Analytic expressions for the constitutive parameters of magnetoelectric metamaterials

Electromagnetic metamaterials are artificially structured media typically composed of arrays of resonant electromagnetic circuits, the dimension and spacing of which are considerably smaller than the free-space wavelengths of operation. The constitutive parameters for metamaterials, which can be obtained using full-wave simulations in conjunction with numerical retrieval algorithms, exhibit artifacts related to the finite size of the metamaterial cell relative to the wavelength. Liu showed that the complicated, frequency-dependent forms of the constitutive parameters can be described by a set of relatively simple analytical expressions. These expressions provide useful insight and can serve as the basis for more intelligent interpolation or optimization schemes. Here, we show that the same analytical expressions can be obtained using a transfer-matrix formalism applied to a one-dimensional periodic array of thin, resonant, dielectric, or magnetic sheets. The transfer-matrix formalism breaks down, however, when both electric and magnetic responses are present in the same unit cell, as it neglects the magnetoelectric coupling between unit cells. We show that an alternative analytical approach based on the same physical model must be applied for such structures. Furthermore, in addition to the intercell coupling, electric and magnetic resonators within a unit cell may also exhibit magnetoelectric coupling. For such cells, we find an analytical expression for the effective index, which displays markedly characteristic dispersion features that depend on the strength of the coupling coefficient. We illustrate the applicability of the derived expressions by comparing to full-wave simulations on magnetoelectric unit cells. We conclude that the design of metamaterials with tailored simultaneous electric and magnetic response-such as negative index materials-will generally be complicated by potentially unwanted magnetoelectric coupling. © 2010 The American Physical Society.

Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials

We present a generalized nonlinear susceptibility retrieval method for metamaterials based on transfer matrices and valid in the nondepleted pump approximation. We construct a general formalism to describe the transfer matrix method for nonlinear media and apply it to the processes of three- and four-wave mixing. The accuracy of this approach is verified via finite element simulations. The method is then reversed to give a set of equations for retrieving the nonlinear susceptibility. Finally, we apply the proposed retrieval operation to a three-wave mixing transmission experiment performed on a varactor loaded split ring resonator metamaterial sample and find quantitative agreement with an analytical effective medium theory model. © 2010 The American Physical Society.

Phase conjugation and negative refraction using nonlinear active metamaterials.

We present an experimental demonstration of phase conjugation using nonlinear metamaterial elements. Active split-ring resonators loaded with varactor diodes are demonstrated theoretically to act as phase-conjugating or time-reversing discrete elements when parametrically pumped and illuminated with appropriate frequencies. The metamaterial elements were fabricated and shown experimentally to produce a time-reversed signal. Measurements confirm that a discrete array of phase-conjugating elements act as a negatively refracting time-reversal rf lens only 0.12λ thick.

Construction of invisibility cloaks of arbitrary shape and size using planar layers of metamaterials

Transformation optics (TO) is a powerful tool for the design of electromagnetic and optical devices with novel functionality derived from the unusual properties of the transformation media. In general, the fabrication of TO media is challenging, requiring spatially varying material properties with both anisotropic electric and magnetic responses. Though metamaterials have been proposed as a path for achieving such complex media, the required properties arising from the most general transformations remain elusive, and cannot implemented by state-of-the-art fabrication techniques. Here, we propose faceted approximations of TO media of arbitrary shape in which the volume of the TO device is divided into flat metamaterial layers. These layers can be readily implemented by standard fabrication and stacking techniques. We illustrate our approximation approach for the specific example of a two-dimensional, omnidirectional "invisibility cloak", and quantify its performance using the total scattering cross section as a practical figure of merit. © 2012 American Institute of Physics.

Broadband electromagnetic cloaking with smart metamaterials.

