Left-handed Materials Research Articles

Negative refraction in terbium at ultraviolet frequencies.

One of the key challenges in the development of negative index metamaterials is creating a sufficiently strong magnetic response in the material. Rare-earth ions can contain a strong optical magnetic response even in the ultraviolet region of the spectrum, which can be enhanced using magneto-electric cross-coupling. Using energies, transition strengths, and linewidths from atomic structure software, along with realistic inhomogeneous broadenings and densities in a solid, we simulate a negative index scheme using a terbium crystal at a wavelength of 282 nm.

Wave propagation in a dual-periodic elastic metamaterial with multiple resonators

The behaviour of elastic metamaterials is dominated by the local structure of their representative cells and their periodicity. Previous works indicated that introducing multiple resonators in the representative cells can generate better performance, such as wider band gaps. Another interesting phenomenon observed in previous studies is that elastic metamaterials featuring dual periodicity can generate asymmetric wave transmission and negative effective mass and/or modulus. However, the general property of dual-periodic metamaterials coupled with multiple local resonators are rarely explored. In the current paper, the general mechanism of implementing multiple local resonators into dual-periodic metamaterial cells is systematically studied and a new elastic metamaterial model featuring negative effective mass and/or modulus based on translational resonances is presented. In this new model, the property of the multiple local resonators and the dual-periodicity can be conveniently adjusted to achieve single negativity (negative mass or negative modulus) or double negativity (negative mass and modulus) in different frequency ranges. Due to the great flexibility of generating negative effective parameters stemming from its unique structure, the proposed elastic metamaterial can generate a broad band gap in the low frequency range with exponential wave attenuation, and the positions of the frequency ranges featuring negative phase velocity can be modified according to the desired working frequencies. To elucidate the versatility of this model, numerical validation of typical examples has been provided to demonstrate the phenomena of wave attenuation and backward wave propagation.

Designing “Metamolecules” for Photonic Function: Reduced Backscattering

Metamaterials, subwavelength nanostructured materials, can exhibit novel optical properties such as a negative index of refraction. Dielectric core–nanoparticle satellite clusters, termed “metamolecules,” can have strong optical magnetic resonances in the visible wavelength range—a requirement to achieve negative refractive index materials. However, achieving the desired photonic properties is challenging due to limited control in forming the metamolecule structures. Here, polystyrene (PS) core–gold nanoparticle (AuNP) satellite metamolecules with highly ordered single layers (monolayers) of AuNPs are fabricated and single particle spectroscopy, electron tomography structural measurements, and electrodynamics simulations are conducted to study the photonic properties of metamolecules constituted of ≈100 AuNPs. The simulated and experimental spectra of the many metamolecules studied, including excitation with azimuthally and radially polarized light, are in excellent agreement. It is shown that the scattering properties of the metamolecules are dominated by the AuNPs near the “equator” of the cluster, and that backscattering is strongly suppressed when different multipolar modes (e.g., dipolar and quadrupolar) of electric or optical magnetic character have comparable intensity due to the π‐phase shift of their scattering. Both the optical excitation fields and the ordering of the nanoparticles within metamolecules affect their optical excitation and scattering properties, providing new insights into designing novel photonic metamaterials.

Chirped optical soliton and Jacobian elliptic function solutions in a metamaterial waveguide

The extended nonlinear Schrödinger equation depicts the pulse propagation in the negative index material with self-steepening and magnetooptic effects. By means of the F-function method, Jacobian elliptic sine and cosine function solutions and bright soliton solution are constructed. From these solutions, the amplitude, width and phase chirp of bright soliton are related to parameters of self-steepening and magnetooptic effects, linear phase and group velocity dispersion.

Extraordinary spin-orbit interaction in the plasmonic lens with negative index material.

