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Frequency-selective surfaces (FSSs) with in-band electromagnetic (EM) wave transmission and out-of-band electromagnetic waves shielding properties are highly demanded. The recent rise of metacomposites offers a new way to construct FSSs which integrates double negative electromagnetic property and electromagnetic interference (EMI) performance in one material. Herein, the buckypaper (BP)/yttrium iron garnet (YIG)-graphene aerogel (GA)/BP metacomposites with sandwich structure were constructed in this research. The combined effects of conductive networks formed in BP and GA, and the magnetic resonance of YIG particles led to double negative performance of composites with 30 wt% YIG content from 810 MHz to 1 GHz. Besides, the composite exhibited great EMI properties derived from poor impedance match and good microwave absorption. With negative refraction and interference of microwaves in different frequency range, this metacomposite provides a novel approach for the construction of frequency-selective surfaces.

The novel phenomena in nanophotonic materials, such as the angle-dependent reflection and negative refraction effect, are closely related to the photonic dispersions E ( p ) . E ( p ) describes the relation between energy E and momentum p of photonic eigenmodes, and essentially determines the optical properties of materials. As E ( p ) is defined in momentum space (k-space), the experimental method to detect the energy distribution, that is the spectrum, in a momentum-resolved manner is highly required. In this review, the momentum-space imaging spectroscopy (MSIS) system is presented, which can directly study the spectral information in momentum space. Using the MSIS system, the photonic dispersion can be captured in one shot with high energy and momentum resolution. From the experimental momentum-resolved spectrum data, other key features of photonic eigenmodes, such as quality factors and polarization states, can also be extracted through the post-processing algorithm based on the coupled mode theory. In addition, the interference configurations of the MSIS system enable the measurement of coherence properties and phase information of nanophotonic materials, which is important for the study of light-matter interaction and beam shaping with nanostructures. The MSIS system can give the comprehensive information of nanophotonic materials, and is greatly useful for the study of novel photonic phenomena and the development of nanophotonic technologies.

Double negative elastic metamaterials are a kind of novel artificial materials with unique ability to manipulate elastic wave propagation in the subwavelength scale. They are generally designed by inducing the combination of multiple resonance with different negative effective parameters. However, due to the limitation of empirical structural shape and design tools, these metamaterials are made by complex multiphase materials but possess a relatively narrow frequency range with double negativity, which is unsuitable for practical engineering applications. In this work, a shape optimization and single-phase chiral elastic metamaterials (EMMs) based strategy is presented for designing the EMMs with a broadband double negativity (negative mass density and bulk modulus). Several numerical examples are presented to validate the method by considering different initial shapes, target frequency ranges and design variables. Besides, numerical simulations related to double negativity including negative refraction and imaging are investigated by using the optimized chiral EMMs. Interestingly, elastic wave mode conversion and super-resolution imaging of 0.28λ are observed. The proposed metamaterial combined with the design approach is a very efficient way to obtain double negativity over a broad frequency band and it may thus have great potential for designing new elastic metamaterials.

International audience; Wave propagation through a locally resonant metamaterial characterized by anisotropic dynamic mass density is studied. The polarizations and velocities of waves are obtained from an extended Christoffel matrix. The set of waves induced by a body wave coming through the interface with an elastic material is described. Reflexion and refraction coefficients corresponding to the ratio of real Poynting vectors are obtained, showing that some of these coefficients are singular. In this case, the Poynting vector of the set of coupled waves must be used. This Poynting vector can display a negative refraction. The conditions leading to negative refraction are described and several examples of negative refraction are displayed.

Acoustic black holes (ABHs) in plates have shown great potential in a variety of applications that range from passive noise and vibration reduction, to energy harvesting thanks to localization, or to unusual flexural wave manipulation like lensing, or negative refraction and bi-refraction. The ABH effect can be typically achieved in plates by embedding regular arrays of circular cuneate indentations, with power-law profile. In this paper, we suggest new ring-shaped ABH designs that may be used for vibration isolation. Many common situations in the vibroacoustics of built-up structures involve wave propagation in plates excited at a small source area. This could be the case, for instance, of a beam/plate connection. It is herein proposed to surround the plate excitation region by means of ring-shaped ABHs to prevent the transmission of vibrations outside them. Several configurations of ABHs are tested, from concentric annular ABHs in different number and sizes to traditional circular ABHs in a ring arrangement. The inclusion of stiffeners to prevent excessive structural plate weakness due to the ABH indentations is also addressed. The performance of the ABH designs are analyzed by means of a semi-analytical approach that uses two-dimensional Gaussian functions to approximate the plate flexural displacement field, in the framework of the Rayleigh-Ritz method. The annular ABHs are shown to exhibit remarkable good isolation for the whole frequency range. An explanation is provided for their behavior.

This paper proposed a metamaterial with dual-band, wide bandwidth, high quality negative refractive band and quasi-zero refractive band. It consists of a symmetrical double-opening ring and bimetallic wire, and is verified by classical triangle method. The mechanism of dual-band negative refraction is studied, and the analysis of surface current and field distribution is completed. Through the novel test scheme, the free-space measurement of electromagnetic parameters was carried out. The test results are highly matched with the simulation results.

