# <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.