Spin-orbit interactions are inherent in many basic optical processes in anisotropic and inhomogeneous materials, under tight focusing or strong scattering, and have attracted enormous attention and research efforts. Since the spin-orbit interactions depend on the materials where they occur, the study of the effects of materials on the spin-orbit interactions could play an important role in understanding and utilizing many novel optical phenomena. Here, we investigate the effect of negative-index material on the spin-orbit interactions in a plasmonic lens structure in the form of a circular slot in silver film. Numerical simulations are employed to study the influence of the negative-index material on the plasmonic vortex formation and the plasmonic focusing in the structure under circularly polarized excitations bearing different orbital angular momentum. We reveal that the presence of negative-index material leaves the plasmonic vortex field distribution and the corresponding topological charge unaltered during the spin-to-orbital angular momentum conversion, whereas reverses the rotation direction of in-plane energy flux of the plasmonic vortex and shifts the surface plasmon polariton focus position to the opposite direction compared to the case without negative-index material. This work will help further the understanding of the regulation of optical spin-orbital interactions by material properties and design optical devices with novel functions.

"Fast" Plasmons Propagating in Graphene Plasmonic Waveguides with Negative Index Metamaterial Claddings.

We propose the monolayer graphene plasmonic waveguide (MGPW), which is composed of graphene core sandwiched by two graphene metamaterial (GMM) claddings and investigate the properties of plasmonic modes propagating in the waveguide. The effective refraction index of the GMMs claddings takes negative (or positive) at the vicinity of the Dirac-like point in the band structure. We show that when the effective refraction index of the GMMs is positive, the plasmons travel forward in the MGPW with a positive group velocity (vg > 0, vp > 0). In contrast—for the negative refraction index GMM claddings—a negative group velocity of the fundamental mode (vg < 0, vp > 0) appears in the proposed waveguide structure when the core is sufficiently narrow. A forbidden band appears between the negative and positive group velocity regions, which is enhanced gradually as the width of the core increases. On the other hand, one can overcome this limitation and even make the forbidden band disappear by increasing the chemical potential difference between the nanodisks and the ambient graphene of the GMM claddings. The proposed structure offers a novel scheme of on-chip electromagnetic field and may find significant applications in the future high density plasmonic integrated circuit technique.

A modified rhombus shaped flexible wideband double negative (DNG) metamaterial for S, C, X, and Ku band applications

Abstract In this paper a wideband, flexible, and novel structured double negative (DNG) metamaterial is designed for S, C, X, and Ku microwave applications. The 12 mm × 12 mm sized metamaterial is fabricated on a flexible FR4 substrate with thickness 0.25 mm. The metamaterial shows a total wide DNG region of 8.2 GHz (3.8–4.3 GHz and 6.8–14.5 GHz). The transmission coefficient of the unit cell has a total band gap bandwidth of 8.3 GHz from frequency range 2 to 16 GHz. The designed metamaterial also exhibits an extra-large and continuous negative refractive index (NRI) bandwidth of 13 GHz (2–15 GHz). The stop band regions along with DNG and NRI regions individually cover S, C, X, and Ku microwave regions. The complete analysis is done using CST microwave studio. The simulated and measured transmission coefficient curves of the proposed metamaterial are in good agreement. The structure is simple, cost effective, flexible, light weight, and wideband covering S, C, X, and Ku microwave spectra.

Limiting Absorption Principle and Well-Posedness for the Time-Harmonic Maxwell Equations with Anisotropic Sign-Changing Coefficients

We study the limiting absorption principle and the well-posedness of Maxwell equations with anisotropic sign-changing coefficients in the time-harmonic domain. The starting point of the analysis is to obtain Cauchy problems associated with two Maxwell systems using a change of variables. We then derive a priori estimates for these Cauchy problems using two different approaches. The Fourier approach involves the complementing conditions for the Cauchy problems associated with two elliptic equations, which were studied in a general setting by Agmon, Douglis, and Nirenberg. The variational approach explores the variational structure of the Cauchy problems of the Maxwell equations. As a result, we obtain general conditions on the coefficients for which the limiting absorption principle and the well-posedness hold. Moreover, these {\it new} conditions are of a local character and easy to check. Our work is motivated by and provides general sufficient criteria for the stability of electromagnetic fields in the context of negative-index metamaterials.

