An array of pairs of parallel gold nanorods is shown to have a negative refractive index n'=-0.3 at the optical communication wavelength of 1.5 micron. This effect results from the plasmon resonance in the pairs of nanorods for both the electric and magnetic components of light. The refractive index is retrieved from the direct phase and amplitude measurements for transmission and reflection, which are all in excellent agreement with our finite difference time domain simulations. The refraction critically depends on the phase of the transmitted wave, which emphasizes the importance of phase measurements in finding n'.
We show that nanosphere dispersed liquid crystal (NDLC) metamaterial can be characterized in near IR spectral region as an indefinite medium whose real parts of effective ordinary and extraordinary permittivities are opposite in signs. Based on this fact we design a novel electrooptic effect: external electric field driven switch between normal refraction, negative refraction and reflection of TM incident electromagnetic wave from the boundary vacuum/NDLC. A detailed analysis of its functionality is given based on effective medium theory combined with a study of negative refraction in anisotro…
We demonstrate a scheme to utilize the stacked fishnet metamaterial for all-angle negative refraction and subwavelength imaging within a wide frequency range starting from zero frequency. The theoretical predictions are verified by the finite-difference-in-time-domain (FDTD) numerical simulations. The phenomena come from the negative evanescent coupling between the adjacent slab waveguides through the breathing air holes perforated on metal layers.
By introducing a new mechanism based on purely imaginary conjugate metamaterials (PICMs), we reveal that bidirectional negative refraction and planar focusing can be obtained using a pair of PICMs, which is a breakthrough to the unidirectional limit in parity time (PT) symmetric systems. Compared with PT symmetric systems that require two different kinds of materials, the proposed negative refraction can be realized with only two identical media. In addition, asymmetric excitation with bidirectional total transmission is observed in our PICM system. Therefore, a new way to realize negative ref…
Artificial magnetism, negative permeability and negative refractive index are demonstrated in 3D-chiral metamaterial that shows giant polarization rotation and circular dichroism.
In this article, it has been theoretically shown that broad angle negative refraction is possible with asymmetric anisotropic metamaterials constructed by only dielectrics or loss less semiconductors at the telecommunication and relative wavelength range. Though natural uniaxial materials can exhibit negative refraction, the maximum angle of negative refraction and critical incident angle lie in a very narrow range. This notable problem can be overcome by our proposed structure. In our structures, negative refraction originates from the highly asymmetric elliptical iso-frequency.This is artifi…
We present experimental demonstration of phase conjugation using nonlinear metamaterial elements. Active split-ring resonators loaded with varactor diodes are demonstrated theoretically to act as phase-conjugating or time-reversing discrete elements when parametrically pumped and illuminated with appropriate frequencies. The metamaterial elements were fabricated and shown experimentally to produce a time reversed signal. Measurements confirm that a discrete array of phase-conjugating elements act as a negatively-refracting time reversal RF lens only 0.12$λ$ thick.
Polarization is one of the basic properties of electromagnetic waves conveying valuable information in signal transmission and sensitive measurements. Conventional methods for advanced polarization control impose demanding requirements on material properties and attain only limited performance. Here, we demonstrate ultrathin, broadband, and highly efficient metamaterial-based terahertz polarization converters that are capable of rotating a linear polarization state into its orthogonal one. Based on these results we create metamaterial structures capable of realizing near-perfect anomalous refr…
We develop a theory to compute and interpret the photonic band structure of a periodic array of metallic helices for the first time. Interesting features of band structure include the ingenuous longitudinal and circularly polarized eigenmodes, the wide polarization gap [Science 325, 1513 (2009)], and the helical symmetry guarantees the existence of negative group velocity bands at both sides of the polarization gap and band crossings pinned at the zone boundary with fixed frequencies. A direct proof of negative refraction via a chiral route [Science 306, 1353 (2004)] is achieved for the first …
Chalcogenide glasses are exceptional materials that show a wide contrast in optical properties upon phase change and are highly researched for reconfigurable electronic and nanophotonic devices. Here, we report the first proof-of-concept demonstration of a non-volatile, switchable hyperbolic metamaterial based on a chalcogenide glass. By using the $Ge_{2}Sb_{2}Te_{5}$ (GST) alloy as one of the components of a multilayered nanocomposite structure and exploiting its phase change property, we demonstrate a hyperbolic metamaterial in which the Type-I hyperbolic dispersion $(ε_{\perp} < 0, ε_{\para…
Bi-isotropic and isotropic negative refractive index (NRI) 3D metamaterials made from periodic arrangements of chiral split ring resonators (SRRs) are proposed and demonstrated. An analytical theory for the characterization and design of these metamaterials is provided and validated by careful full-wave electromagnetic simulations. The reported results are expected to pave the way to the design of practical 3D bi-isotropic and isotropic NRI metamaterials made from a single kind of inclusions.
