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Abstracts and Talk Materials

Allan Boardman (University of Salford)

http://www.imr.salford.ac.uk/people/academic staff/allan boardman.shtml

http://www.imr.salford.ac.uk/people/academic staff/allan boardman.shtml

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.

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.

Metamaterials, which are engineered composite media with unconventional electromagnetic and optical properties, can be formed by
embedding sub-wavelength inclusions as artificial molecules in host media in order to exhibit specific desired response
functions. They can have exciting characteristics in manipulating and processing RF, microwave, IR and optical signal
information. Various features of these media are being investigated and some of the fundamental concepts and theories and modeling
of wave interaction with a variety of structures and systems involving these material media are being developed. From our
analyses and simulations, we have found that the devices and components formed by these media may be ultracompact and
subwavelength, while supporting resonant and propagating modes. This implies that in such structures RF, microwave, IR and optical
signals can be controlled and reshaped beyond the diffraction limits, leading to the possibility of miniaturization of optical
interconnects and design and control of near-field devices and processors for the next generation of information technology. This
may also lead to nano-architectures capable of signal processing in the near-field optics, which has the potential for significant
size reduction in information processing and storage. Furthermore, the nanostructures made by pairing these media can be compact
resonant components, resulting in either enhanced wave signatures and higher directivity or in transparency and scattering
reduction. We are also interested in nano-optics of metamaterial structures that effectively act as lumped
nano-circuit-elements. These may provide nano-inductors, nano-capacitors, nano-resistors, and nanodiodes as part of field
nanocircuits in the optical regimes or optical-field nanoelectronics--, and can provide roadmaps to more complex nanocircuits
and systems formed by collection of such nanostructures. All these characteristics may offer various potential applications in
high-resolution near-field imaging and microscopy, enhancement or reduction of wave interaction with nano-particles and
nano-apertures, nanoantennas and arrays, far-field sub-diffraction optical microscopy (FSOM), nano-circuit-filters, optical data
storage, nano-beam patterning and spectroscopy, optical-molecular signaling and optical coupling and interfacing with cells, to
name a few. In this talk, we present an overview of the concepts, salient features, recent developments, and some of the
potential applications of these metamaterials and structures, and will forecast some futures ideas and directions in this area.

Joint work with I Vitebskiy.

Wave propagation in spatially periodic media, such as photonic crystals, can be qualitatively different from any uniform substance. The differences are particularly pronounced when the electromagnetic wavelength is comparable to the minimal translation of the periodic structure. In such a case, the periodic medium cannot be assigned any meaningful refractive index. Still, such important features as negative refraction and/or opposite phase and group velocities for certain directions of light propagation can be found in almost any photonic crystal. The only reservation is that unlike hypothetical uniform left-handed media, photonic crystals are essentially anisotropic at frequency range of interest. Consider now a plane wave incident on a semi-infinite photonic crystal. One can assume, for instance, that in the case of positive refraction, the normal components of the group and the phase velocities of the transmitted Bloch wave have the same sign, while in the case of negative refraction, those components have opposite signs. What happens if the normal component of the transmitted wave group velocity vanishes? Let us call it a "zero-refraction" case. At first sight, zero normal component of the transmitted wave group velocity implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possibility. Instead, the transmitted wave can appear in the form of an abnormal grazing mode with huge amplitude and nearly tangential group velocity. This spectacular phenomenon is extremely sensitive to the frequency and direction of propagation of the incident plane wave. We also discuss some possible applications of this effect.

REFERENCES:

- A. Figotin, and I. Vitebskiy. Phys. Rev. E68, 036609 (2003).

- J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy. Phys. Rev. E71, (2005).

Wave propagation in spatially periodic media, such as photonic crystals, can be qualitatively different from any uniform substance. The differences are particularly pronounced when the electromagnetic wavelength is comparable to the minimal translation of the periodic structure. In such a case, the periodic medium cannot be assigned any meaningful refractive index. Still, such important features as negative refraction and/or opposite phase and group velocities for certain directions of light propagation can be found in almost any photonic crystal. The only reservation is that unlike hypothetical uniform left-handed media, photonic crystals are essentially anisotropic at frequency range of interest. Consider now a plane wave incident on a semi-infinite photonic crystal. One can assume, for instance, that in the case of positive refraction, the normal components of the group and the phase velocities of the transmitted Bloch wave have the same sign, while in the case of negative refraction, those components have opposite signs. What happens if the normal component of the transmitted wave group velocity vanishes? Let us call it a "zero-refraction" case. At first sight, zero normal component of the transmitted wave group velocity implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possibility. Instead, the transmitted wave can appear in the form of an abnormal grazing mode with huge amplitude and nearly tangential group velocity. This spectacular phenomenon is extremely sensitive to the frequency and direction of propagation of the incident plane wave. We also discuss some possible applications of this effect.

REFERENCES:

- A. Figotin, and I. Vitebskiy. Phys. Rev. E68, 036609 (2003).

- J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy. Phys. Rev. E71, (2005).

December 31, 1969

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.

Anand Gopinath (University of Minnesota, Twin Cities)

http://www.msi.umn.edu/cgi-bin/pi/pi_detail.html?piid=1040

Jaewon Kim

http://www.msi.umn.edu/cgi-bin/pi/pi_detail.html?piid=1040

Jaewon Kim

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.