Metamaterials with hyperbolic equal-frequency contours possess unique properties, which offer novel means in elastic wave manipulation. The existing designs are either resonant-structure based that have large damping loss or have a relatively narrow working frequency range. In this paper, a topology optimization approach is developed to design non-resonant hyperbolic elastic metamaterials over a broad frequency range. Based on the physical nature of hyperbolic metamaterials, a two-step topology optimization design scheme is formulated and solved by a gradient-based optimizer. By engineering the dispersion band structure, non-resonant hyperbolic metamaterials have been successfully designed. Novel features such as negative refraction, wave partial focusing and super-resolution imaging have been numerically demonstrated.

A plano-concave lens based on a one-dimensional (1D) ternary photonic crystal (PhC) was proposed, which was formed by periodic repetition of dielectric material layers MgF2, Ge, and SiO2. The dispersion relation and transmission spectrum of the 1D ternary PhC were obtained by the transfer matrix method (TMM). The plano-concave lens can achieve sub-wavelength focusing due to negative refraction. The negative refraction band can be moved to the visible light band with specific parameter adjustment. A broadband focusing in the visible wavelength range from 580 nm to 755 nm was demonstrated. Changes of light intensity and full width at half maximum (FWHM) with focusing wavelength (FW) were investigated and a focal point with almost a theoretical minimum FWHM of 0.275 λ was obtained at a wavelength of 675 nm. The functional relationship between the FW and the focal distance was derived theoretically. The theoretical calculation results are basically consistent with the numerical results. The results provide a promising methodology and theoretical guidance for the application of sub-wavelength focusing of 1D ternary PhC plano-concave lenses.

In the non-stationary process of doubling the frequency of high-power laser radiation in metamaterials, the effects of self- and cross-phase modulation, related to the cubic nonlinearity of the medium, are considered. It is assumed that the pump wave propagates in a region with negative refraction. It is shown that in the case of a nonlinear optical process of frequency doubling of an intense light wave in a metamaterial, it is important to take into account the influence of a powerful pump wave. It is shown that the frequency shift of the maximum of the harmonic spectrum in the metamaterial is related to the cubic nonlinearity of the medium. It is shown how the width of the spectrum of the second-harmonic depends on the pump intensity, linear and nonlinear phase detuning. In addition, analytical expressions are obtained for the optimal values of frequency detuning and group velocities on which the maximum of the harmonic spectrum is obtained for non-stationary generation in a metamaterial. Estimations of the quasistatic interaction lengths and the frequency shift of the second-harmonic spectrum are given. By varying the linear phase detuning or the pump intensity, it is possible to manipulate the frequency shift of the maximum of the harmonic spectrum, and from here one can realize a smooth rearrangement of the central frequency of the harmonic spectrum.

Focusing by the designed negative Luneburg lens which is based on graded annular photonic crystals (GAPCs) are studied in this paper. The GAPCs are composed of ring-shaped silicon pillars in a hexagonal lattice. The gradient of refractive index is achieved by modifying the radii of inner holes. The effective negative refractive index is analyzed based on the photonic band structures and verified by the simulation of negative refraction in APCs flat lens. Numerical simulation results show that a 0.6λ focusing spot can be realized by our designed Luneburg lens and it has the potential to be utilized in photonic integrated circuits.

Negative refraction (NR) metamaterials are featured with unique physical properties and potential to realize full control of electromagnetic waves, which have attracted much attention since the last decade. However, few researches focus on the realization of three-dimensional dielectric NR metamaterials in optic frequency, and the current design methods need further development. In this paper, a three-dimensional all-dielectric NR metamaterial with two NR bands has been realized based on proper excitation of electric and magnetic multipoles. It is also predicted that the coupling of magnetic dipole and electric dipole can lead to the NR bands in near-infrared frequencies, and NR in the visible frequencies can be achieved by the coupling of magnetic quadrupole and electric dipole. Band structures and equal-frequency surfaces of proposed metamaterial arranged in the periodic cubic lattice are solved by adopting the plane wave expansion method, and then the results verify the existence of these two NR frequency bands in periodic metamaterials. In this way, the characteristic parameters such as transmission and absorption of light in two NR bands are also analyzed. In the meantime, the finite-deference time-domain method is used to intuitively display the phenomenon of NR and investigate the effects of disorder in particle arrangement. Besides, it is found that the proposed metamaterials have fine robustness to the disorder in particle arrangement, and these two NR bands can be tuned by adjusting volume fraction. In brief, this work provides means for preliminary designing, profound analysis and intuitively exhibition of NR metamaterials based on dielectric particles.

Creating optical illusion by using interior cavity cloak in 2D is discussed in this paper. An antiobject is embedded in the cloak shell and the corresponding imaginary object (under transformation optics) is observed in virtual space instead of any other object which was really exist inside the cavity cloak in physical space. Cylindrical single (twin) cavity cloak is used in this paper, that making one (two) object with arbitrary shape and material properties appears exactly like another object(s) with different shape and material make up for an observer who lies outside the cloaking shell. The simulation results prove that this illusion device with the proposed parameters is operationally possible. The advantage of using internal cloak instead of folded geometry which is usually used is that there is no negative refraction in the structure of the device.