Electrodeposited Negative Index Metamaterials with Visible and Near Infrared Response

AbstractNegative index metamaterials have revolutionized the field of photonics because of their unconventional electromagnetic properties absent in naturally occurring materials. It remains a challenge however, to achieve strong negative refractive index at optical frequencies over large areas in a device compatible fashion. In this work, a scalable method for the straightforward production of fishnet‐like negative index metamaterials combining soft nanoimprinting and electrodeposition is reported. In four simple steps, 2D arrays of pillars surrounded by metal–insulator–metal stacks made of gold and air gaps are created. The proper design of the geometrical features leads to negative indices from the visible to the near infrared, with values from ‐1.2 at 700 nm to ‐2.8 at 910 nm. The metamaterials are prepared on transparent conductive electrodes hence ready for device implementation. In addition, the nanostructures display high optical quality, which is corroborated with numerical simulations under normal and oblique incidence. As a proof of concept, the accessibility to the porosity of the metamaterial by studying the spectral changes produced when infiltrating different liquids through the metallic layers is demonstrated. The resonant wavelength increasing with the refractive index of the media makes the metamaterials potential platforms for both negative index structures and optical sensors.

Machine learning-based design of meta-plasmonic biosensors with negative index metamaterials

In this work, we explore the performance of plasmonic biosensor designs that integrate metamaterials based on machine learning algorithms. The meta-plasmonic biosensors were designed for optimized detection of DNA with a layer of double negative metamaterial modeled by an effective medium. An iterative transfer matrix approach was employed to generate training and test sets of resonance characteristics in the parameter space for machine learning. As a machine learning-based prediction of optical characteristics of a meta-plasmonic biosensor, multilayer perceptron and autoencoder (AE) were used as an algorithm, while the clustering algorithm was constructed by dimensional reduction based on AE and t-Stochastic Neighbor Embedding (t-SNE) as well as k-means clustering. Use of meta-plasmonic structure with analysis based on machine learning has found that enhancement of detection sensitivity by more than 13 times over conventional detection should be achievable with excellent reflectance curves. Further enhancement may be attained by expanding the parameter space.

Directing Cherenkov photons with spatial nonlocality

Abstract Cherenkov radiation in natural transparent materials is generally forward-propagating, owing to the positive group index of radiation modes. While negative-index metamaterials enable reversed Cherenkov radiation, the forward photon emission from a swift charged particle is prohibited. In this work, we theoretically investigate emission behaviours of a swift charged particle in the nanometallic layered structure. Our results show that Cherenkov photons are significantly enhanced by longitudinal plasmon modes resulting from the spatial nonlocality in metamaterials. More importantly, longitudinal Cherenkov photons can be directed either forward or backward, stringently depending on the particle velocity. The enhanced flexibility to route Cherenkov photons holds promise for many practical applications of Cherenkov radiation, such as novel free-electron radiation sources and new types of Cherenkov detectors.

Tunable terahertz optical bistability and multistability in photonic metamaterial multilayers containing nonlinear dielectric slab and graphene sheet

In this study, optical bistability and multistability phenomena are numerically investigated in the terahertz frequency domain based on the quasiperiodic photonic metamaterial multilayers, in which both the regular positive index and special negative index materials are artificially arranged, according to the interesting Fibonacci sequence structure. In order to obtain the tunable bistability and multibistability behaviors, the Kerr-type nonlinear dielectric layer and graphene sheet are sandwiched between two Fibonacci quasiperiodic one-dimensional photonic crystals. Results show that the intensity-dependent hysteresis curves including bistability and multistability are thoroughly discussed by judiciously changing the systematical parameters such as the frequency of incident wave, thickness of each layer, incident angle, as well as the chemical potential of graphene which can produce strong influences on the switch-up/down threshold values and widths of hysteresis loops.

