. We compare the results of our
    simulations with predictions of the bianisotropic description, and
    summarize our observations.

  • Optimization and control of energy transmission across

    photonic crystal slabs

    Robert Lipton (Louisiana State University)
    A variational approach is developed for the design of defects
    within a
    two-dimensional lossless photonic crystal slab to create and
    manipulate
    the location of high Q transmission spikes within band gaps.
    This phenomena is connected to the appearance of resonant
    behavior within
    the slab for certain crystal defects. The methodology is
    applied to design
    crystals constructed from circular dielectric rods embedded in
    a
    contrasting dielectric medium. This is joint work with Stephen
    Shipman and
    Stephanos Venakides.
  • Directed seeding of three-dimensional metal-semiconductor

    nanocomposites for negative index metamaterials

    Rachel Goldman (University of Michigan)
    Negative index of refraction materials (NIMs) are promising for
    several applications including near-field imaging and steering of EM
    radiation. Although NIMs have been demonstrated using hybrid
    metamaterials at microwave frequencies, high losses and narrow
    bandwidths are presently limiting their wide application. We are
    developing a novel approach to fabricating low-loss high density NIM
    semiconductor-metal nanocomposites, which consists of alternating
    sequences of focused-ion beam nanopatterning of metallic droplet
    arrays and film growth using molecular-beam epitaxy. We will
    discuss the formation and ordering of Ga and In droplets and droplet
    motifs on a variety of semiconductor surfaces. In addition, we will
    discuss the extension of this approach to 3D. In particular,
    information from scattering measurements of 1D and 2D droplet motifs
    will be input into theoretical NIMs calculations to guide the
    fabrication of 3D arrays of appropriate motifs.