Metasurface, which does not exist in nature, has exhibited exotic essence on the manipulation of both electromagnetic and acoustic waves. In this paper, the concept of metasurface is extended to the field of elastic SH waves, and the anomalous refractions of SH waves across the designed elastic SH wave metasurfaces (SHWMs) are demonstrated numerically. Firstly, a SHWM is designed with supercells, each supercell is composed of four subunits. It is demonstrated that this configuration has the ability of deflecting the vertical and oblique incident waves in an arbitrary desired direction. Then, a unique SHWM with supercell composed of only two subunits is designed. Numerical simulation shows its ability of splitting the vertical and oblique incident waves into two tunable transmitted wave beams, respectively. In the process of steering SH waves, it is also found that two kinds of leakages of transmitted waves across the designed SHWM will occur in some particular situations, which will affect the desired transmitted wave. The mechanisms of the leakages, which are different from that of the common high-order diffraction mentioned in existing literatures, are revealed. The current study can offer theoretical guidance not only for designing devices of directional ultrasonic detection and splitting SH waves but also for steering other kinds of classical waves.

In this paper, a method of rotating scatterers was used to design a graded negative refraction index phononic crystal (GNRI PC) plate lens. The present plate lens contains the periodic perforated three-fan holes as the scatterers in the epoxy plate matrix. For a given rotation angle of the scatterer, the rotation would result in a variation of the second A0 band dispersion curve, which is related to a specific negative refraction index. Based on the Snell’s law, the negative refraction index was calculated by utilizing the equifrequency contour and wave vector space for the different rotation angle. Then, the graded negative refraction index plate lens was designed by the specific distribution of the rotation angle of the scatterer. The results show that the plate lens exhibits an obvious focus efficiency in the work frequency range from 16 kHz to 19 kHz. The influence of the work frequency and the dimension of the lens on the focal length was also discussed. Combining with the present plate lens, the energy harvesting analysis was performed numerically, and the energy harvesting efficiency with the plate lens is about 10.5 times larger than that without a lens. This work provides a new way to fabricate GNRI PC plate lens and energy harvesting devices.

This paper proposes a level set-based topology optimization method for acoustic metasurfaces consisting of multiple types of unit cells. As a type of acoustic metasurface, we focus on a two-layered metasurface, where each layer contains various types of unit cell designs. To handle this metasurface, we first propose a two-scale homogenization method based on previous studies targeting metasurfaces composed of a single type of unit cell structure. As a result of homogenization, each layer of the array of unit cells is replaced with an interface with a nonlocal transmission condition. Next, an optimization problem is formulated. We set an objective function to achieve negative refraction, and macroscopic responses obtained by the homogenization method are used to define the objective function. The material distributions in each unit cell of the metasurface are set as the design variables. Based on these settings, we perform a sensitivity analysis based on the concept of the topological derivative. A level set-based topology optimization method is introduced to solve the optimization problem, and two-dimensional numerical examples are provided to demonstrate the validity of the proposed method. An optimal design of a two-layered acoustic metasurface that induces negative refraction is proposed, and a discussion of its mechanism is provided.

To achieve broadband negative refraction, which is useful for many practical applications, recent studies have shown that the use of hybridization is one of the most effective methods. Nevertheless, reported studies often propose changing structural parameters rather than external factors. In this article, a method to control actively the bandwidth of negative refractive index (NRI) metamaterials based on second-order hybridization operating in the terahertz regime is proposed numerically by use of a simple disk-grid dimer. By use of the semiconductor InSb as the metallic component, the conductivity is tunable according to temperature, which changes the separation of magnetic resonant frequencies in second-order hybridization scheme and the plasma frequency of metamaterial. Consequently, the fractional bandwidth of the double-NRI region is extended. The mechanism of the phenomenon is explained clearly by both calculations and simulation. Finally, the fractional bandwidth of the NRI region was optimized by variation of the dielectric thickness of the disk-grid monomer and the thickness of the interlayer between the two monomers. The optimal fractional bandwidth is 10.4%, with a high transmitted power of 94% and a high figure of merit of 52.9 at 1.68 THz. Our results pave the way for the implementation of diverse semiconductors in tunable broadband NRI metamaterials at terahertz frequencies.

Two novel chalcone derivatives C12 & C13 are designed and synthesized. Terthiophene group is employed to provide the planar π-conjugated system in these molecules while the molecular planarity is tuned by the different substitutions at the terminal group. The ultrafast optical nonlinearities are investigated via transient absorption spectrum and Z-scan. It is generally assumed that a large planar π-system and strong intramolecular charge transfer can enhance the optical nonlinearities in organic nonlinear optical materials. However, the molecule with larger planar molecular structure displayed weaker nonlinear absorption due to the competition between saturable absorption and reverse saturable absorption. With DFT calculation, the structure-property relation and the enhancement of π-conjugated system on nonlinear absorption and refraction are discussed. The investigations and discussions may provide a different perspective of the nonlinear absorption and refraction in these organic molecules and the results also suggest that these chalcone derivatives are potential nonlinear refraction materials for all-optical applications.

Manipulating electromagnetic response of materials provides a powerful means of controlling the interaction between light and matter. Negative refraction is one of the signature effects of metamaterial physics and its exciting demonstration became a frontier for material and electromagnetic research. The dramatic Physics exhibited by the metamaterial is underpinned by the resonant response of the metamolecules. A wide range of tunable THz resonance frequency provides a technological breakthrough in metamaterials. In the course of work, we show that magnetic terahertz spin wave response can be achieved in a kagome shaped unit cell composed of cobalt and iron magnetic resonant elements. The magnetization dynamics of the proposed system is numerically studied using mumax3. The six-fold rotational symmetry of the kagome lattice yields dipolar field-dependent magnetization. The field dependent magnetization obtained from numerical studies is used to investigate the negative refraction behavior.

