Left-handed Materials Research Articles

On Dyakonov–Voigt surface waves guided by the planar interface of dissipative materials

Dyakonov-Voigt (DV) surface waves guided by the planar interface of (i) material $A$ which is a uniaxial dielectric material specified by a relative permittivity dyadic with eigenvalues $\epsilon^s_A$ and $\epsilon^t_A$, and (ii) material $B$ which is an isotropic dielectric material with relative permittivity $\epsilon_B$, were numerically investigated by solving the corresponding canonical boundary-value problem. The two partnering materials are generally dissipative, with the optic axis of material $A$ being inclined at the angle $\chi \in [ 0^\circ, 90^\circ ]$ relative to the interface plane. No solutions of the dispersion equation for DV surface waves exist when $\chi=90^\circ$. Also, no solutions exist for $\chi \in ( 0^\circ, 90^\circ )$, when both partnering materials are nondissipative. For $\chi \in [ 0 ^\circ, 90^\circ )$, the degree of dissipation of material $A$ has a profound effect on the phase speeds, propagation lengths, and penetration depths of the DV surface waves. For mid-range values of $\chi$, DV surface waves with negative phase velocities were found. For fixed values of $\epsilon^s_A$ and $\epsilon^t_A$ in the upper-half-complex plane, DV surface-wave propagation is only possible for large values of $\chi$ when $| \epsilon_B|$ is very small.

Effects of a low pressure plasma on a negative-permeability metamaterial

This article is focused on understanding of the effect of a low-pressure argon plasma on split ring resonator (SRR) metamaterial resonance. After an experimental characterization of SRR arrays that denies reaching critical density at 2.45 GHz, we present an alternative SRR, called sparse SRR, tunable in resonance frequency, that admits higher plasma density in its structure. This innovative structure is characterized with plasma to search for left-handed material signature. Several plasma effects such as gradients and sheaths are quantified. It is shown that plasma shifts the SRR resonance to higher frequencies. The amplitude of the resonance shift can not be estimated without taking into account the sheath thickness. Moreover, the plasma gradient causes the appearance of several distinguishable dips of resonances. These different effects are studied with simulations, highlighting the difficulty to create a left-handed material based on plasma-metamaterial.

Experimental realization of aqueous double negative metamaterials in near-megahertz range

Ultrasound is strongly attenuated and aberrated by the skull, principally due to the complex structure and acoustic impedance mismatch of skull which generates strong scattering. Analytical models and finite element methods have shown that negative index metamaterials matching skull properties can enable the transmission of US which enhances bidirectional transmission of ultrasonic signal for imaging. However, it is difficult to realize double-negative metamaterials in near-megahertz range experimentally because of the limitation of fabrication and characterization methods. Here we show the experimental realization of waterborne double negative acoustic metamaterials by coupling micrometer-size membrane-based negative density metamaterials with Helmholtz resonator-based negative modulus materials. Numerical simulation and experimental verification consistently exhibit the double negative behavior between 230 kHz and 410 kHz. We demonstrated the feasibility of creating ultrasonic-range metamaterials for non-invasive ultrasound imaging and neuron stimulation.

Self-adjoint indefinite Laplacians

Let $\Omega_-$ and $\Omega_+$ be two bounded smooth domains in $\mathbb{R}^n$, $n\ge 2$, separated by a hypersurface $\Sigma$. For $\mu>0$, consider the function $h_\mu=1_{\Omega_-}-\mu 1_{\Omega_+}$. We discuss self-adjoint realizations of the operator $L_{\mu}=-\nabla\cdot h_\mu \nabla$ in $L^2(\Omega_-\cup\Omega_+)$ with the Dirichlet condition at the exterior boundary. We show that $L_\mu$ is always essentially self-adjoint on the natural domain (corresponding to transmission-type boundary conditions at the interface $\Sigma$) and study some properties of its unique self-adjoint extension $\mathcal{L}_\mu:=\overline{L_\mu}$. If $\mu\ne 1$, then $\mathcal{L}_\mu$ simply coincides with $L_\mu$ and has compact resolvent. If $n=2$, then $\mathcal{L}_1$ has a non-empty essential spectrum, $\sigma_\mathrm{ess}(\mathcal{L}_{1})=\{0\}$. If $n\ge 3$, the spectral properties of $\mathcal{L}_1$ depend on the geometry of $\Sigma$. In particular, it has compact resolvent if $\Sigma$ is the union of disjoint strictly convex hypersurfaces, but can have a non-empty essential spectrum if a part of $\Sigma$ is flat. Our construction features the method of boundary triplets, and the problem is reduced to finding the self-adjoint extensions of a pseudodifferential operator on $\Sigma$. We discuss some links between the resulting self-adjoint operator $\mathcal{L}_\mu$ and some effects observed in negative-index materials.