We design three-dimensional (3D) metallic nanowire media with different structures and numerically demonstrate that they can be homogeneous effective indefinite anisotropic media by showing that their dispersion relations are hyperbolic. For a finite slab, a nice fitting procedure is exploited to obtain the dispersion relations from which we retrieve the effective permittivities. The pseudo focusing for the real 3D wire medium agrees very well with the homogeneous medium having the effective permittivity tensor of the wire medium. Studies also show that in the long-wavelength limit, the hyperb…
The polarization-sensitive propagation in the anisotropic metamaterial (AMM) with double-sheeted hyperboloid dispersion relation is investigated from a purely wave propagation point of view. We show that TE and TM polarized waves present significantly different characteristics which depend on the polarization. The omnidirectional total reflection and oblique total transmission can occur in the interface associated with the AMM. If appropriate conditions are satisfied, one polarized wave exhibits the total refraction, while the other presents the total reflection. We find that the opposite amph…
Asymmetric Negative Refraction in Nonlocal Double-Wire Metamaterials
Instituto de Telecomunicações and Department of Electrical and Computer Engineering, University of Coimbra（科英布拉大学电信研究所与电气与计算机工程系）；Photonics Initiative, Advanced Science Research Center, City University of New York（纽约市立大学高级科学研究中心光子学倡议项目）；Physics Program, The Graduate Center, City University of New York（纽约市立大学研究生院物理学项目）；University of Lisbon–Instituto Superior Técnico and Instituto de Telecomunicações（里斯本大学高等技术学院与电信研究所）
A robust wedge setup is proposed to unambiguously demonstrate negative refraction for negative index metamaterials. We applied our setup to several optical metamaterials from the literature and distinctly observed the phenomena of negative refraction. This further consolidates the reported negative-index property. It is found there generally exists a lateral shift for the outgoing beam through the wedge. We derived a simple expression for calculating this beam shift and interestingly, it provides us a strategy to quantitatively estimate the loss of the wedge material (Im[n]). Addition- ally, w…
Noble metals such as gold and silver are the primary metallic building blocks of metamaterial devices. Making subwavelength-sized structural elements from these metals seriously limits the optical performance of a device, however, and complicates the manufacturing process of nearly all metamaterial devices in the optical wavelength range. As an alternative to noble metals, we propose to use heavily-doped oxide semiconductors that offer both functional and fabrication advantages in the near-infrared. In this letter, we report an experimental demonstration of negative refraction in a near-infrar…
A wedge-shaped structure made of split-ring resonators (SRR) and wires is numerically simulated to evaluate its refraction behavior. Four frequency bands, namely, the stop band, left-handed band, ultralow-index band, and positive-index band, are distinguished according to the refracted field distributions. Negative phase velocity inside the wedge is demonstrated in the left-handed band and the Snell's law is conformed in terms of its refraction behaviors in different frequency bands. Our results confirmed that negative index of refraction indeed exists in such a composite metamaterial and also…
We propose a design for a plasmonic copper metamaterial with a negative index of refraction at visible/near-infrared wavelengths. Using numerical simulations, we demonstrate negative refraction by a copper metamaterial prism, and perform a parameter extraction technique to verify the sign of the effective, electric permittivity and magnetic permeability. Our proposed design has a figure of merit comparable to similar silver-based metamaterials operating in the visible/near-infrared range. These findings have implications for the design of low cost plasmonic devices and negative-index metamater…
We present an analytical nonlocal effective medium approximation to describe the optical nonlocal effects in metallic nanorod metamaterials based on Mie scattering theory. It is shown that the developed nonlocal effective medium theory can predict a coexistence state of two modes around the epsilon-near-zero region, where strong optical nonlocal effects lead to the behavior of both positive refraction and negative refraction in the nanorod metamaterials. Outside of the coexistence region, only one mode can be excited and its behavior can be well described using the local effective medium theor…
