Negative refractive index

We consider some nonlinear phenomena in metamaterials with negative refractive index properties. Our consideration includes a survey of previously known results as well as identification of the phenomena that are important for applications of this new field. We focus on optical behavior of thin films as well as multi-wave interactions.

This paper introduces nonlinear transmission lines based on left-handed (LH) media and simulates harmonic generation and parametric generation in a material that, in two dimensions, could also focus microwaves. This paper discusses physical phenomena that lead to and affect self-supporting harmonic generation and parametric generation in LH nonlinear transmission-line media and outline advantages of these media for developing new types of compact and efficient frequency multipliers and "active lens" devices.

In this paper we report directivity enhancement by a short-focal-length plano-concave lens engineered by stacked subwavelength hole arrays (fishnet-like stack) with an effective negative index of refraction close to zero, n → 0, that arises from ε and μ near-zero extreme values. The plano-concave lens frequency response shows two enhancement peaks, one at the wavelength corresponding to n = −1 and, prominent in this configuration, another unexpected peak when n → 0 that comes as a result of the similar low values of ε and μ. The frequency-dependent negative refractive index and beam-forming properties of the lens are supported by finite-integration-frequencyand time-domain simulations and experimental results. This near-zero metamaterial lens can find applications in terahertz and even optics since the building block, stacked extraordinary optical transmission layers, has already been reported for those regimes under the name of fishnet structure.

Metamaterials are structures that provide electromagnetic properties not found in naturally occurring media; properties such as negative index of refraction, negative permittivity, or negative permeability. Since the appearance of Pendry's seminal work in the year 2000 on the feasibility of creating material with negative refractive index, a deluge of papers were published on metamaterials proposing the existence of phenomena and applications never conceived before. So why would such excitement about something that was not intended to be present naturally? The answer is simple. We tend to design or envision applications based on what we believe to exist. It is fair to argue that many applications were not envisioned simply because they would have to be based on materials that do not exist. With the realization of metamaterials, new phenomena and applications became not only possible, but even practical. In this paper, we discuss metamaterial applications that our group at the University of Waterloo has focused on. These applications are mostly related to wireless communication systems including sensing.

In this paper, we report a tunable planar metamaterial that is designed to achieve dual-band negative refractive index response in microwave regime. Its distinctive characteristic is the usage of tuning open stub-loaded stepped-impedance resonators. The frequency tunability of the second band is achievable via the adjustable open stub-loaded at the fixed tune of the first band. Parameter retrieval algorithm and full-wave simulation of prism-shaped structure were carried out to validate the negative refraction characteristics of metamaterial structure. The results predict its prospect as a very promising alternative to the conventional ones, which is compatibly applicable on various potential microwave devices especially when a dual-band function is required. In addition to that, its design flexibility offers various frequency bands at any possible choice, which alterable with the design parameters.

The race toward engineering metamaterials comprising of negative refractive indexes in the optical range started with the realization of negative-index materials for gigahertz frequencies six years ago. Sheer miniaturization of the gigahertz resonant structures is one approach. Alternative designs make use of localized plasmon resonant metal nanoparticles or nanoholes in metal films. Following this approach, a negative refractive index has

A double-periodic array of pairs of parallel gold nanorods is shown to have a negative refractive index in the optical range. Such behavior results from the plasmon resonance in the pairs of nanorods for both the electric and the magnetic components of light. The refractive index is retrieved from direct phase and amplitude measurements for transmission and reflection, which are all in excellent agreement with simulations. Both experiments and simulations demonstrate that a negative refractive index n' approximately -0.3 is achieved at the optical communication wavelength of 1.5 microm using the array of nanorods. The retrieved refractive index critically depends on the phase of the transmitted wave, which emphasizes the importance of phase measurements in finding n'.

