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.

Brillouin light scattering by spin waves in magnetic metamaterials based on Co nanorods

We report on the investigations of spin wave modes in arrays of densely packed Co nanorods using Brillouin light scattering. We have observed a significant role of spin wave modes along the nanorod axis in contrast to infinite magnetic nanowires. Unusual optical properties featuring an inverted Stokes/anti-Stokes asymmetry of the Brillouin scattering spectra have been observed. The spectrum of spin wave modes in the nanorod array has been calculated and compared with the experiment. Experimental observations are explained in terms of a combined numerical-analytical approach taking into account both the low aspect ratio of individual magnetic nanorods and dipolar magnetic coupling between the nanorods in the array. The optical studies of spin-wave modes in the metamaterials with low aspect ratio nanorods have revealed new magnetic and magneto-optical properties compared to continuous magnetic films or infinite magnetic nanowires. Such magnetic metamaterials are important class of active metamaterials needed for prospective data storage and signal processing applications. (c) 2012 Optical Society of America

Harmonic generation and wave mixing in nonlinear metamaterials and photonic crystals (Invited paper)

The basic concepts and phenomenology of wave mixing and harmonic generation are reviewed in context of the recent advances in the enhanced nonlinear activity in metamaterials and photonic crystals. The effects of dispersion, field confinement and phase synchronism are illustrated by the examples of the on-purpose designed artificial nonlinear structures. (c) 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22:469482, 2012.

Electric and magnetic losses and gains in determining the sign of refractive index

Within the framework of classic electromagnetic theories, we have studied the sign of refractive index of optical medias with the emphases on the roles of the electric and magnetic losses and gains. Starting from the Maxwell equations for an isotropic and homogeneous media, we have derived the general form of the complex refractive index and its relation with the complex electric permittivity and magnetic permeability, i.e. n = root epsilon mu, in which the intrinsic electric and magnetic losses and gains are included as the imaginary parts of the complex permittivity and permeability, respectively, as epsilon = epsilon(r) + i(epsilon i) and mu = mu(r) + i mu(i). The electric and magnetic losses are present in all passive materials, which correspond, respectively, to the positive imaginary permittivity and permeability epsilon(i) > 0 and mu(i) > 0. The electric and magnetic gains are present in materials where external pumping sources enable the light to be amplified instead of attenuated, which correspond, respectively, to the negative imaginary permittivity and permeability epsilon(i) < 0 and mu(i) < 0. We have analyzed and determined uniquely the sign of the refractive index, for all possible combinations of the four parameters epsilon(r), mu(r), epsilon(i), and mu(i), in light of the relativistic causality. A causal solution requires that the wave impedance be positive Re {Z} > 0. We illustrate the results for all cases in tables of the sign of refractive index. One of the most important messages from the sign tables is that, apart from the well-known case where simultaneously epsilon < 0 and mu < 0, there are other possibilities for the refractive index to be negative n < 0, for example, for epsilon(r) < 0, mu(r) > 0, epsilon(i) > 0, and mu(i) > 0, the refractive index is negative n < 0 provided mu(i)/epsilon(i) > mu(r)/vertical bar epsilon(r)vertical bar. (c) 2006 Elsevier B.V. All rights reserved.

Single-negative negative index metamaterials with broad bandwidth - art. no. 683109

The theoretical method to design negative refractive index metamaterials by single negative permittivity metamaterials is presented. By designing the electric and magnetic response metamaterials separately, the complexity of the design work can be simplified a lot. For the magnetic response metamaterials, the metallic post structure is adopted. Varying the height of the post, the response wavelength can be adjusted linearly. For electric metamaterials, wire-mesh structure is adopted. The effective material parameters, including refractive index, impedance, permittivity and permeability are given. Such a structure has negative refractive index during a broad frequency band and easy to design.