The ability to render objects invisible with a cloak that fits all objects and sizes is a long-standing goal for optical devices. Invisibility devices demonstrated so far typically comprise a rigid structure wrapped around an object to which it is fitted. Here we demonstrate smart metamaterial cloaking, wherein the metamaterial device not only transforms electromagnetic fields to make an object invisible, but also acquires its properties automatically from its own elastic deformation. The demonstrated device is a ground-plane microwave cloak composed of an elastic metamaterial with a broad operational band (10-12 GHz) and nearly lossless electromagnetic properties. The metamaterial is uniform, or perfectly periodic, in its undeformed state and acquires the necessary gradient-index profile, mimicking a quasi-conformal transformation, naturally from a boundary load. This easy-to-fabricate hybrid elasto-electromagnetic metamaterial opens the door to implementations of a variety of transformation optics devices based on quasi-conformal maps.

Probing the ultimate limits of plasmonic enhancement.

Metals support surface plasmons at optical wavelengths and have the ability to localize light to subwavelength regions. The field enhancements that occur in these regions set the ultimate limitations on a wide range of nonlinear and quantum optical phenomena. We found that the dominant limiting factor is not the resistive loss of the metal, but rather the intrinsic nonlocality of its dielectric response. A semiclassical model of the electronic response of a metal places strict bounds on the ultimate field enhancement. To demonstrate the accuracy of this model, we studied optical scattering from gold nanoparticles spaced a few angstroms from a gold film. The bounds derived from the models and experiments impose limitations on all nanophotonic systems.

Control of radiative processes using tunable plasmonic nanopatch antennas.

The radiative processes associated with fluorophores and other radiating systems can be profoundly modified by their interaction with nanoplasmonic structures. Extreme electromagnetic environments can be created in plasmonic nanostructures or nanocavities, such as within the nanoscale gap region between two plasmonic nanoparticles, where the illuminating optical fields and the density of radiating modes are dramatically enhanced relative to vacuum. Unraveling the various mechanisms present in such coupled systems, and their impact on spontaneous emission and other radiative phenomena, however, requires a suitably reliable and precise means of tuning the plasmon resonance of the nanostructure while simultaneously preserving the electromagnetic characteristics of the enhancement region. Here, we achieve this control using a plasmonic platform consisting of colloidally synthesized nanocubes electromagnetically coupled to a metallic film. Each nanocube resembles a nanoscale patch antenna (or nanopatch) whose plasmon resonance can be changed independent of its local field enhancement. By varying the size of the nanopatch, we tune the plasmonic resonance by ∼ 200 nm, encompassing the excitation, absorption, and emission spectra corresponding to Cy5 fluorophores embedded within the gap region between nanopatch and film. By sweeping the plasmon resonance but keeping the field enhancements roughly fixed, we demonstrate fluorescence enhancements exceeding a factor of 30,000 with detector-limited enhancements of the spontaneous emission rate by a factor of 74. The experiments are supported by finite-element simulations that reveal design rules for optimized fluorescence enhancement or large Purcell factors.

A Plasmonic Gold Nanostar Theranostic Probe for In Vivo Tumor Imaging and Photothermal Therapy.

Nanomedicine has attracted increasing attention in recent years, because it offers great promise to provide personalized diagnostics and therapy with improved treatment efficacy and specificity. In this study, we developed a gold nanostar (GNS) probe for multi-modality theranostics including surface-enhanced Raman scattering (SERS) detection, x-ray computed tomography (CT), two-photon luminescence (TPL) imaging, and photothermal therapy (PTT). We performed radiolabeling, as well as CT and optical imaging, to investigate the GNS probe's biodistribution and intratumoral uptake at both macroscopic and microscopic scales. We also characterized the performance of the GNS nanoprobe for in vitro photothermal heating and in vivo photothermal ablation of primary sarcomas in mice. The results showed that 30-nm GNS have higher tumor uptake, as well as deeper penetration into tumor interstitial space compared to 60-nm GNS. In addition, we found that a higher injection dose of GNS can increase the percentage of tumor uptake. We also demonstrated the GNS probe's superior photothermal conversion efficiency with a highly concentrated heating effect due to a tip-enhanced plasmonic effect. In vivo photothermal therapy with a near-infrared (NIR) laser under the maximum permissible exposure (MPE) led to ablation of aggressive tumors containing GNS, but had no effect in the absence of GNS. This multifunctional GNS probe has the potential to be used for in vivo biosensing, preoperative CT imaging, intraoperative detection with optical methods (SERS and TPL), as well as image-guided photothermal therapy.