In this investigation, anatase TiO 2 thin films were grown by radio frequency magnetron sputtering on glass substrates at a high sputtering pressure and room temperature. The anatase films were then annealed at 300-600 °C in air for a period of 1 hour. To examine the structure and morphology of the films, X-ray diffraction (XRD) and atomic force microscopy (AFM) methods were used respectively. From X-ray diffraction patterns of the TiO 2 films, it was found that the as-deposited film showed some differences compared with the annealed films and the intensities of the peaks of the crystalline phase increased with the increase of annealing temperature. From AFM images, the distinct variations in the morphology of the thin films were also observed. The optical constants were characterized using the transmission spectra of the films obtained by UV-VIS-IR spectrophotometer. Besides, optical thickness of the film deposited at room temperature was calculated and cross-checked by taking a cross-sectional image through SEM. The optical band gaps were evaluated through Tauc model. It was observed that TiO 2 films produced at room temperatures exhibited high visible transmittance and transmittance decreased slightly with the increase of annealing temperatures. The films were found to be crystalline having anatase phase. The refractive index of the films was found from 2.31-2.35 in the visible range. The extinction coefficient was nearly zero in the visible range and was found to increase with annealing temperature. The allowed indirect optical band gap of the films was estimated to be in the range from 3.39 to 3.42 eV which showed a small variation. The allowed direct band gap was found to increase from 3.67 to 3.72 eV. The porosity was also found to decrease at a higher annealing temperature making the film compact and dense.

We discuss the feasibility of negative refraction with reduced absorption in coherently driven atomic media. Coherent coupling of an electric and a magnetic dipole transition by laser fields induces magnetoelectric cross coupling and negative refraction at dipole densities which are considerably smaller than necessary to achieve a negative permeability. At the same time the absorption gets minimized due to destructive quantum interference and the ratio of negative refraction index to absorption becomes orders of magnitude larger than in systems without coherent cross coupling. The proposed scheme allows for a fine tuning of the refractive index. We derive a generalized expression for the impedance of a medium with magnetoelectric cross coupling and show that impedance matching to vacuum can easily be achieved. Finally we discuss the tensorial properties of the medium response and derive expressions for the dependence of the refractive index on the propagation direction.

Metamaterials are artificially engineered structures that have properties, such as a negative refractive index 1-4 , not attainable with naturally occurring materials. Negative-index metamaterials (NIMs) were first demonstrated for microwave frequencies 5,6 , but it has been challenging to design NIMs for optical frequencies and they have so far been limited to optically thin samples because of significant fabrication challenges and strong energy dissipation in metals 7,8 . Such thin structures are analogous to a monolayer of atoms, making it difficult to assign bulk properties such as the index of refraction. Negative refraction of surface plasmons was recently demonstrated but was confined to a two-dimensional waveguide 9 . Three-dimensional (3D) optical metamaterials have come into focus recently, including the realization of negative refraction by using layered semiconductor metamaterials and a 3D magnetic metamaterial in the infrared frequencies; however, neither of these had a negative index of refraction 10,11 . Here we report a 3D optical metamaterial having negative refractive index with a very high figure of merit of 3.5 (that is, low loss). This metamaterial is made of cascaded 'fishnet' structures, with a negative index existing over a broad spectral range. Moreover, it can readily be probed from free space, making it functional for optical devices. We construct a prism made of this optical NIM to demonstrate negative refractive index at optical frequencies, resulting unambiguously from the negative phase evolution of the wave propagating inside the metamaterial. Bulk optical metamaterials open up prospects for studies of 3D optical effects and applications associated with NIMs and zero-index materials such as reversed Doppler effect, superlenses, optical tunnelling devices 12,13 , compact resonators and highly directional sources 14 .

Since Abbe formulated his wave theory for microscopic imaging, the improvement of resolution of optical microscopes has been the aim of many research efforts. In the search for the maximum resolution, emphasis has been generally placed on the use of modern microscope objectives with the highest available numerical aperture (NA). But even with the best optical elements the use of conventional optical microscopes to image three-dimensional fluorescent samples has the drawback that any image focused at certain depth in the sample contains blurred information from the rest of the sample. This fact gives rise to 3-D images with strongly deteriorated contrast. In this context, this talk will be mainly devoted to optical-sectioning fluorescence techniques. Among them we cite single-photon confocal microscopes, confocal theta microscopy, structured-illumination microscopy, or selective plane illumination microscopy. Other solution is achieved by the use of two-photon excitation scanning microscopy, like in the case of 4Pi microscopes or the stimulated emission depletion microscopy.

Metamaterials exhibiting negative index of refraction has attracted a great amount of attention in recent years. These materials are artificial structures that exhibit characteristics not found in nature. Microstrip antennas covered by metamaterial are one of the interesting areas of study. In this paper fractal shape antenna is proposed and covered by two layers of modified split ring resonator. The results shows an enhancement in Reflection Coefficients, gain, directivity and far field shapes.