All-angle negative refraction (AANR) contributes to a subwavelength imaging with the ability to collect light from all incident angles to generate negative refraction. However, it is challenging to realize a broadband AANR with the conventional photonic crystal (PhC) structures due to the dispersion nature, which makes the refracted light highly sensitive to the incident angle. In this work broadband AANR PhCs are proposed based on the supercircle void or rod design, for transverse electric (TE) and transverse magnetic (TM) polarizations respectively. By adjusting the filling ratio of the dielectric material, the nearly optimal AANR range is realized. Flat lenses based on the supercircle designs are able to form subwavelength imaging in a frequency range 3 times broader than the state-of-the-art for TE polarization and 1.1 times for TM polarization, respectively.

A high refractive index metamaterial was theoretically designed in the terahertz region, and the proposed structure is to easy implementation. By decreasing the diamagnetic effect with a thin “I”-shaped metallic patch structure and drastically increasing the effective permittivity through strong capacitive coupling in the unit cell, the higher refractive index of designed metamaterial can be obtained while maintaining low losses in the resonant frequency. The physical mechanism of metamaterial possessing an enhanced refractive index is revealed by the surface current, the electric field and magnetic field distributions. Besides, the polarization characteristics and broad incident angles robustness for the high refractive index are demonstrated.

Metal-dielectric multilayers can be designed to exhibit remarkable optical properties, including negative refraction for subwavelength superlensing. In this study, the applicability of the medium-homogenized effective medium theory (EMT) in place of multilayered thin-film optics is examined. Three metal-dielectric material and thin film thickness combinations that give rise to hyperbolic dispersion in different spectral regions are considered. In addition to investigating the radiative properties, the energy streamline method is used to determine the refraction angle and lateral displacement of rays. The electromagnetic fields inside the films are depicted to illustrate the coherent effect or the lack thereof. The radiative penetration depth is profiled to understand the effectiveness and limits of such multilayers in optical manipulation. The conditions and mechanism for the breakdown of EMT are elucidated in this case study.

Achieving vibration and/or wave attenuation with locally resonant metamaterials has attracted a great deal of attention due to their frequency dependent negative effective mass density. Moreover, adaptive phononic crystals with shunted piezoelectric patches have also demonstrated a tunable wave attenuation mechanism by controlling electric circuits to achieve a negative effective stiffness. In this paper, we propose an adaptive hybrid metamaterial that possesses both a negative mass density as well as an extremely tunable stiffness by properly utilizing both the mechanical and electric elements. A multi-physical analytical model is first developed to investigate and reveal the tunable wave manipulation abilities in terms of both the effective negative mass density and/or bending stiffness of the hybrid metamaterial. The programmed flexural wave manipulations, broadband negative refraction and waveguiding are then illustrated through three-dimensional (3D) multi-physical numerical simulations in hybrid metamaterial plates. Our numerical results demonstrate that the flexural wave propagation can essentially be switched between “ON/OFF” states by connecting different shunting circuits.

As the counterpart of electromagnetic and acoustic metamaterials, elastic metamaterials are artificial periodic elastic composite materials offering the possibility to manipulate elastic wave propagation in the subwavelength scale through different mechanisms. For the promising superlensing in the medical ultrasonic detection, double-negative metamaterials possessing the negative effective mass density and elastic modulus simultaneously can be utilized as the ideal superlens for breaking the diffraction limit. In this paper, we present a topology optimization scheme to design the two-dimensional (2D) single-phase anisotropic elastic metamaterials with broadband double-negative effective material properties and demonstrate the superlensing effect at the deep-subwavelength scale. We also discuss the impact of several design parameters adopted in the objective function and constraints on the optimized results. Unlike all previously reported mechanisms, the present optimized structures exhibit the novel quadrupolar or multipolar resonances for the negative effective mass density and negative effective elastic modulus. In addition, negative refraction of the transverse waves in a single-phase material is observed. Most optimized structures in this paper can serve as the anisotropic zero-index metamaterials for the longitudinal or transverse waves at a certain frequency. The cloaking effect is demonstrated for both the longitudinal and transverse waves. Moreover, with the particular constraints in the optimization procedure, a super-anisotropic metamaterial exhibiting the double-negative and hyperbolic dispersions in two principal directions within two different frequency ranges is obtained. The developed optimization scheme provides a robust computational tool for negative-index engineering of elastic metamaterials and may guide the design and optimization of other types of metamaterials, including the electromagnetic and acoustic metamaterials. The unusual properties of our optimized structures can inspire new ideas and novel applications including the low-frequency vibration attenuation, flat lens and ultrasonography for elastic waves.

We prove existence of weak solutions to certain refraction problems in the setting of materials with negative refractive index, both in the near and far field. Solutions are obtained when the target measure is discrete, as well as when it is given by a general Radon measure. The far field problem is treated using techniques from optimal mass transport. As such a fully nonlinear PDE of Monge–Ampere type arises in this setting, and we calculate the coefficients explicitly. Finally, we produce an example in which the A3w condition holds but the A3s condition does not.