We identify a route towards achieving a negative index of refraction at optical frequencies based on coupling between plasmonic waveguides that support backwards waves. We show how modal symmetry can be exploited in metal-dielectric waveguide pairs to achieve negative refraction of both phase and energy. By properly controlling coupling between adjacent waveguides, a metamaterial consisting of a one-dimensional multilayer stack exhibiting an isotropic index of -1 can be achieved at a free-space wavelength of 400 nm. The general concepts developed here may inspire new low-loss metamaterial desi…
Hyperbolic metamaterials are materials in which at least one principal dielectric constant is negative. We describe the refractive index surface, and the resulting refraction effects, for a biaxial hyperbolic metamaterial, with principal dielectric constants $ε_1<0$, $0<ε_2\neqε_3$. In this general case the two sheets of the index surface intersect forming conical singularities. We derive the ray description of conical refraction in these materials, and show that it is topologically and quantitatively distinct from conical refraction in a conventional biaxial material. We also develop a wave o…
In this letter first we show that the equation of null geodesics in spherically symmetric spacetimes in isotropic coordinates is identical to the equation of light ray trajectories in isotropic media in flat spacetime. Based on this analogy we introduce an exact simulation of the light ray trajectories both in these spacetimes and in their metamaterial analogs in terms of the spacetime index of refraction. As unstable light trajectories, the photon spheres form in these metamaterial analogs at {\it exactly} the same radial distances as expected from the corresponding black hole geometries. Usi…
We derive an approach to define the causal direction of the wavevector of modes in optical metamaterials, which in turn, determines signs of refractive index and impedance as a function of {\it real and imaginary} parts of dielectric permittivity and magnetic permeability. We use the developed technique to demonstrate that the interplay between resonant response of constituents of metamaterials can be used to achieve efficient dispersion management. Finally we demonstrate broadband dispersion-less index and impedance matching in active nanowire-based negative index materials. Our work opens ne…
A general energy dispersion relation is developed for metamaterials having the negative-refraction (NR) property. It is shown that absorption effects are involved with NR phenomena, and the conditions under which NR occurs are discussed. Simple equations for NR are developed using Lorentzian models.
Negative reflection and negative refraction are exotic phenomena that can be achieved by platforms such as double-negative metamaterial, hyperbolic metamaterial, and phase-discontinuity metasurface. Recently, natural biaxial van der Waals (vdW) materials, which support extremely anisotropic, low-loss, and highly confined polaritons from infrared to visible regime, are emerging as promising candidates for planar reflective and refractive optics. Here, we introduce three degrees of freedom, namely interface, crystal direction, and electric tunability to manipulate the reflection and refraction o…
The paper establishes explicit lower bounds for the lattice cell size of periodic structures (metamaterials and photonic crystals) capable of supporting backward waves and producing negative refraction. At optical frequencies, this result implies strong inhomogeneity, in the sense that the cell size cannot be negligible relative to the vacuum wavelength and the Bloch wavelength.
Phase delays, spectral, orientation, and angular dependences of radiation refraction in metamaterial targets have been experimentally studied within the millimeter-wave range. It has been shown that angular and spectral dependences have a complicate structure, which demonstrated properties typical both for positive and negative refraction indexes. At this, a change of refraction nature occurs in radiation wavelength interval comparable with the sizes of metamaterial structural elements.
A metamaterial with a negative effective index of refraction is made from a three-dimensional hexagonal lattice photonic crystal with a metallic basis embedded in foam. It has been simulated with Ansoft HFSSTM in a frequency range from 7.0 to 12.0 GHz. Simulated results tested experimentally and negative refraction verified in some frequencies. Experimental results are in excellent agreement with simulations.