This study reports on tunable planar metamaterial design that is capable to achieve dual-band negative index of refraction responses operating in microwave regime. Its distinctive characteristic is the usage of tuning open stub-loaded stepped-impedance resonators. Parameters retrieval algorithm, and full-wave simulation of prismshaped structure were carried out to validate the negative refraction characteristics of metamaterial structure. The results predict its prospect as a very promising alternative to the conventional ones, which is compatibly applicable on various potential microwave devices especially when dual-band function is required. In addition to that, its design flexibility offers a various frequency bands at any possible choice, which is alterable together with any design parameters changes.

We study nonlinear transmission of an asymmetric multilayer structure created by alternating slabs of two materials with positive and negative refractive indices. We demonstrate that such a structure exhibits passive spatially nonreciprocal transmission of electromagnetic waves, the analog of the electronic diode. We study the properties of this left-handed diode and confirm its highly nonreciprocal and bistable transmittance by employing direct simulations.

The dispersive part of the refractive index, 1
−
δ
, of vanadium is determined by measuring the angular dependence of the Bragg peakat the V L
2
,
3
edge energy region using a Fe/V superlattice. This X-ray scattering technique provides access to the direct determination of the dispersive part of the refractive index across an absorption resonance and to the change of values from below unity to above unity. Wedemonstrate that previously tabulated values tend to underestimate the amplitude of the change in the real part of the refractive index. We alsoexamine the need for applying absorption and polarization corrections.

The properties and characteristics of a recently proposed anisotropic metamaterial based upon layered arrays of tightly coupled pairs of “dogbone” shaped stripe conductors have been explored in detail. It has been found that a metamaterial composed of such stacked layers exhibits artificial magnetism and may support backward wave propagation. The equivalent network models of the constitutive conductor pairs arranged in

The properties of periodic pairs of mutually twisted metallic (silver) crosses separated by dielectric layer have been investigated by numerical simulation. The results show that the exceptionally strong polarization rotation and circular dichroism, negative permeability and negative refractive index are found at the infrared communication wavelength (1.55µm).

| In this paper, we discuss the development of a bulk negative refractive index metamaterial made of cascaded Bfishnet[ structures, with a negative index existing over a broad spectral range. We describe in detail the design of bulk metamaterials, their fabrication and characterization, as well as the mechanism of how coupling of the unit cells can reduce loss in the material through an optical transmission-line approach. Due to the lowered loss, the metamaterial is able to achieve the highest figure of merit to date for an optical negative index metamaterial (NIM) in the absence of gain media. The increased thickness of the metamaterial also allows a direct observation of negative refraction by illuminating a prism made of the material. Such an observation results in an unambiguous demonstration of negative phase evolution of the wave propagating inside the metamaterial. Furthermore, the metamaterial can be readily accessed from free space, making it functional for optical devices. As such, bulk optical metamaterials should open up new prospects for studies of the unique optical effects associated with negative and zero index materials such as the superlens, reversed Doppler effect, backward Cerenkov radiation, optical tunneling devices, compact resonators, and highly directional sources.

This paper develops a quasi-analytical and self-consistent model to compute the polarizabilities of split ring resonators (SRRs). An experimental setup is also proposed for measuring the magnetic polarizability of these structures. Experimental data are provided and compared with theoretical results computed following the proposed model. By using a local field approach, the model is applied to the obtaining of the dispersion characteristics of discrete negative magnetic permeability and left-handed metamaterials. Two types of SRRs, namely, the so-called edge coupled-and broadside coupled-SRRs, have been considered. A comparative analysis of these two structures has been carried out in connection with their suitability for the design of metamaterials. Advantages and disadvantages of both structures are discussed.

Metamaterials are structures that provide electromagnetic properties not found in naturally occurring media; properties such as negative index of refraction, negative permittivity, or negative permeability. Since the appearance of Pendry's seminal work in the year 2000 on the feasibility of creating material with negative refractive index, a deluge of papers were published on metamaterials proposing the existence of phenomena and

The phenomenon of population ageing is becoming a major concern for the policy makers all over the world, for both developed and developing countries, during last two decades. But the problems arising out of it will have varied implications for underdeveloped, developing and developed countries.