Comparison of sensitivity for methods of positive and negative ion mass spectrometry, exemplified by nitrotoluenes

For a model series of nitro aromatic compounds comprising mono-, di- and trinitrotoluenes, and dinitrobenzene, using the same commercial experimental set up consisting of gas chromato-graphy/mass spectrometry (GC/MS) instrument equipped with a quadrupole analyzer, the two types of mass spectra were recorded, of positive ions (in the conventional, standard mode of electron ionization at 70 eV) and of negative ions (NI, generated at low, pre-ionization electron energies by resonant electron capture, REC). The comparative analysis of characteristic fragmentation processes was carried out for molecular ions of both signs. The sensitivity of REC NI MS method was established to enhance upon increasing the number of electron-withdrawing nitro groups, reaching or even outperforming that of the classical method of electron ionization (EI). Thus, the detection limit for trinitrotoluene in a solution was estimated as 5 ppm, which is by an order of magnitude lower as compared to the conventional EI mode of analysis. Comparison of the ion composition of NI mass spectra and of the relative intensities of ion peaks with the corresponding data obtained previously for the studied group of compounds by means of different types of mass spectrometers, has revealed a satisfactory inter-instrumental reproducibility of the NI mass spectra. The results reported herein indicate that the NI generation/registration mode, which can technically be readily available even without modifications of design of commercial GC/MS instrument in their basic configuration, is suitable to be introduced in laboratory practice as the additional tool for increasing the selectivity and reliability in detection/identification of trace amounts of compounds possessing a high electron af nity and for solving extraordinary structural and analytical problems.

Engineering lattice metamaterials for extreme property, programmability, and multifunctionality

Making materials lightweight while attaining a desirable combination of mechanical, thermal, and other physical properties is the “holy grail” of material science. Lattice materials, because of their porous structures and well-defined unit cell geometries, are suitable candidates to achieve lightweight with precisely tailored material properties. Aided by additive manufacturing techniques, a variety of lattice metamaterials with exceptional and unusual properties have been fabricated recently, yet, the rational designs of lattice metamaterials with programmability and multifunctionality are still challenging topics. In this perspective, we identify three emerging directions for lattice metamaterials: (1) developing architected lattice metamaterials with extreme and unusual properties that are non-typical in bulk materials, (2) designing lattice metamaterials with programmable mechanical properties that respond differently at different environments, loading paths, or controls, and (3) exploiting lattice metamaterials with multifunction, including tailorable thermal, mechanical, optical, piezoelectric, and negative-index material properties. These emergent directions portend the transitioning of lattice metamaterials from the stage of conventional materials to smart, adaptive, and versatile materials, which provide solutions to realistic problems in transport systems, wearable devices, and robotics, and continue to push the boundary of possibilities of architected metamaterials.

Chirped solitons in negative index materials generated by Kerr nonlinearity

In this paper, we are concerned with chirped solitary wave solutions in negative indexed materials having Kerr nonlinearity and self-phase modulation term. An auxiliary equation method together with an ansatz technique are employed. New chirped dark solitons, bright solitons, and trigonometric map solutions by using the auxiliary equation technique are obtained. Both 2- and 3-dimensional graphs are provided to illustrate the obtained results. The presented research will be useful especially for scientists who are studying solitons.

Reduced Linear Constrained Elastic and Viscoelastic Homogeneous Cosserat Media as Acoustic Metamaterials

We consider the reduced constrained linear Cosserat continuum, a particular type of a Cosserat medium, for three different material behaviors or symmetries: the isotropic elastic case, a special type of elastic transversely isotropic case, and the isotropic viscoelastic case. Such continua, in which stresses do not work on rates of microrotation gradients, behave as acoustic metamaterials for the (pure) shear waves and also for one branch of the mixed wave in the considered anisotropic material case. In elastic media, those waves do not propagate for frequencies exceeding a certain threshold, whence these media exhibit a single negative acoustic metamaterial behavior in this range. In the isotropic viscoelastic case, dissipation destroys the bandgap and favors wave propagation. This curious effect is, probably, due to the fact that the bandgap is associated not with the dissipation, but with the wave localization which can be destroyed by the viscosity. The dispersion curve is now decreasing in some part of the former bandgap, above a certain frequency, whence the medium is a double negative acoustic metamaterial. We prove the existence of a boundary wavenumber in the viscoelastic case and estimate its value. Below the characteristic frequency corresponding to the boundary of the elastic bandgap, the wave attenuation (logarithmic decrement) is a growing function of the viscous dissipation parameter. Above this frequency, the attenuation decreases as the viscosity increases.