Magnetic resonant cavity composing of a three layered plasmonic nanostructure

The magnetic-type plasmon resonant of a metal-dielectric-metal nanocavity working at the wavelength of 1.55 mu m is explored, in which the upper layer is periodically patterned with metallic nanostrip arrays. In the dielectric film layer, the magnetic energy intensity is enhanced about 1700 times when irradiated with a p-polarized plane wave. We numerically studied the dispersion of the modes and the Q-value of this periodic cavity arrays. Q value is estimated about 18 and still has room for further improvement. It provides a new type of nanocavity that exhibits a strong magnetic response.

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.

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.

Magnetization of left-handed metamaterials

We propose a possible mechanism for the generation of magnetic fields in negative refraction index composite metamaterials. Considering the propagation of a high-frequency modulated amplitude electric field in a left-handed material (LHM), we show that the ponderomotive interaction between the field and low-frequency potential distributions leads to spontaneous generation of magnetic fields, whose form and properties are discussed.

Higher-order effects and ultrashort solitons in left-handed metamaterials

Starting from Maxwell's equations, we use the reductive perturbation method to derive a second-order and a third-order nonlinear Schrodinger equation, describing ultrashort solitons in nonlinear left-handed metamaterials. We find necessary conditions and derive exact bright and dark soliton solutions of these equations for the electric and magnetic field envelopes.

Tailoring Alphabetical Metamaterials in Optical Frequency: Plasmonic Coupling, Dispersion, and Sensing

Tailoring optical properties of artificial metamaterials, whose optical properties go beyond the limitations of conventional and naturally occurring materials, is of importance in fundamental research and has led to many important applications such as security imaging, invisible cloak, negative refraction, ultrasensitive sensing, transformable and switchable optics. Herein, by precisely controlling the size, symmetry and topology of alphabetical metamaterials with U, S, Y, H, U-bar and V shapes, we have obtained highly tunable optical response covering visible-to-infrared (Vis-NIR) optical frequency. In addition, we show a detailed study on the physical origin of resonance modes, plasmonic coupling, the dispersion of electronic and magnetic surface plasmon polaritons, and the possibility of negative refraction. We have found that all the electronic and magnetic modes follow the dispersion of surface plasmon polaritons thus essentially they are electronic- and magnetic-surface-plasmon-polaritons-like (ESPP-like and MSPP-like) modes resulted from diffraction coupling between localized surface plasmon and freely-propagating light. Based on the fill factor and formula of magnetism permeability, we predict that the alphabetical metamaterials should show the negative refraction capability in visible optical frequency. Furthermore, we have demonstrated the specific ultrasensitive surface enhanced Raman spectroscopy (SERS) sensing of monolayer molecules and femtomolar food contaminants by tuning their resonance to match the laser wavelength, or by tuning the laser wavelength to match the plasmon resonance of metamaterials. Our tunable alphabetical metamaterials provide a generic platform to study the electromagnetic properties of metamaterials and explore the novel applications in optical frequency.

Electromagnetic energy within coated spheres containing dispersive metamaterials

An exact expression is derived for the time-averaged electromagnetic energy within a magneto-dielectric coated sphere, which is irradiated by a plane and time-harmonic electromagnetic wave. Both the spherical shell and core are considered to be dispersive and lossy, with a realistic dispersion relation of an isotropic split-ring resonator metamaterial. We obtain analytical expressions for the stored electromagnetic energies inside the core and the shell separately and calculate their contributions to the total average energy density. The stored electromagnetic energy is calculated for two situations involving a metamaterial coated sphere: a dielectric shell and dispersive metamaterial core, and vice versa. An explicit relation between the stored energy and the optical absorption efficiency is also obtained. We show that the stored electromagnetic energy is an observable sensitive to field interferences responsible for the Fano effect. This result, together with the fact that the Fano effect is more likely to occur in metamaterials with negative refraction, suggest that our findings may be explored in applications.

Planar magneto-photonic and gradient-photonic structures : crystals and metamaterials.