The invisibility via anomalous localized resonance of a source for electromagnetic waves

We investigate the invisibility via anomalous localized resonance of a general source in anisotropic media for electromagnetic waves. To this end, we first introduce the concept of doubly complementary media in the electromagnetic setting. These are media consisting of negative-index metamaterials in a shell and positive-index materials in its complement for which the shell is complementary to a part of the core and a part of the exterior of the core–shell structure. We then provide criteria for establishing the invisibility of a source in these media. We show that (i) a source is invisible if the power is blown up; (ii) a source is invisible if it is sufficiently close to the plasmonic shell structure, and it is visible if it is far from this plasmonic structure; (iii) if the plasmonic structure is complementary to an annulus of constant isotropic medium, there is a critical length that characterizes the cloaking phenomena, as first observed in the two-dimensional acoustic quasistatic setting by Milton and Nicorovici.

Nonlinear anti-directional couplers with gain and loss.

Following the concept of PT-symmetric couplers, we propose a linearly coupled system of nonlinear waveguides, made of positive- and negative-index materials, which carry, respectively, gain and loss. We report novel bi- and multistability states pertaining to transmitted and reflective intensities, which are controlled by the ratio of the gain and loss coefficients, and phase mismatch between the waveguides. These states offer transmission regimes with extremely low threshold intensities for transitions between coexisting states, and very large amplification ratios between the input and output intensities leading to an efficient way of controlling light with light.

Distributed feedback lasing based on a negative-index metamaterial waveguide.

This Letter lays the foundation of a new type of distributed feedback (DFB) laser whose optical feedback is due to the evanescent coupling between an active positive-index material (PIM) waveguide and a lossy negative-index metamaterial (NIM) waveguide. Active PIM-NIM coupled-mode equations are presented and solved to characterize the dispersion relation, resonant optical gain, and lasing. The photonic bandgap of this grating-less DFB laser does not depend on a Bragg wavenumber, but depends on the difference between the wavenumbers of the PIM and NIM waveguides; controlling this wavenumber difference allows for single-mode lasing and, ultimately, single-mode broadband lasing.

Optical Properties of Dielectric-Graphene Left Hand Material Structure

ABSTRACTIt is well known the remarkable optical properties of both graphene and left handed materials, for which we study the optical properties of a multilayer system building by graphene-dielectric-left hand material. In this work, we show the transmission, reflection and absorption spectra for a different set of parameters of the left-handed material structure. It is important to highlight that the inclusion of graphene remarkably modifies the transmission and absorption spectra. The optical properties of the graphene-LHM can be modulated via the different parameters of system. We showed that the fill function do not change the line form of the spectra, however, modify their amplitudes. With respect to light polarization, it’s possible to observe that the spectra are widen for TM respect to TE polarization.

Dark state, zero-index and topology in phononic metamaterials with negative mass and negative coupling

Phononic metamaterials have attracted extensive attention since they are flexibly adjustable to control the transmission. Here we study a one-dimensional phononic metamaterial with negative mass and negative coupling, made of resonant oscillators and chiral couplings. At the frequency where the effective mass and coupling are both infinite, a flat band emerges that induces a sharply high density of states, reminiscent of the phononic dark states. At the critical point of band degeneracy, a phononic Dirac-like point emerges where both the effective mass and the inverse of effective coupling are simultaneously zero, so that zero-index is realized for phonons. Moreover, the phononic topological phase transition is observed when the phononic band gap switches between single mass-negative and single coupling-negative regimes. When these two distinct single negative phononic metamaterials are connected to each other, a phononic topological interface state is identified within the gap, manifested as the phononic counterpart of the topological Jackiw–Rebbi solution.

Ghost resonance in anisotropic materials: negative refractive index and evanescent field enhancement in lossless media

We show that dielectric waveguides formed by materials with strong optical anisotropy support electromagnetic waves that combine the properties of propagating and evanescent fields. These “ghost waves” are created in tangent bifurcations that “annihilate” pairs of positive- and negative-index modes and represent the optical analogue of the “ghost orbits” in the quantum theory of nonintegrable dynamical systems. Ghost waves can be resonantly coupled to the incident evanescent field, which then grows exponentially through the anisotropic media—as in the case of negative index materials. As ghost waves are supported by transparent dielectric media, the proposed approach to electromagnetic field enhancement is free from the “curse” of material loss that is inherent to conventional negative index composites.