The recent study of the Lorenz-Mie scattering from a graphene-coated sphere is extended to the case when the sphere is of negative refractive index, focusing on the two intriguing phenomena observed previously for a “bare” negative index sphere of sub-wavelength sizes, namely, the non-Rayleigh behavior and the low-frequency resonances. It is observed that while the graphene coating can regulate the non-Rayleigh scattering back towards Rayleigh, manifested with its own low frequency plasmonic resonances in the IR region; the low-frequency peak observed previously can be significantly suppressed with the result rather insensitive to the doping level of the graphene layer. These graphene-induced effects are clarified via a study of the Bohren-Hunt theory in the limit of small size parameters for the negative refracting sphere.

Quantum lossy left-handed transmission lines (LHTLs) are central to the miniaturized application in microwave band. This work discusses the NRI of the quantized lossy LHTLs in the presence of the resistance and the conductance in a displaced squeezed Fock state (DSFS). And the results show some novel specific quantum characteristics of NRI caused by the DSFS and dissipation, which may be significant for its miniaturized application in a suit of novel microwave devices., Comment: 11 pages,5 figures

Silver metal is known to share some of the peculiar features of metamaterials in optical frequency domain. In this article, we investigate the occurrence of negative and/or orthogonal phase velocity, negative refraction and counterposition phenomena in silver with fractional dimensions. For this purpose an interface of free space and silver metal is considered for various values of fractional dimensions of both the half spaces. The observed values of the refracted poynting vector relate to the occurrence of the above mentioned phenomena. It is noted that although the fractionality of either of the half space does not alter the occurrence of the said phenomena, the absolute values of the refracted poynting vector vary greatly with a change in the fractionality of dimensions, indicating a possible control of energy flow in refracted fields via fractional parameters.

It is shown, for the first time, that negative refraction with positive phase velocity refraction can be realized (and controlled) on a wide frequency-range of the first (lowest) pass band of simple photonic and phononic crystals. First a unified approach is presented to accurately, efficiently, and uniquely produce the homogenized effective material properties of doubly periodic phononic crystals for anti-plane shear (SH) and photonic crystals for transverse electric (TE) and transverse magnetic (TM) electromagnetic Bloch-form waves in such a manner that they exactly reproduce the band structure of the composite over any desired frequency band. Then the correspondence between phononic and photonic field equations is established and their effective homogenized material parameters are calculated. Finally the actual calculation procedure is detailed and illustrative examples are worked out for each case, revealing a rich body of refractive characteristics of these crystals, and showing by means of illustrative examples that the homogenized effective parameters do in fact yield the exact results. Thus the resulting homogenized solid embodies exactly the actual band structure and dispersive properties of the considered phononic/photonic crystal, which clearly distinguishes it from any anisotropic normal material. When in contact with a normal homogeneous half-space, the homogenized medium would display positive, negative, or even no energy refraction depending on the frequency and wave vector of plane waves incident from the normal homogeneous solid to the interface. Remarkably, using the same volume fraction of the same constituents, it is possible to design a (homogenized) material that would display negative energy refraction with positive phase velocity refraction even on the first (acoustic) pass band. The window of the frequency and the range of wave-vector values at which, say, the negative energy refraction would occur can be controlled by judicious selection and design of the unit cell’s constituent geometry and properties. The unit cell of the crystal may consist of anisotropic constituents of any constant or variable properties that may also admit large discontinuities. For elliptical and rectangular inclusion geometries, analytical expressions are given for the calculation of the key quantities.

A remarkable property of intrinsic graphene is that upon doping, electrons and holes travel through the monolayer thick material with constant velocity which does not depend on energy up to about $0.3$ eV (Dirac fermions), as though the electrons and holes are massless particles and antiparticles which move at the Fermi velocity $v_F$. Consequently, there is Klein tunneling at a $p-n$ junction, in which there is no backscattering at normal incidence of massless Dirac fermions. However, this process yielding perfect transmission at normal incidence is expected to be affected when the group velocity of the charge carriers is energy dependent and there is non-zero effective mass for the target particle. We investigate how away from normal incidence the combined effect of incident electron energy $\epsilon$ and band gap parameter $\Delta$ can determine whether a $p-n$ junction would allow focusing of an electron beam by behaving like a Veselago lens with negative refractive index. We demonstrate that there is a specific region in $\epsilon-\Delta$ space where the index of refraction is negative, i.e., where monolayer graphene behaves as a metamaterial. Outside this region, the refractive index may be positive or there may be no refraction at all. We compute the ballistic conductance across a $p-n$ junction as a function of $\Delta$ and $\epsilon$ and compare our results with those for a single electrostatic potential barrier and multiple barriers., Comment: 15 pages and 8 figures

This work is concerned with the reflection and transmission of waves at a plane interface between a homogeneous elastic half-space and a half-space of elastic material that is periodically laminated. The lamination is always in the direction of the x1-coordinate axis and the displacement is always longitudinal shear, so that the only non-zero displacement component is u 3 ( x 1 , x 2 , t ) . After an initial discussion of Floquet–Bloch waves in the laminated material, brief consideration is given to the reflection–transmission problem, when the interface between the two media is the plane x 1 = 0 . Nothing unusual emerges: there are just a single reflected wave and a single transmitted wave, undergoing positive group-velocity refraction. Then, the problem is considered when the interface between the two media is the plane x 2 = 0 . The periodic structure of the interface induces an infinite set of reflected waves and an infinite set of transmitted waves. All need to be taken into account, but most decay exponentially away from the interface. It had previously been recognized that, if the incident wave had appropriate frequency and angle of incidence, a propagating transmitted wave would be generated that would undergo negative group-velocity refraction – behaviour usually associated with a metamaterial. It is established by an example in this work that there is, in addition, a propagating transmitted wave with smaller wavelength but larger group velocity that undergoes positive group-velocity refraction. The work concludes with a brief discussion of this finding, including its implications for the utility (or not) of “effective medium” theory.