This paper introduces an extension of the original finite-difference time-domain (FDTD) method for modeling doublenegative media characterized by high-order frequency-dependent permittivity and permeability. The approach basically consists of adding electric and magnetic current densities to Maxwell's curl equations and considering Ohm's law as a constitutive relationship. Current densities are discretized by using a weighted average in time and Ohm's law by applying the Mobius transformation technique.

We study linear guided waves propagating in a slab waveguide made up of a negative-refractive-index material, the so-called left-handed waveguide. We reveal that the guided waves in left-handed waveguides possess a number of peculiar properties such as the absence of the fundamental modes, mode double degeneracy, and sign-varying energy flux. In particular, we predict the guided waves with a dipole-vortex structure of their Poynting vector.

A novel distributed microstrip negative refractive index material (NRI) is presented, which comprises of microstrip line sections loaded with interdigital capacitance and short-circuited stub inductance. This new NRI removes the discrete lumped components and associated fabrication problems of conventional NRI. Simulation and experimental results show that the novel distributed NRI yields larger passbands and more distinct stopbands.

Este trabalho apresenta um estudo de revisão de modos propagantes em um guia-de-onda slab constituído de materiais com índices de refração negativo, os chamados metamateriais, Mostra-se que os modos guiados em um slab metamaterial possuem algumas propriedades particulares, tais como a propagação de ondas lentas simétricas ou anti-simétricas, a ausência de modos fundamentais para ondas rápidas e a possibilidade de propagação de ondas guiadas em um meio menos denso. A análise é baseada em expansões de campo no guia e nos espaços superior e inferior ao mesmo.

A comparison between exact solutions and surface impedance boundary condition method, for the phenomenon of light scattering from one-dimensional random rough metallic surfaces in both cases of polarization (s-and p-) is presented. The reflective properties of random rough metallic surfaces at a large angle of incidence have been reported on due to their potential applications in some of the radiative heat transfer research areas. The influence of surface roughness, shadowing effects, the nature of polarization, and the nature of the material on the behavior of reflectivity and emissivity has been quantified.

A low losses broadband planar negative refractive index metamaterial based on split-ring resonator (SRR) pairs is proposed and investigated experimentally and numerically at microwave frequency range. The transmission spectra of the single-layer SRR pairs were measured, and exhibited left-handed (LH) transmission passband clearly. The metal-dielectric-metal structure exhibits strong magnetic and electric responses simultaneously, and leads to negative permeability and negative permittivity. To further verify the LH properties of planer structure metamaterials, effect media parameters were retrieved, a refraction phenomenon based on a wedge-shaped model and negative phase advance between consecutive numbers of layers were also demonstrated.

Volumetric negative-refractive-index transmission-line (NRI-TL) metamaterials possessing homogeneous negative permittivity, negative permeability, and negative refractive index have been realized by stacking planar NRI-TL metamaterials in a multilayer form. One example is the "Veselago-Pendry Superlens" developed by Iyer and Eleftheriades (A. K. Iyer and G. V. Eleftheriades, IEEE Trans. Antennas Propag., 57, 1720-1727, 2009) which was able to experimentally demonstrate subdiffraction imaging in free space at microwave frequencies by virtue of its inherent designability and ease of implementation. In this work, we consider a new cylindrical topology in which the same planar NRI-TL metamaterial layers are arranged radially, resulting in inhomogeneous effective material properties that can vary with both radius and azimuth angle. Previous analytical studies involving cylindrical metamaterial structures have investigated the scattering of incoming plane waves, which has applications in stealth and cloaking (see, for exampleRadio Sci., 42, 2007). We, on the other hand, investigate the ability of inhomogeneous cylindrical metamaterial enclosures to manipulate the near and far fields produced by antennas placed within them. Such enclosures may provide a mechanism for antenna beam forming, in which the metamaterial's properties may be engineered to produce complex radiation patterns from simple antennas, and also imaging, in which it may be possible to produce magnification of subwavelength features of a source and other exotic phenomena. Our study models radially inhomogeneous cylindrical metamaterials using discrete, concentric cylindrical shells, each with homogeneous material properties. This model is suited to the radially periodic nature of the NRI-TL implementation, and facilitates both analytical and numerical solution. First, full-wave finite-element-method simulations are employed to determine the range of obtainable effective material parameters as different geometrical parameters of the NRI-TL metamaterial layers are varied. These effective material-parameter values are then assigned to the discrete multilayer model and an analytical approach based on a cylindrical-wave expansion is used to iteratively obtain the desired field distributions in all regions. These results are supplemented by full-wave simulations, and a variety of imaging phenomena and radiation patterns are observed. Since these results are based on NRI-TL metamaterial layers used in the fabrication of previous volumetric metamaterials, they lend themselves to subsequent experimental validation.