Transmission Characteristics of Ultrasonic Longitudinal Wave Signals in Negative Refractive Index Materials

Longitudinal waves have important applications in modern scientific research and production; as a special acoustic wave, longitudinal waves have a sound transmission performance in negative refractive index materials. This paper has designed a new structure for negative refractive index materials by virtue of COMSOL software and conducted related simulation analysis. Experimental results illustrated that the structure designed had good acoustic longitudinal wave transmission performance. Besides, the effect of sound wave focusing could be achieved by a combination of existing test methods. The design proposed could break the limitation of previous structures on acoustic longitudinal wave transmission. This study is expected to have important implications for the development of solid metamaterial structures.

A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

SUMMARYOther than commonly assumed in seismology, the phase velocity of Rayleigh waves is not necessarily a single-valued function of frequency. In fact, a single Rayleigh mode can exist with three different values of phase velocity at one frequency. We demonstrate this for the first higher mode on a realistic shallow seismic structure of a homogeneous layer of unconsolidated sediments on top of a half-space of solid rock (LOH). In the case of LOH a significant contrast to the half-space is required to produce the phenomenon. In a simpler structure of a homogeneous layer with fixed (rigid) bottom (LFB) the phenomenon exists for values of Poisson’s ratio between 0.19 and 0.5 and is most pronounced for P-wave velocity being three times S-wave velocity (Poisson’s ratio of 0.4375). A pavement-like structure (PAV) of two layers on top of a half-space produces the multivaluedness for the fundamental mode. Programs for the computation of synthetic dispersion curves are prone to trouble in such cases. Many of them use mode-follower algorithms which loose track of the dispersion curve and miss the multivalued section. We show results for well established programs. Their inability to properly handle these cases might be one reason why the phenomenon of multivaluedness went unnoticed in seismological Rayleigh wave research for so long. For the very same reason methods of dispersion analysis must fail if they imply wave number kl(ω) for the lth Rayleigh mode to be a single-valued function of frequency ω. This applies in particular to deconvolution methods like phase-matched filters. We demonstrate that a slant-stack analysis fails in the multivalued section, while a Fourier–Bessel transformation captures the complete Rayleigh-wave signal. Waves of finite bandwidth in the multivalued section propagate with positive group-velocity and negative phase-velocity. Their eigenfunctions appear conventional and contain no conspicuous feature.

Homogenization of artificial media with a transmission line approach

The scientific research on metamaterials has achieved significant progress in recent years. In contrast, the related practical applications have encountered tough challenges. The insufficient homogeneity makes these artificial media lose its competitiveness to conventional continuous media. In this work, we propose a generalized approach to realize microwave metamaterials with ultra-subwavelength unit cells constructed with rolled-up transmission lines. As an illustration, we design and fabricate a bulk left-handed material sample with standard printed circuit board technique. With the normalized periodicity of the unit cells ranging from 1/61 to 1/48 of wavelength, the negative refractive index can be clearly measured in the frequency range between 1.02 and 1.3 GHz. Simulation shows that by employing the planar process for semiconductor integrated circuits, this homogeneity can be further improved to a level of 1/300 of the wavelength at gigahertz frequencies. Our work also provides a new method for obtaining ultra-small microwave resonators, which can be widely used for all kinds of planar technologies.

On the Accuracy of the Uniform Asymptotic Physical Optics Solution for the Diffraction by a PEC–DNG Metamaterial Junction

The effectiveness of the uniform asymptotic physical optics approach is tested with reference to the plane wave diffraction by a nonplanar junction that is formed by a perfect electrically conducting sheet and a lossy double-negative metamaterial layer. In particular, attention is paid to the accuracy of the total field that is obtained by adding the geometrical optics contributions to the diffraction one. Numerical tests and comparisons with full-wave numerical simulations are performed to assess the limits of validity of the approach.