The behaviors of negative refraction of electromagnetic waves propagation at the dielectric–magnetized plasma interface are investigated in detail. The Faraday and Voigt effects on the properties of negative refraction are calculated and discussed. The results show that the behavior of negative refraction can be tuned and controlled correspondingly due to the magneto-optical effects. The properties of negative refraction behave differently in different frequency region and the magnitude of external magnetic field. Moreover, negative refraction can be realized at the dielectric–magnetized plasma interface above the plasma frequency, which is different from the case of dielectric–plasma interface.

We investigate the optical transmission spectra for $s$-polarized (TE) and $p$-polarized (TM) waves in one-dimensional photonic quasicrystals on a quasiperiodic multilayer structure made up by alternate layers of SiO$_{2}$ and \textit{metamaterials}, organized by following the Octonacci sequence. Maxwell's equations and the transfer-matrix technique are used to derive the transmission spectra for the propagation of normaly and obliquely incident optical fields. We assume Drude-Lorentz-type dispersive response for the dielectric permittivity and magnetic permeability of the metamaterials. For normally incident waves, we observe that the spectra does not have self-similar behavior or mirror symmetry and it also features the absence of optical band gap. Also for normally incident waves, we show regions of full transmittance when the incident angle $\theta_{C} = 0^{\circ}$ in a particular frequency range., Comment: This paper has been withdrawn by the author due to it be an uncorrected proof

Negative refraction of elastic waves has attracted significant research interest due to its potential prospects in acoustic imaging, communication, and structural health monitoring. However, previous implementations based on Bragg interference suffer from lattice-scale size restrictions or defect-sensitive characteristics, hindering their application in compact subwavelength systems. Here, we propose a new design of ternary valley-Hall phononic crystals (PCs) with subwavelength topological negative refraction. By introducing the subwavelength resonators into a complex lattice similar to graphene allotrope, the valley polarized edge modes induced by locally resonant state are obtained, and the defect-immune topological negative refraction of the edge states outcoupling into free space is established. Furthermore, the total mode conversion from longitudinal to transverse waves is demonstrated by the wave mode separation and the equifrequency curves (EFCs) analysis on the negative refraction. Finally, utilizing the valley-selective excitation, a topological elastic valley filter is designed by coupling the valley-projected edge states with bulk valley polarizations. The research provides new possibilities for robust control of isolated transverse elastic waves in the deep subwavelength regime that can be employed for designing compact communication devices.

We design a switch based on a switchable magnetic hyperbolic metamaterial that consists of a one-dimensional periodic stacking of dielectric and gyromagnetic layers. The isofrequency curve of the structure can be switched between elliptical and hyperbolic shapes via the external DC magnetic field. The isofrequency curve relates directly to the propagation property of electromagnetic waves. By analyzing the different isofrequency curves, we predict that positive refraction, total reflection, and negative refraction can occur in a TE polarized Gaussian beam incident from air into the structure. The electric field distribution is simulated, and results confirm our predictions. Therefore, our switchable magnetic hyperbolic metamaterial can be used as an efficient switch. To be specific, with the adjustment of the external DC magnetic field, when the isofrequency curve transforms between a circle and a one-sheeted hyperbola, it can switch between positive refraction and total reflection; when the curve transforms between a circle and a two-sheeted hyperbola, it can switch between positive and negative refraction.

In this article we have proposed a novel graphene based tunable semiconductor metamaterial which can be effectively tuned in the long wavelength infrared region of the electromagnetic spectrum by only changing the chemical potential of graphene via a gate voltage without needing to vary the doping concentration of semiconductor. The previously reported semiconductor metamaterial constructed from doped InGaAs and intrinsic AlInAs layers shows all angle negative refraction Hoffman et al.. However, it cannot be tuned without changing the doping concentration of semiconductor and changing doping concentration makes the material lossy. Since Graphene possesses tunable surface conductivity which can be tuned effectively by changing the chemical potential of graphene, we have proposed a novel structure where graphene sheet is inserted between the InGaAs and AlInAs layers. Through rigorous mathematical analysis we have shown that by changing only the chemical potential, without needing to modify the structural properties, it is possible to tune the spectral region of permittivity where negative refraction occurs which in turns gives tunability to iso-frequency wave vector dispersion, transmittance, reflectance and absorption coefficient. The proposed method would simplify the tuning process of semiconductor metamaterials. This unique graphene based tunable semiconductor metamaterial would be an attractive feature in the rapid and continuously developing semiconductor industry.

A closely-spaced periodic array of identical thin rigid plates illuminated by incident waves is shown to exhibit properties of a negative refraction metamaterial under certain conditions. The close-spacing assumption is used as a basis for an approximation in which the region occupied by the plate array acts as an effective medium. Effective matching conditions on the plate array boundary are also derived. The approximation allows explicit expressions to be derived to wave scattering problems involving tilted plate arrays. This approximation is tested for its accuracy against an exact treatment of the problem based on Bloch–Floquet theory. Both the exact and effective medium theory predict perfect wave transmission at all wave frequencies through the array when the tilt angle of plates in the array is the reverse of the incident wave direction: the array acts as an all-frequency perfectly-transmitting negative-refraction medium. For certain frequencies the array is also shown to act as an all-angle perfectly-transmitting negative-refraction material.