We discuss and clarify some misleading statements appeared in a recent article on negative refraction in metamaterials. In this comment, we straighten the physical meaning and underlying phenomena behind negative refraction and negative index metamaterials and show that these phenomena are perfectly consistent with causality. It is hoped that this comment draws the attention of authors, reviewers and readers to the large body of rigorous analytical, numerical, and experimental evidence in favor of negative refraction at a single interface, so as to avoid reviving settled debates which mislead,…
We inspect the optical properties of dissipative double-negative metamaterials (DNMM) and find explicit expression for the total reflection angle and the correct Fresnel formulae describing the reflection and refraction for the DNMM at the oblique incident of the electromagnetic wave on the interface for \textit{TE} as well as \textit{TM} electromagnetic wave polarization. The reflectivity and transmissivity of DNMM film embedded in a positive refraction index (PIM) surrounding are presented and discussed.
Research on photonics and metamaterials constantly challenges our intuitive understanding of the behaviour of light. In recent years we have seen negative refraction, focusing of light by a flat slab, a ``perfect'' prism, and an ``invisibility cloak'' [1-6]. It is generally understood that the cause of this unusual behaviour is the strong (anomalous) dispersion, i.e., dependence of the material properties on the frequency of light. Dispersion can be either due to a natural microscopic resonance of the material as with surface plasmons-polaritons, or due to an effective resonance (band-gap) of …
We report the experimental demonstration of broadband negative refractive index obtained in a labyrinthine acoustic metamaterial structure. Two different approaches were employed to prove the metamaterial negative index nature: one-dimensional extractions of effective parameters from reflection and transmission measurements, and two-dimensional prism-based measurements that convincingly show the transmission angle corresponding to negative refraction. The transmission angles observed in the latter case also agree very well with the refractive index obtained in the one-dimensional measurements …
We demonstrate that surface plasmons of a thin metal film interacting with a periodic array of nano-structures around it can be utilized to make bulk negative index metamaterials at visible spectrum with simultaneously negative permittivity and permeability. These surface plasmon driven metamaterials have high figure of merit and can be tuned arbitrarily to operate at any wavelength in the visible spectrum and possibly at ultraviolet spectrum. We numerically demonstrate the idea by a metamaterial structure which exhibits a strong magnetic response resulting in a negative index of refraction in…
It has been shown that for left-handed metamaterials and generally for negative refraction media the refraction index cannot be entered unequivocally and cannot be considered as real, and especially as negative. This index for above referred media is not expedient
This work demonstrates the existence of both negative refraction and a negative refractive index in an optical uniaxial absorbent medium that can be characterized by ordinary and extraordinary refractive indices. Negative refraction occurs in any absorbent uniaxial medium if the real part of the extraordinary index is less than its imaginary part. The refractive index is negative when the incident medium is sufficiently dense and the incident angle exceeds a critical angle that is defined here.
A detailed theoretical and numerical analysis of the localization length in alternating metamaterial-birefringent random layered stacks, under uncorrelated thickness-disorder, has been performed. Similar structures have recently been reported to suppress the Brewster delocalization for $\it{p}$-polarized light, when "standard" isotropic layers (with positive index of refraction) are considered instead of metamaterial layers, providing a generic means to produce polarization-insensitive, broadband reflections. However, this enhancement of localization is valid for short wavelengths $λ$ compared…
Electromagnetic negative refraction in metamaterials has attracted increasingly great interest, since its first experimental verification in 2001. It potentially leads to the applications superior to conventional devices including compact antennas for mobile stations, imaging beyond the diffraction limit, and high-resolution radars, not to mention the anamolous wave propagation in fundamental optics. Here, we report how metamaterials could be used to simulate the "negative refraction of spin-zero particles interacting with a strong potential barrier", which gives rise to the Klein paradox--a c…
In this paper, we numerically demonstrate a near-infrared negative-index metamaterial (NIM) slab consisting of multiple layers of perforated metal-dielectric stacks and exhibiting low imaginary part of index over the wavelength of negative refraction. The effective index is obtained using two different numerical methods and found to be consistent. Backward phase propagation is verified by calculation of fields inside the metamaterial. These results point to a new design of low loss thick metamaterial at optical frequencies.