A graphene‐based tunable negative refractive index metamaterial and its application in dynamic beam‐tilting terahertz antenna

AbstractGraphene is emerging as a kind of promising 2D material in designing reconfigurable terahertz (THz) devices owning to its tunability of the surface conductivity, which can be tuned by changing the chemical potential. In this work, we demonstrated a graphene‐based THz tunable negative refractive index metamaterial. The proposed metamaterial unit consists of a metallic resonant structure and embedded graphene, which presents a dynamic negative refractive index in the corresponding bands by modulating the chemical potential of the embedded graphene. In addition, a dynamic beam‐tilting antenna loaded with the metamaterial‐based stacked configuration has been designed. Through changing the refractive index of the metamaterial or the number of layers in the stacked configuration, the steering angle can be adjusted from 0° to −27°. This work demonstrates the great potential of graphene in THz tunable negative refractive index materials, provides a classic case about the practical application of controllable negative refractive index, and also gives an effective way to design dynamic beam‐tilting antenna.

Computational analysis of cutoff wavenumbers in rectangular waveguides filled with left‐handed material and/or right‐handed material

This paper investigates the cutoff wavenumbers and their geometric and dielectric dependence in rectangular waveguides filled with left-handed material (LHM) and/or right-handed material (RHM). A rigorous hybrid mode analysis of these structures produces the dispersion equations and the formulations of cutoff wavenumbers for the first three modes. It is shown how the geometric and dielectric parameters may influence the cutoff wavenumbers of the waveguides filled with LHM and/or RHM. The graphs of cutoff wavenumbers over a range of geometric and dielectric parameters sufficiently wide to cover most requirements of design and application have been plotted. The cutoff wavenumbers of waveguides with LHM increase as the thicknesses or the absolute values of permittivity of LHM increase. It is noted that the variation rules of cutoff wavenumbers in waveguides with LHM show different changing tendencies compared with the waveguides with RHM.

Surface waves with negative phase velocity supported by temperature-dependent hyperbolic materials

A numerical investigation was undertaken to elucidate the propagation of electromagnetic surface waves guided by the planar interface of two temperature-sensitive materials. One partnering material was chosen to be isotropic and the other to be anisotropic. Both partnering materials were engineered composite materials, based on the temperature-sensitive semiconductor InSb. At low temperatures the anisotropic partnering material is a non-hyperbolic uniaxial material; as the temperature is raised this material becomes a hyperbolic uniaxial material. At low temperatures, a solitary Dyakonov wave propagates along any specific direction in a range of directions parallel to the planar interface. At high temperatures, up to three different surface waves can propagate in certain directions parallel to the planar interface; one of these surface waves propagates with negative phase velocity (NPV). At a fixed temperature, the range of directions for NPV propagation decreases uniformly in extent as the volume fraction of InSb in the isotropic partnering material decreases. At a fixed volume fraction of InSb in the isotropic partnering material, the angular range for NPV propagation varies substantially as the temperature varies.

Characterization of a planar NID chiral interface under negative and/or positive phase velocity conditions

Using positive and/or negative phase velocity conditions, characteristics of a planar non-integer dimensional (NID) chiral interface are explored for specific values of NID parameter. For this purpose, discussion is divided into four cases. It is noted how characteristics of the interface changes when the situation is changed from one case to another. Impact of variation of NID parameter on the reflected power is also noted for each case.

Analysis of properties of metamaterial-based composite system

Magneto tunable left-handed material (LHM) which acts as a composite system has been theoretically demonstrated. The variation of the real and imaginary parts of the effective refractive index of the system is studied. The resonance that occurs in these studies are analyzed. The variation of impedance, reflectivity, absorptivity with frequency of the composite system was observed. The changes in resonance frequency with applied magnetic field are investigated. It is found that the resonance frequency increases with applied magnetic field.

Role of higher order nonlinearities in the instability spectra of two core oppositely directed saturated coupler

We theoretically investigate the impact of modified form of saturable nonlinearity in the modulational instability (MI) spectra of an opposite directed two core coupler with a negative index material channel. Particularly, our emphasize is on the interplay between the nonlinear saturation and the higher order nonlinear effects in fibers such as self-steepening and intrapulse Raman scattering. Using the modified nonlinear Schrödinger equation we appropriately model the light propagation in the two core opposite coupler with saturation of nonlinearity. A standard approach like the linear stability analysis was used to derive the dispersion relation pertaining to the MI. For a comprehensive picture, we consider both the normal and the anomalous dispersion regimes and special attention is paid to understand the influence of system parameters such as the power, coupling coefficient, saturation parameter, and nonlinear coefficient on the MI. Effect of different combinations of self-steepening as well as the contribution of intrapulse Raman scattering are discussed and its role on the instability bands are highlighted. Thus we report new ways to generate and manipulate the MI in two core oppositely directed couplers with the effect of saturation of nonlinearity.

