The authors introduce a general mechanism, based on electrostatic and magnetostatic considerations, for designing three-dimensional isotopic metamaterials that possess an enhanced refractive index over an extremely large frequency range. The mechanism allows nearly independent control of effective electric permittivity and magnetic permeability without the use of resonant elements.
The set of realizable refractive indices as a function of frequency is considered. For passive media we give bounds for the refractive index variation in a finite bandwidth. Special attention is given to the loss and index variation in the case of left-handed materials.
The paper considers an opportunity for the creation of an artificial two-component metamaterial with a negative refractive index within the radio and optical frequency band, which possesses a spatial dispersion. It is shown that there exists a spectral region where, under certain ratio of volume fraction unit occupied with components, the metamaterial appears transparent without attenuating the electromagnetic wave passing through it and possessing a phase and group velocity of the opposite sign.
We discuss optical constants in artificial metamaterials showing negative magnetic permeability and electric permittivity. Using effective field theory, we calculate effective permeability of nanofabricated media composed of pairs of identical gold nano-pillars with magnetic response in the visible spectrum.
We demonstrate a metamaterial that cannot be described by a single set of refractive-index and impedance values, even for fixed frequency and polarization. The metamaterial structure is a stack of dissimilar waveguides with subwavelength width and spacing, which guide light at different phase velocities. This multi-refractive-index metamaterial (MRIM) can be viewed as a spatial superposition of multiple homogeneous materials. Using full-wave simulations, we demonstrate several optical components based on MRIMs, including prisms that deflect light to multiple angles, lenses with multiple focal …
We demonstrated a 2D helical chiral metamaterial that exhibits broadband strong optical activity resulting nonresonant Drude-like response. The strong chirality leads to broadband negative refractive index with high figure of merit (>90) and extremely low loss (<2% per layer). The optical activity are insensitive to the angles of incident electromagnetic waves, thereby enabling more flexibility in polarization manipulation applicaitons.
An effective medium model is developed for disordered metamaterials containing a spatially random distribution of dielectric spheres. Similar to effective medium models for ordered metamaterials, this model predicts resonances in the effective permeability and permittivity arising from electric- and magnetic-dipole Mie resonances in the spheres. In addition, the model predicts a redshift of the electric resonance with increasing particle loading. Interestingly, when the particle loading exceeds the percolation threshold of 33\%, the model predicts that the electric resonance overlaps with the …
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.
On the basis of a full-vectorial three-dimensional Maxwell-Bloch approach we investigate the possibility of using gain to overcome losses in a negative refractive index fishnet metamaterial. We show that appropriate placing of optically pumped laser dyes (gain) into the metamaterial structure results in a frequency band where the nonbianisotropic metamaterial becomes amplifying. In that region both the real and the imaginary part of the effective refractive index become simultaneously negative and the figure of merit diverges at two distinct frequency points.
To study the scattering properties of metamaterials, we generalize two scattering methods developed for conventional (non-magnetic) isotropic materials to the case of materials with arbitrary values (positive or negative) of magnetic permeability and electric permittivity. The generalized methods are used to study the changes in the reflectivity of a metamaterial surface with localized roughness when the relative refractive index changes sign. Our results show that, unlike the case of a plane surface whose reflectivity is unaffected by the change of sign of the relative refractive index, in ro…
Refractive index enhancement is crucial in the field of lithography, imaging, optical communications, solar devices and many more. We present a review of advancements in the process of designing high refractive index metamaterials, starting from quantum coupling and photonic bandgap materials to metamaterials utilizing deep subwavelength coupling to achieve ever-high values of refractive index. A crisp and critical impression of each scheme are presented. The understanding of evolution of material design from intrinsic electronic states manipulation to meta-atoms design is not only fascinating…
We demonstrate numerically and experimentally a conjugated gammadion chiral metamaterial that uniaxially exhibits huge optical activity and circular dichroism, and gives a negative refractive index. This chiral design provides smaller unit cell size and larger chirality compared with other published planar designs. Experiments are performed at GHz frequencies (around 6GHz) and in good agreement with the numerical simulations.
Perfect lensing and cloaking based on complementary media are possible applications of negative refractive index materials. Metamaterials represent the natural candidates to realize such property by tailoring the effective dielectric permittiviy and magnetic permeability. The fine tuning of $n<0$ of metamaterials is limited by coarse grained inclusions which give discreteness to the electromagnetic parameters as a function of their density. We study the negative refractive index of a metamaterial as a function of the linear density of the lattice period at microwave frequency. The negative ref…
Plasmonic metamaterials support the localized surface plasmon resonance (LSPR), which is sensitive to the change in the dielectric environment and highly desirable for ultrasensitive biochemical sensing. In this work, a novel design of supercell metamaterials of four mutually rotating split ring resonators (SRRs) is proposed, where simultaneous excitations of odd (N=1 and N = 3) and even (N=2) resonance modes are realized due to additional asymmetry from the rotation and show insensitivity to two orthogonal polarizations. The full utilization of these three resonance dips show bright prospects…
We propose deep-subwavelength optical waveguides based on metal-dielectric multilayer indefinite metamaterials with ultrahigh effective refractive indices. Waveguide modes with different mode orders are systematically analyzed with numerical simulations based on both metal-dielectric multilayer structures and the effective medium approach. The dependences of waveguide mode indices, propagation lengths and mode areas on different mode orders, free space wavelengths and sizes of waveguide cross sections are studied. Furthermore, waveguide modes are also illustrated with iso-frequency contours in…
A uniaxial chiral metamaterial is constructed by double-layered four "U" split ring resonators mutually twisted by 90 degrees. It shows a giant optical activity and circular dichroism. The retrieval results reveal that a negative refractive index is realized for circularly polarized waves due to the large chirality. The experimental results are in good agreement with the numerical results.