In the field of photonics, two new types of material structures, photonic crystals and metamaterials, are presently of great interest. Both are studied in the present work, which focus on planar magnetic materials in the former and planar gradient metamaterials in the latter. These planar periodic structures are easy to handle and integrate into optical systems. The applications are promising field for future optical telecommunication systems and give rise to new optical, microwave and radio technologies. The photonic crystal part emphasizes the utilization of magnetic material based photonic crystals due to its remarkable magneto-optical characteristics. Bandgaps tuning by magnetic field in bismuth-gadolinium-substituted lutetium iron garnet (Bi0.8 Gd0.2 Lu2.0 Fe5 O12) based one- dimensional photonic crystals are investigated and demonstrated in this work. Magnetic optical switches are fabricated and tested. Waveguide formulation for band structure in magneto photonic crystals is developed. We also for the first time demonstrate and test two- dimensional magneto photonic crystals optical. We observe multi-stopbands in two- dimensional photonic waveguide system and study the origin of multi-stopbands. The second part focus on studying photonic metamaterials and planar gradient photonic metamaterial design. We systematically study the effects of varying the geometry of the fishnet unit cell on the refractive index in optical frequency. It is the first time to design and demonstrate the planar gradient structure in the high optical frequency. Optical beam bending using planar gradient photonic metamaterials is observed. The technologies needed for the fabrication of the planar gradient photonic metamaterials are investigated. Beam steering devices, shifter, gradient optical lenses and etc. can be derived from this design.

Negative index metamaterials and metaspacers for optical frequencies

Metamaterials are artificial materials that exhibit properties, such as negative index of refraction, that are not possible through natural materials. Due to many potential applications of negative index metamaterials, significant progress in the field has been observed in the last decade. However, achieving negative index at visible frequencies is a challenging task. Generally, fishnet metamaterials are considered as a possible route to achieve negative index in the visible spectrum. However, so far no metamaterial has been demonstrated to exhibit simultaneously negative permittivity and permeability (double-negative) beyond the red region of the visible spectrum. This study is mainly focused on achieving higher operating frequency for low-loss, double-negative metamaterials. Two double-negative metamaterials have been proposed to operate at highest reported frequencies. The first proposed metamaterial is based on the interaction of surface plasmon polaritons of a thin metal film with localized surface plasmons of a metallic array placed close to the thin film. It is demonstrated that the metamaterial can easily be scaled to operate at any frequency in the visible spectrum as well as possibly to the ultraviolet spectrum. Furthermore, the underlying physical phenomena and possible future extensions of the metamaterial are also investigated. The second proposed metamaterial is a modification to the so-called fishnet metamaterial. It has been demonstrated that this ‘modified fishnet’ exhibits two double-negative bands in the visible spectrum with highest operating frequency in the green region with considerably high figure of merit. In contrast to most of the fishnet metamaterials proposed in the past, behavior of this modified fishnet is independent of polarization of the incident field. In addition to the two negative index metamaterials proposed in this study, the use of metamaterial as a spacer, named as metaspacer, is also investigated. In contrast to naturally available dielectric spacers used in microfabrication, metaspacers can be realized with any (positive or negative) permittivity and permeability. As an example, the use of a negative index metaspacer in place of the dielectric layer in a fishnet metamaterial is investigated. It is shown that fishnet based on negative index metaspacer gives many improved optical properties over the conventional fishnet such as wider negative index band, higher figure of merit, higher optical transmission and stronger magnetic response. In addition to the improved properties, following interesting features were observed in the metaspacer based fishnet metamaterial. At the resonance frequency, the shape of the permeability curve was ‘inverted’ as compared to that for conventional fishnet metamaterial. Furthermore, dependence of the resonance frequency on the fishnet geometry was also reversed. Moreover, simultaneously negative group and phase velocities were observed in the low-loss region of the metaspacer based fishnet metamaterial. Due to interesting features observed using metaspacer, this study will open a new horizon for the metamaterial research.