We study the propagation of light in a three-dimensional double-periodic Ag/TiO2 multilayer metamaterial composed of coupled plasmonic waveguides operating in the visible and UV spectral range. For these frequencies, light propagation in the plane of the waveguides is described by a negative phase velocity, while for the orthogonal direction light propagation is described by a Bloch wave composed of a large number of harmonics. As a result, the material cannot generally be described by a single phase index: decomposing the Bloch wave into different harmonics we show that for the wavelength ran…
A type of 3-dimensional optical negative-refractive-index metamaterials composed of all dielectric nanospheres is proposed and demonstrated theoretically. The metamaterials are constructeded by pairing together two kinds of dielectric nanospheres as concentric shells embedded in a host medium. Mie-based extended effective theory shows that the dielectric core and the dielectric shell provide the negative permeability and the negative permittivity, respectively, both due to the strong Mie resonances. Within the coupled resonant frequency region, the negative index of refraction can be achieved.
In this work, we treat the rotation of the optical axis as a new degree of freedom and theoretically propose a tilted linear-crossing metamaterials (TLCMM). Specifically, the conical dispersions of the NLCMM and TLCMM have the same shapes as type-I and type-II Dirac cones, respectively, in condensed matter physics. Upon rotating the optical axis angle such that it is equal to the cone angle, we find that this special TLCMM has the shape of a type-III Dirac cone. This critical TLCMM can have many unique properties and is of a fundamentally different nature than neighboring phases. When EM waves…
We study numerically the propagation of two-color light pulses through a metamaterial doped with active atoms such that the carrier frequencies of the pulses are in resonance with two atomic transitions in the $Λ$ configuration and that one color propagates in the regime of positive refraction and the other in the regime of negative refraction. In such a metamaterial, one resonant color of light propagates with positive and the other with negative group velocity. We investigate nonlinear interaction of these forward- and backward-propagating waves, and find self-trapped waves, counter-propagat…
Metamaterials--artificially structured materials with tailored electromagnetic response--can be designed to have properties difficult to achieve with existing materials. Here we present a structured metamaterial, based on conducting split ring resonators (SRRs), which has an effective index-of-refraction with a constant spatial gradient. We experimentally confirm the gradient by measuring the deflection of a microwave beam by a planar slab of the composite metamaterial over a broad range of frequencies. The gradient index metamaterial represents an alternative approach to the development of gr…
We propose to go away from the electromagnetic wave description of light and to explain through a purely corpuscular and neutral approach, the phenomenon of the slowing down of light in a transparent medium. The quantum predictions and ours are compared against experimental refractive indices. In our framework the optical Kerr phenomenon finds a very natural interpretation and its numerical values are obtained easily
We have recently started to investigate 2D arrays of confocal lens pairs. Miniaturization of the lens pairs can make the array behave ray-optically like a homogeneous medium. Here we generalize the geometry of the lens pairs. These generalisations include a sideways shift of the lens centres and a change in the orientation of both lenses in each pair. We investigate the basic ray optics of the resulting arrays, and illustrate these with movies rendered using ray-tracing software. We suggest that confocal lenslet arrays could be used to realize ray-optically some recent metamaterials concepts s…
In this paper we show that a negative index of refraction is not a direct implication of transformation optics with orientation-reversing diffeomorphisms. Rather a negative index appears due to a specific choice of sign freedom. Furthermore, we point out that the transformation designed lens, which relies on the concept of spacetime folding, does not amplify evanescent modes, in contrast to the Pendry-Veselago lens. Instead, evanescent modes at the image point are produced by a duplicated source and thus no imaging of the near field (perfect lensing) takes place.
A nanofabricated regular array of coupled gold nano-pillars is employed to detect local indices of refraction of different liquids using a shift of an antisymmetric plasmon resonance peak observed in the reflection spectra. The peak spectral position is found to be a unique function of the local refractive index for a wide range of indices. We discuss possible applications of the fabricated nanostructured arrays in bio and chemical sensors.
