<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.