Channelled Waves in Anisotropic Mesh Metamaterials

Channelled waves in 2-D periodic anisotropic L-C mesh metamaterials have been investigated. Circuit simulation and the newly developed analytical model of a unit cell have demonstrated full qualitative agreement for both lossless and lossy cases. Isofrequencies for a lattice unit cell and the circuit simulations of finite meshes have shown that propagating waves are channelled from a point source as pencil beams which can travel only along specific trajectories. The beam direction varies with frequency, and at the resonance frequency, the phase and group velocities of the travelling wave are orthogonal. The effect of losses was explored, and it was shown that losses cause qualitative changes of the channelled wave type. It was proven that the channelled waves do not follow the laws of geometrical optics (Snell's law, specular reflection, etc.) at the interfaces of L-C meshes but are governed by the conditions of phase synchronism and impedance matching. Only in the special case of dual L-C and C-L meshes with the interface parallel to the axis of rectangular grid excited at the resonance frequency (X=1) do the channels follow the trajectories of optical rays. A planar mesh test cell has been designed and used for retrieving the unit cell L-C parameters from the S-parameter measurements.

Uniaxial metallo-dielectric metamaterials with scalar positive permeability

The dispersion relation for plane waves in uniaxial metamaterials with indefinite dielectric tensors and scalar positive permeability is theoretically investigated. It is found, that the isofrequency surfaces of the plane extraordinary waves have a hyperbolic shape which allows the propagation of waves with infinitely long wave vectors. As an example a metallodielectric multilayer was considered and the dispersion relations were determined using an effective medium approximation and an analytically exact Bloch wave calculation. The extraordinary waves in this structure are identified as multilayer plasmons and the validity of the effective medium approximation is examined.

WAVES IN 2D ANISOTROPIC L-C LATTICE METAMATERIALS:PHENOMENOLOGY AND PROPERTIES

Anisotropic metamaterials composed of 2D periodic infi- nite and finite periodic lattices of lumped inductor (L) and capacitor (C) circuits have been explored. The unique features of wave channeling on such anisotropic lattices and scattering at their interfaces and edges are reviewed and illustrated by the examples of the specific arrangements. The lattice unit cells composed of inductors and capacitors (basic mesh) as well as of assemblies comprised of double series, double parallel, and mixed parallel-series L-C circuits are discussed.

Electrically switchable nonreciprocal transmission of plasmonic nanorods with liquid crystal

The electro-optic response of a cell consisting of a thin layer of liquid crystal deposited onto gold nanorods embedded in thin film alumina with a transparent top electrode has been investigated. For p-polarized light incident from the liquid crystal side, the extinction peak associated with the nanorod longitudinal plasmon resonance is completely suppressed. The peak could be recovered by applying an external electric field parallel to the long axis of the nanorods. No extinction peak suppression is observed when the light was incident from the nanorod side of the cell. The effect is explained by polarization properties of liquid crystal.

Self-focusing and envelope pulse generation in nonlinear magnetic metamaterials

The self-modulation of waves propagating in nonlinear magnetic metamaterials is investigated. Considering the propagation of a modulated amplitude magnetic field in such a medium, we show that the self-modulation of the carrier wave leads to a spontaneous energy localization via the generation of localized envelope structures (envelope solitons), whose form and properties are discussed. These results are also supported by numerical calculations.

METAMORPHOSE European Doctoral Programs on Metamaterials - State-of-the-art

A new European Doctoral Program on Metamaterials has been initiated by the European Union (EU) Network of Excellence METAMORPHOSE. So far, twenty European academic institutions have established a consortium that operates a geographically distributed doctoral school in the emerging and multidisciplinary field of metamaterials.