In this paper we show that a 1-D phononic crystal (laminate) can exhibit metamaterial wave phenomena which are traditionally associated with 2- and 3-D crystals. Moreover, due to the absence of a length scale in 2 of its dimensions, it can outperform higher dimensional crystals on some measures. This includes allowing only negative refraction over large frequency ranges and serving as a near-omnidirectional high-pass filter up to a large frequency value. First we provide a theoretical discussion on the salient characteristics of the dispersion relation of a laminate and formulate the solution of an interface problem by the application of the normal mode decomposition technique. We present a methodology with which to induce a pure negative refraction in the laminate. As a corollary to our approach of negative refraction, we show how the laminate can be used to steer beams over large angles for small changes in the incident angles (beam steering). Furthermore, we clarify how the transmitted modes in the laminate can be switched on and off by varying the angle of the incident wave by a small amount. Finally, we show that the laminate can be used as a remarkably efficient high-pass frequency filter. An appropriately designed laminate will reflect all plane waves from quasi-static to a large frequency, incident at it from all angles except for a small set of near-normal incidences. This will be true even if the homogeneous medium is impedance matched with the laminate. Due to the similarities between SH waves and electromagnetic (EM) waves it is expected that some or all of these results may also apply to EM waves in a layered periodic dielectric.

This study numerically investigates the spatio-spectral sound transmission properties of a sonic crystal flat lens and presents a discussion on the effects of negative refraction on the spatio-spectral selectivity of sonic crystals. For this propose, pulse response analyses are carried out to demonstrate the spatio-spectral acoustic transmission features of a triangular lattice two-dimensional sonic crystal flat lens at the bottom edge of the second frequency band. The spectral analysis indicates the existence of a spatial filtering effect resulting from the wave focalization of the negative refracted wave beams emitted from a point source. We theoretically demonstrate that this effect can be utilized in the implementation of highly frequency-selective spatial sound filters by using sonic crystal flat lenses from point type acoustic sources.

In this paper we present a theoretical analysis of the generalized Lorenz–Mie theory for negative refractive index (NRI) media and spherical scatterers, extending the well-known concepts and definitions found in the literature involving dielectric or positive refractive index (PRI) particles. The consequences of a negative phase velocity and an anti-parallelism of the wave vector with respect to the Poynting vector are investigated and interpreted in this framework and, together with the symmetries found for the beam-shape coefficients when compared to the conventional PRI case, it is shown that the description of plane waves, Gaussian beams and, more generally, on-axis azimuthally symmetric waves along a NRI medium, their fields and all physical properties can be conveniently correlated with that of dielectric media once the electromagnetic response functions are replaced by their corresponding dielectric counterparts.

This paper proposes a new topology optimization algorithm based on the bi-directional evolutionary structural optimization (BESO) method to design photonic crystals with broad all-angle negative refraction (AANR) frequency range. The photonic crystals are assumed to be two-dimensional periodical structures, which consist of dielectric materials and air. The conditions for the occurrence of AANR are identified and the design objective is to enlarge the AANR frequency range. The BESO algorithm is proposed based on finite element analysis for band diagrams of photonic crystals and the derived sensitivity numbers. Starting from a simple initial design without any AANR, BESO gradually re-distributes the dielectric materials within the periodical unit cell so that the AANR property emerges and its frequency range is enlarged accordingly. The numerical results show that the proposed BESO algorithm can effectively obtain AANR photonic crystals with novel patterns. The effects of dielectric permittivity contrast of two constituent materials, mesh-refinement and filter are discussed. A new topology optimization algorithm for photonic crystals is proposed.Novel photonic crystals for all-angle negative refraction (AANR) are found.The optimized solutions are analyzed and discussed in detail.

Numerical simulation analysis of a new kind of resonator is presented. The proposed structure operates as a magnetic resonator that provides dual band negative permeability behavior as a result of magnetic resonance produced due to self and mutual coupling of the inclusions. It also shows negative permittivity for a broad frequency band. The proposed structure is capable of achieving negative refractive index at the frequency where both negative permittivity and negative permeability overlapping each other. The design of the resonator is simple and, thus, it allows playing with geometric contents for potential applications.

We theoretically study the reflection and refraction of ultra-cold atoms in optical lattices exposed to a nonuniform artificial magnetic field. The introduction of the nonuniform artificial magnetic field to the optical lattice for suitable designer magnetic potential barrier can lead to a series of intriguing reflection and refraction phenomena of atoms, including reflection, positive refraction, negative refraction and atomic matter wave splitting. Both the occurrence and the distribution of these reflection and refraction scenarios can be coherently controlled by the nonuniform artificial magnetic field. In particular, the regions close to the boundary of reflection demonstrate two more interesting propagation modes, i.e., a reflected branch of atoms comprising a positive or negative refracted branch of atoms with almost same atom population will be excited simultaneously at the magnetic potential barrier. The results can be a guide for the coherent control of the matter waves in optical lattices and the design of new atom optics devices.