Nonlinear electromagnetic metamaterials: Aspects on mathematical modeling and physical phenomena

Electromagnetic metamaterials with simultaneously negative effective dielectric permittivity ε and magnetic permeability μ (double-negative or left-handed or negative-index metamaterials) have a long history going back to the seminal paper of Veselago in 1968. Such metamaterials exhibit unusual and remarkable effects, like, e.g., the reversal of Snell's law, the support of backward-propagating waves, and the possibility of obtaining a perfect lens. Nonlinear left-handed metamaterials are also very useful in tunable structures with intensity-controlled transmission and in switching the material properties from left- to right-handed and back. In this paper, we present aspects on mathematical modeling and physical phenomena governing electromagnetic wave propagation in nonlinear metamaterials. The metamaterials under consideration are described by a Drude-Lorentz frequency model of the linear parts and a Kerr-type behavior of the nonlinear parts of ε and μ, respectively. We show that in the left-handed band of the metamaterial wave propagation is governed by a higher-order nonlinear Schrödinger (NLS) equation, and derive analytically ultra-short bright or dark solitons solutions. Then, we investigate wave propagation in the frequency band gaps, i.e., in the frequency regimes where ε and μ have different signs, and, hence, linear waves are evanescent. In these band gaps localization of waves is possible if a nonlinearity is induced in the metamaterial medium. We derive a dissipative short-pulse equation (DSPE) governing ultrashort pulses that may be formed in the band gaps and discuss its solitons solutions.

Double-negative acoustic metamaterials

The aim of this paper is to provide a mathematical theory for understanding the mechanism behind the double-negative refractive index phenomenon in bubbly fluids. The design of double-negative metamaterials generally requires the use of two different kinds of subwavelength resonators, which may limits the applicability of double-negative metamaterials. Herein we rely on media that consists of only a single type of resonant element, and show how to turn the acoustic metamaterial with a single negative effective property obtained in [H. Ammari and H. Zhang, Effective medium theory for acoustic waves in bubbly fluids near Minnaert resonant frequency. SIAM J. Math. Anal., 49 (2017), 3252--3276.] into a negative refractive index metamaterial, which refracts waves negatively, hence acting as a superlens. Using bubble dimers made of two identical bubbles, it is proved that both the effective mass density and the bulk modulus of the bubbly fluid can be negative near the anti-resonance of the two hybridized Minnaert resonances for a single constituent bubble dimer. A rigorous justification of the Minnaert resonance hybridization, in the case of a bubble dimer in a homogeneous medium, is established. The acoustic properties of a single bubble dimer are analyzed. Asymptotic formulas for the two hybridized Minnaert resonances are derived. Moreover, it is proved that the bubble dimer can be approximated by a point scatterer with monopole and dipole modes. For an appropriate volume fraction of bubble dimers with certain conditions on their configuration, a double-negative effective medium when the frequency is near the anti-resonance of the hybridized Minnaert resonances can be obtained.

Design and Analysis of a Novel LHM Structure Realized in Low-Frequency Band

The left-handed material (LHM) composed of a combination of magnetic and electrical resonator is an important method for designing the structure of the LHM. In this paper, a novel structure of LHM is designed and analyzed based on the traditional LHM structure. The parameter extraction method is applied to calculate the effective dielectric constant and effective magnetic permeability. The simulation results indicate that the effective dielectric constant and effective magnetic permeability can achieve negative value in a specific frequency band with about 200 MHz. It will provide important theoretical and practical guiding for designing the novel LHM structure with low-frequency band.

Optical properties of two-dimensional square lattices with smooth and randomly rough surfaces that include dispersive left-handed materials

The study of photonic crystals (PCs) is very importance for the development of new optical technologies. An interest in the investigation of PCs is the search of totally optical control of information in a circuit, with the idea of developing new technological applications that have great advantages over conventional electronic devices in the miniaturization of circuits. In the present work, we show a numerical study of the electromagnetic response of two-dimensional square lattices such as finite photonic structures formed by cylinders embedded in air and air holes in a finite plate composed of metamaterial. We applied a numerical technique known as Integral Equation Method (IEM) to calculate the optical response by calculating reflectance and transmittance as a function of the angle of incidence of finite systems proposed. The calculations were performed by varying the filling fractions and introducing a random roughness on the surfaces of the cylindrical inclusions that form our proposed systems, for the transverse magnetic field (TM) polarization. The results obtained show that the random roughness on the surfaces of the cylindrical inclusions affects their reflective and transmissive properties of two-dimensional square lattices. This is an important result to consider in manufacturing of finite two-dimensional square lattices, despite the existence of a well-developed technology for the manufacture of surfaces. These structures can be used, for example, for the development of filters, mirrors and lenses.