This talk will describe negative refractive index metamaterials that are
based on transmission-line networks. It will focus on microwave structures
that consist of transmission lines loaded with reactive elements. Both
planar and volumetric negative refractive index metamaterials will be
presented and their operation explained. Finally, ways to push these
transmission-line based structures to optical frequencies using plasmonic
materials will be described.

We will review the analytic and computational foundations of
Green's function-based methods for electromagnetic scattering,
including high order integral representations, fast solvers,
and quasi-periodicity. We will then discuss the development of
easy-to-use numerical simulation environments, and present some
applications to photonic crystals, random microstructures, and
negative index materials.

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.

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.

A twisting and turning tale promises unimaginable
gains for the savvy investor of time and effort in metamaterials research.

December 31, 1969

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.

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.

December 31, 1969

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.

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.

December 31, 1969

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.

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.

We show how a slightly lossy superlens of thickness d cloaks
collections of polarizable line dipoles or point dipoles or finite
energy dipole sources that lie
within a distance of d/2 of the lens. In the limit as the loss
in the lens tends to zero, these become essentially invisible
from the outside through the cancelling effects of localized resonances
generated by the interaction of the source and the superlens. The
lossless perfect Veselago lens has
attracted a lot of debate. It is shown that as time
progresses the lens becomes increasingly opaque
to any physical dipole source located within a distance d/2 from
the lens and which has been turned on at time t=0. Here a physical
source is defined as one which supplies a
bounded amount of energy per unit time. In fact the lens cloaks the source
so that it is not visible from behind the lens either. For sources which
are turned on exponentially slowly there is an exact correspondence
between the response of the perfect lens in the long time constant limit
and the response of lossy lenses in the low loss limit. This is joint
work with Nicolae Nicorovici and Ross McPhedran.

October 4, 2006

We develop a new approach to negative index materials and
subwavelength imaging in the far field based on
strong anisotropy of the dielectric response. In contrast to
conventional negative refraction systems, our method does not rely on
magnetic resonance and does not require periodic patterning--leading
to lower losses and high tolerance to fabrication defects.

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.

We outline recent achievements in creating structural composite
materials with controlled electromagnetic properties, as an integral
part of a multifunctional material system. The electromagnetic
response is tailored by incorporating within the material small
amounts of suitably configured, periodically distributed, electric
conductors to produce distributed electric inductance and
capacitance. The small-scale response of the conductors can be
homogenized to give overall macroscopic EM material properties at
wavelengths that are orders of magnitude larger than the dimensions
of the periodicity of the structure. Periodic arrays of inductive
elements such as thin straight wires, loop-wires, coils, and other
conductive thin metallic structures can modify the effective electric
permittivity and the effective magnetic permeability of a composite
and make it negative. I will discuss the process of design, analysis,
manufacturing, and measurement of such composites. In particular, I
will review the UCSD's work on the design, production, and
experimental characterization of a 2.7 mm thick composite panels
having negative refractive index between 8.4 and 9.2 GHz. I will
also examine our work on a flat lens having a gradient variation of
negative index of refraction that can focus in the 10GHz range,
showing excellent agreement with full-wave simulations.

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.

December 31, 1969

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.

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.

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.

Metamaterials, i.e. artificial engineered structures with properties not available in nature are expected to open a gateway to unprecedented electromagnetic properties and functionality unattainable from naturally occurring materials. Negative-refractive index metamaterials create entirely new prospects for guiding light on the nanoscale, some of which may have revolutionary impact on present-day optical technologies. We review this new emerging field of metamaterials and recent progress in demonstrating a negative refractive index in the optical range, where applications can be particularly important. We also discuss strategies how to push the wavelength region of negative refractive index into the visible range by using plasmon resonant metal nanostructures.

December 31, 1969

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.

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.

October 3, 2006

Plane-wave representations are used to formulate the exact solutions to
frequency-domain and time-domain sources illuminating a magnetodielectric
slab with complex permittivity and permeability. In the special case
of a line source at *z=0* a distance *d<L* in front of an
*L* wide lossless double negative (DNG) slab with
permittivity and permeability equal to *-1*, the single-frequency
solution exhibits not only "perfectly focused" fields for *z>2L*
but also divergent infinite fields in the region *2d<z<2L*. In
contrast, the solution to the same lossless –1 DNG slab illuminated
by a sinusoidal wave that begins at some initial time *t=0* (and
thus has a nonzero bandwidth, unlike the single-frequency excitation
that begins at *t=-infinity*) is proven to have imperfectly
focused fields and convergent finite fields everywhere for all finite
time *t*. The proof hinges on the variation of permittivity and
permeability having a lower bound imposed by causality and energy
conservation. The minimum time found to produce a given resolution is
proportional to the estimate obtained by [Gomez-Santos, Phys. Rev. Lett.,
90, 077401 (2003)]. Only as *t* approaches infinity do the fields
become perfectly focused in the region *z>2L* and divergent
in the region *2d<z<2L*. These theoretical results, which
are confirmed by numerical examples, imply that divergent fields of the
single-frequency solution are not caused by an inherent inconsistency in
assuming an ideal lossless –1 DNG material, but are the result of
the continuous single-frequency wave (which contains infinite energy)
building up infinite reactive fields during the infinite duration of
time from *t=-infinity* to the present time *t* that the
single-frequency excitation has been applied.