The scope of this paper is to design and simulate a novel structure having simultaneous negative permittivity and permeability so called double negative metamaterial or left handed material. The DNG structure consists of five rectangular split ring resonators on one side of dielectric medium and a couple of wires on other side. The complex permittivity, permeability and refractive index are determined from simulated Scattering parameters using direct retrieval method. Simulations of DNG structure are carried out using CST MWS. MATLAB is used for verification of negative values of structure's parameter.

We present here a finite slab of triangular checkerboard of negative refractive index material that exhibits a form of extraordinary transmission. We show that such a checkerboard can be used to confine light and can act as an open resonator. Effectively even a single point of intersection between three triangular wedges of negative refractive index may act as a resonator that confines light in the limit when n tends toward −1. We find that the quality of the confinement improves by adding more triangular wedges around the initial point in a checkerboard fashion. The confinement effect is also demonstrated by using a photonic crystal that shows the negative refraction effect.

Based on two versions of Maxwell's Equations we investigate the Poynting vector, the energy transport and the dispersion relation both for right-and left-handed systems. Furthermore, it is shown that the latter systems are necessarily dispersive in contrast to the former ones. In the end we discuss a published example where the mixing of expressions of both versions of Maxwell's Equations leads to unphysical conclusions. The presentation demonstrates for students how flexible can be the work with different versions of electrodynamics but also how carefully one has to be thereby.

A magnetic field tunable, broadband, low-loss, negative refractive index metamaterial is fabricated using yttrium iron garnet (YIG) and a periodic array of copper wires. The tunability is demonstrated from 18 to 23 GHz under an applied magnetic field with a figure of merit of 4.2 GHz/kOe. The tuning bandwidth is measured to be 5 GHz compared to 0.9 GHz for fixed field. We measure a minimum insertion loss of 4 dB (or 5.7 dB/cm) at 22.3 GHz. The measured negative refractive index bandwidth is 0.9 GHz compared to 0.5 GHz calculated by the transfer function matrix theory and 1 GHz calculated by finite element simulation.

In this paper we review some metasurfaces with negative values of effective refractive index, as scaffolds for a new generation of surface plasmon polariton-based biological or chemical sensors. The electromagnetic properties of a metasurface may be tuned by its full immersion into analyte, or by the adsorption of a thin layer on it, both of which change its properties as a plasmonic guide. We consider various simple forms of plasmonic crystals suitable for this purpose. We start with the basic case of a freestanding, electromagnetically symmetrical plasmonic slab and analyze different ultrathin, multilayer structures, to finally consider some two-dimensional "wallpaper" geometries like split ring resonator arrays and fishnet structures. A part of the text is dedicated to the possibility of multifunctionalization where a metasurface structure is simultaneously utilized both for sensing and for selectivity enhancement. Finally we give an overview of surface-bound intrinsic electromagnetic noise phenomena that limits the ultimate performance of a metasurfaces sensor.

In 2000, an artificially structured composite was shown to exhibit a negative index of refraction over a band of microwave frequencies 1 . This demonstration of a previously unexploited electromagnetic (EM) property proved the importance of engineered materials and has resulted in an extraordinary amount of continued development by scientists working in optics, electromagnetism, physics, engineering, and materials science. Experimental results revealing new phenomena and potential applications for these artificial materials, more recently termed metamaterials (MMs), have provided the basis for impressive growth in this burgeoning field. EM-MMs exhibit exotic properties not easily achieved using naturally occurring materials. In addition to a negative index (NI) of refraction, properties such as artificial magnetism 2 , negative permittivity, and negative permeability have been observed in fabricated MM composites; these material properties are either absent from conventional materials or are difficult to achieve over various bands of the EM spectrum 3,4 . With encouraging results having been demonstrated at microwave frequencies, there has been a determined push to extend MMs to the terahertz, infrared, and visible bands. The pursuit of these higher frequency MMs has led to the establishment of many research programs, conferences, workshops, and significant funding efforts dedicated to understanding and developing MMs.

