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.

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).

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.

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.

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

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.

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 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.

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 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.

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.

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.

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.

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.

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.