The negative refraction behavior and imaging effect for acoustic waves in a kind of two-dimensional square chiral lattice structure are studied in this paper. The unit cell of the proposed structure consists of four zigzag arms connected through a thin circular ring at the central part. The relation of the symmetry of the unit cell and the negative refraction phenomenon is investigated. Using the finite element method, we calculate the band structures and the equi-frequency surfaces of the system, and confirm the frequency range where the negative refraction is present. Due to the rotational symmetry of the unit cell, a phase difference is induced to the waves propagating from a point source through the structure to the other side. The phase difference is related to the width of the structure and the frequency of the source, so we can get a tunable deviated imaging. This kind of phenomenon is also demonstrated by the numerical simulation of two Gaussian beams that are symmetrical about the interface normal with the same incident angle, and the different negative refractive indexes are presented. Based on this special performance, a double-functional mirror-symmetrical slab is proposed for realizing acoustic focusing and beam separation.

Negative refraction medium can in principle be realized using artificial composites composed of semiconductor/metallic inclusions, which experience negative refraction over certain frequency region due to structural resonant. It would be desirable if we could extend negative refraction to alternative natural semimetal candidates. Here, we show that by employing multilayer-graphene and cubic boron nitride slab, the composite may support negative group refractive angle over certain frequencies due to its anisotropic characteristics. Poynting vector profile numerically demonstrates that transverse magnetic wave propagates with observable negative shift as if they had negative refractive index.

Bulk magneto-phonon and magnetic polaritons of lateral antiferromagnetic superlattices for potential THz applications have been investigated in the framework of the effective medium theory. The dispersion relations applied for the system are displayed. In contrast with lateral FeF2/SiO2 superlattice, some fascinating polariton modes with negative group velocity signifying photonic band gap scenarios and attractive optical properties are observed from the numerical results presented with the example, lateral FeF2/TlBr superlattice.

In view of the peer reviewer's suggestion, we sincerely make a further discussion of the paper published in Appl. Opt. (52 (2013) 6309–6315) titled “Multiple frequency bands of square split resonant rings and metal wires metamaterial”. We choose square split resonant rings (different in size) stacking in the X and Y axes, the same arrangement as the previous paper coupling in the Z axis, to form a two-layer or a three-layer metamaterial unit. All of the two-layer and three-layer units exhibit multiple negative pasbands. A comparison on the resonant frequencies with coupling cells in different directions is accomplished.

In our previous work [B. Guo and M. Q. Xie, Optik 125 , 2137 (2014)], we found that plasma photonic crystal (PC), which proposed is a multilayer stack of alternating plasma layer and dielectric, can show negative refraction not only at the frequency edge of the band gap but also at some other frequencies which do not belong to any band gaps when the frequency of oblique incidence is below the plasma frequency by analyzing the dispersion relations. Here, in this paper, we investigate further the negative refraction in plasma PCs at below plasma frequency by studying the group and phase indices. The negative group and positive phase indices of refraction are observed at below plasma frequency for oblique incidence, which denotes the occurrence of negative refraction. Moreover, the results show that the proposed plasma PCs exhibit negative refraction in two frequency regions which is same to our previous work and the frequency regions of negative refraction can be tunable. Parameter dependence of the effects is examined and discussed.

In this paper, we report design and simulation of “I” shaped split ring resonator (SRR) metamaterial. The prime focus of this manuscript is to a design of a split ring resonance (SRR) based planar metamaterial to achieve the negative refraction in optical communication window. The propagation characteristics in terms of reflection and transmission spectrum of the reported structure are obtained using finite differential time domain (FDTD) method. In this paper all the key electromagnetic parameters i.e. such as permittivity (ɛ), permeability (μ), refractive index (n), etc. have been obtained from the simulation from propagation characteristics for the reported structure. It is observed and reported that the electromagnetic parameters (such as permittivity (ɛ) and permeability (μ)) as well as the refractive index for the reported structure is negative in broad optical communication windows around of 1.55 μm.

Terahertz wireless communication has emerged as a fast-growing research area. Routing, which is designed to control the propagation of terahertz wave, is of great importance for building the terahertz all-optical communication network. Metamaterials provide a good method for manipulating the terahertz wave, which can be used to realize the wave router. To steer the input wave in different directions, for example negative refraction angle, some structures have been proposed, such as stacked structures and nanowire arrays. However, in these metamaterials, the incident wave is generally limited to transverse magnetic polarization. Here, a new terahertz routing method for transverse electric wave is put forward with using graphene magnetic metamaterials. Theoretical analysis is performed to show that this metamaterial has negative components not only in effective permittivity tensor but also in effective permeability tensor. Routing is realized by topological transitions between different dispersion regimes in this metamaterial. Our finding provides a new candidate for signal routing of terahertz wave.

Circular dichroism (CD) is widely used in bio-sensing, chemical analysis, and negative refraction. However, a concise method is required to enhance CD in planar chiral plasmonic nanostructures. In this work, graphene ribbons (GRs) are introduced in planar h-shaped-metal chiral nanostructures (PHCNs) to enhance CD. Calculated results show that the absorption spectra of PHCNs are differently enhanced because of the plasmonic coupling between PHCNs and GRs under different circularly polarized lights, thereby leading to CD enhancement. The loss distributions of PHCNs@GRs reveal that the loss is transferred from PHCNs to GRs. The current distributions of PHCNs@GRs are regarded as equivalent LC resonant circuits to explain the shift of the CD spectra by tuning the geometrical parameters of PHCNs@GRs. The results help design graphene-based chiral plasmonic nanostructures.