One of the most important modern problems in modern electromagnetics is a design and study of negative index metamaterials that may enable sub-wavelength imaging at optical frequencies. Plasmonic periodic metal-dielectric nanostructures present one interesting possibility for both 2D and 3D negative index medium (NIM) systems. The displacement current near plasmonic resonance excitations may produce both negative permittivity and negative permeability (most difficult) in a NIM with e.g. “fishnet” metal-dielectric composite type structure. One obvious problem with a metallic NIM is that the response is strongly dispersive and lossy. Both of these effects are detrimental to sub-wavelength imaging. One way of mitigating losses is to use a gain medium. We address the question of sub-wavelength resolution in the fishnet NIM with and without gain medium.

The main directions of studies of materials with negative index of refraction, also called left-handed or metamaterials, are reviewed. First, the physics of the phenomenon of negative refraction and the history of this scientific branch are outlined. Then recent results of studies of photonic crystals that exhibit negative refraction are discussed. In the third part numerical methods for the simulation of negative index material configurations and of metamaterials that exhibit negative index properties are presented. The advantages and the shortages of existing computer packages are analyzed. Finally, details of the fabrication of different kinds of metamaterials are given. This includes composite metamaterials, photonic crystals, and transmission line metamaterials for different wavelengths namely radio frequencies, microwaves, terahertz, infrared, and visible light. Furthermore, some examples of practical applications of metamaterials are presented.

Novel isotropic planar and three-dimensional negative refractive index (NRI) metamaterial (MTM) designs consisting of periodically arranged cross structures are developed in the terahertz (THz) frequency regime using group theory. The novel designs not only avoid magnetoelectric coupling but also enable a simplified fabrication process. Using Finite-difference Time-Domain (FDTD) simulations, the design exhibits an NRI passband which is in good agreement with the S-parameters obtained from Fresnels equation. Cross-polarized fields are used to characterize the magnetoelectric coupling mechanism and determination of material properties of the medium via group theory aid in the characterization of the isotropy of the structure. Numerical simulations of a wedge composed of the proposed metamaterials prove the negative refractive index of the models.

The presented metamaterial consists of the matrix ͑magnesium diboride MgB 2 in a normal state, at room temperature͒ with randomly ͑or regularly͒ embedded spherical nanoparticles of a polaritonic crystal, SiC. The calculations demonstrate explicitly that the metamaterial exhibits negative refraction index behavior with low losses for a scattered wave. The result stands for both random and regular distributions of SiC nanoparticles inside the MgB 2 matrix. This favorable situation stems from the Drude-like behavior of both the low-energy, p 2 ͑ p 2 Ϸ 1.9 eV͒, and the high-energy, p 1 ͑ p 1 Ϸ 6.3 eV͒, plasmon modes of MgB 2 with plasmon losses, ␥ ഛ 0.25 eV. The effective medium parameters were calculated in the framework of the extended theories of Maxwell-Garnett ͓Philos. Trans. R. Soc. London, Ser. A 203, 385 ͑1904͔͒ and Lewin ͓Proc. Inst. Electr. Eng. 94, 65 ͑1947͔͒, and the obtained results are validated via ab initio finite difference time domain simulations.

We derive equations modeling the resonant interaction of electric and magnetic components of light fields with metal nanostructures. This paired resonance was recently shown to produce negative refractive index. The model equations are a generalization of the well-known Maxwell-Lorentz model. We demonstrate that in the case of nonlinear polarization and linear magnetization, these equations are equivalent to a system of equations describing the resonant interaction of light with plasmonic oscillations in metal nanospheres. A family of solitary wave solutions is found that is similar to pulses associated with self-induced transparency in the framework of the Maxwell-Bloch model. The evolution of incident optical pulses is studied numerically, as are the collision dynamics of the solitary waves. These simulations reveal that the collision dynamics vary from near perfectly elastic to highly radiative, depending on the relative phase of the initial pulses.

Some new band gaps are found in 1D photonic crystals (1D PC) composed of metamaterials (including negative-μ materials, negative-ε materials and negative refractive index materials). These band gaps are investigated by using the transfer matrix method. The ...