Negative index of refraction has become an accepted part of transformation optics, which is encountered in transformations that change the orientation of the manifold. Based on this concept, various designs of perfect lenses have been proposed, which all rely on a folding of space or spacetime, where the maps from electromagnetic space to laboratory space are multi-valued. Recently, a new concept for perfect imaging has been proposed by Leonhardt and Philbin, which also uses multi-valued maps, but does neither include negative index of refraction nor an amplification of evanescent modes. In th…
The condition for a negative index of refraction with respect to the vacuum index is established in terms of permittivity and permeability susceptibilities. It is found that the imposition of analyticity to satisfy the Kramers-Kronig relations is a sufficiently general criterion for a physical negative index. The satisfaction of the Kramers-Kronig relations is a manifestation of the principle of causality and the predicted frequency region of negative index agrees with the Depine-Lakhtakia condition for the phase velocity being anti-directed to the Poynting vector, although the conditions pres…
Negative refraction through a triangular prism may be explained without assigning a negative refractive index to the prism by using array theory. For the case of a beam incident upon the wedge, the array theory accurately predicts the beam transmission angle through the prism and provides an estimate of the frequency interval at which negative refraction occurs. Negative refraction effects not only occur in prisms made of traditional metamaterial unit cells, such as magneto-dielectric spheres, but also in solid prisms made of completely filled, homogenous unit cells. In both prisms, the hypote…
The phenomenon of negative refraction generally requires negative refractive indices or phase discontinuities, which can be realized using metamaterials or metasurfaces. Recent theories have proposed a novel mechanism for negative refraction based on synthetic gauge fields, which affect classical waves as if they were charged particles in electromagnetic fields, but this has not hitherto been demonstrated in experiment. Here, we report on the experimental demonstration of gauge-field-induced negative refraction in a twisted bilayer acoustic metamaterial. The bilayer twisting produces a synthet…
Since the introduction of the artificially designed negative-index metamaterial (NIM) introduced in 2001, its extraordinary electromagnetic properties, which cannot be attained from naturally occurring materials, have continuously attracted many researchers to study them. Various types of NIMs with the resonant frequencies shifted from gigahertz all the way to higher frequencies have been actualized over the past decade. For the actual applications, the most fascinating and significant goal of research on NIMs is to achieve negative refraction at visible wavelengths. According to the effective…
We introduce an improved and simplified structure made of periodic arrays of pairs of H-shaped metallic wires that offer a potentially simpler approach in building negative-index materials. Using simulations and microwave experiments, we have investigated the negative-index n properties of these structures. We have measured experimentally both the transmittance and the reflectance properties and found unambiguously that a negative refractive index with Re(n)<0 and Im(n) <Re(n). The same is true for epsilon and mu. Our results show that H-shaped wire pairs can be used very effectively in produc…
We further miniaturize a recently established silver-based negative-index metamaterial design. By comparing transmittance, reflectance and phase-sensitive time-of-flight experiments to theory, we infer a real part of the refractive index of -0.6 at 780 nm wavelength -- which is visible in the laboratory.
We demonstrate experimentally and numerically that nonplanar chiral metamaterials give giant optical activity, circular dichroism, and negative refractive index. The transmission, reflection, and the retrieval results of the experiments agree pretty well with the simulations. This is an important step toward the design and fabrication of three-dimensional isotropic chiral metamaterials.
Metamaterials offer unprecedented flexibility for manipulating the optical properties of matter, including the ability to access negative index, ultra-high index and chiral optical properties. Recently, metamaterials with near-zero refractive index have drawn much attention. Light inside such materials experiences no spatial phase change and extremely large phase velocity, properties that can be applied for realizing directional emission, tunneling waveguides, large area single mode devices, and electromagnetic cloaks. However, at optical frequencies previously demonstrated zero- or negative-r…
It is found that the amphoteric refraction, i.e. the refraction can be either positive or negative depending on the incident angles, could occur at a planar interface associated with a uniaxially anisotropic positive index media (PIM) or an anisotropic negative index media (NIM). Particularly, the anomalous negative refraction can occur at a planar interface from an isotropic PIM to an anisotropic PIM, whereas the anomalous positive refraction occurs at the interface from an isotropic PIM to an anisotropic NIM. The optimal conditions to yield the two unusual refractions are obtained. The diffe…
We extended the refraction angle of the Eaton lens into arbitrary angles. The refractive index of the Eaton lens is not analytical and can be obtained by numerical calculations only except in the case of the retroreflector. We introduced an approximation for the refractive index of the generalized Eaton lens. It is simple but very close to the exact values obtained from numerical calculations.