We report numerical experiments of optical wave propagation in composites of high refractive index dielectric rods at frequencies where their first electric and magnetic Mie resonances are excited. The arrays of these particles have been extensively studied and proposed as non-absorbing and isotropic metamaterials. We show that negative refraction, observed in ordered particle arrays, is due to diffraction and that an effective medium theory yields constitutive parameters that do not reproduce the observations in these composites, whose transmission also depends on the sample shape. This is fu…
High-index dielectric materials are in great demand for nanophotonic devices and applications, from ultrathin optical elements to metal-free sub-diffraction light confinement and waveguiding. Here we show that chalcogenide topological insulators are particularly apt candidates for dielectric nanophotonic architectures in the infrared spectral range by reporting metamaterial resonances in chalcogenide crystals sustained well inside the mid-infrared, choosing Bi$_2$Te$_3$ as case study within this family of materials. Strong resonant modulation of the incident electromagnetic field is achieved t…
A key optical parameter characterizing the existence of negative refraction in a thin layer of a composite material is the effective refractive index of an equivalent, homogenized layer with the same physical thickness as the initial inhomogeneous composite. Measuring the complex transmission and reflection coefficients is one of the most rigorous ways to obtain this parameter. We dispute Grigorenko's statement (Optics Letters 31, 2483 (2006)) that measuring only the reflection intensity spectrum is sufficient for determining the effective refractive index. We discuss fundamental drawbacks of …
e present a detailed study of the retrieved optical parameters, electrical permittivity, magnetic permeability and refractive index, of the coupled fishnet metamaterial structures as a function of the separation between layers. For the weak coupling case, the retrieved parameters are very close to the one-functional-layer results and converge relatively fast. For the strong coupling case, the retrieved parameters are completely different than the one unit fishnet results. We also demonstrate that the high value of the figure of merit (FOM=|Re(n)/Im(n)|) for the strongly coupled structures is d…
The race to engineering metamaterials comprising of a negative refractive index in the optical range has been fueled by the realization of negative index materials for GHz frequencies six years ago. Sheer miniaturization of the GHz resonant structures is one approach. Alternative designs make use of localized plasmon resonant metal nanoparticles or nanoholes in metal films. Following this approach, a negative refractive index has been realized in the optical range very recently. We review these recent results and summarize how to unambiguously retrieve the effective refractive index of thin la…
The recent advance in the assembly of metallic nanoparticles (NPs) has enabled sophisticated engineering of unprecedented light-matter interaction at the optical domain. In this work, I expand the design flexibility of NP optical metamaterial to push the upper limit of accessible refractive index to the unnaturally high regime. The precise control over the geometrical parameters of NP superlattice monolayer conferred the dramatic increase in electric resonance and related effective permittivity far beyond the naturally accessible regime. Simultaneously, effective permeability, another key fact…
Electromagnetic metamaterials, made from arrangements of subwavelength sized structures, can be used to manipulate radiation. Designing metamaterials that have a positive refractive index along one axis and a negative refractive index along the orthogonal axis can result in birefringences, $Δn>1$. The effect can be used to create wave plates with subwavelength thicknesses. Previous attempts at making wave plates in this way have resulted in very narrow usable bandwidths. In this paper, we use the Pancharatnam method to increase the usable bandwidth. A combination of Finite Element Method and T…
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…
We report extensive enhancement in the refractive index of artificially designed metamaterials by exploiting the deep subwavelength coupling in a free-standing, thin-film metal-dielectric-metal checkboard structure. A record high refractive index of 77.02+43.22i is obtained at terahertz frequencies. The detailed investigations reveal that the enhancement of the effective refractive index of the structure via deep subwavelength coupling in a bilayer design is governed by a power law, which is an effective and simpler approach to design high index metamaterial. The approach relies on deep subwav…
Metamaterials are artificial composite materials that, by virtue of their microstructure, exhibit properties not exhibited by their component materials. Much excitement has been generated by negatively refracting metamaterials, typically consisting of coupled, metallic, subwavelength elements that simulate electric and magnetic dipoles, because of their unusual ability to manipulate visible light, infrared waves and microwaves. In such a metamaterial, an electromagnetic wave propagates so that the direction of its energy flow is opposed to its phase velocity, a condition captured by the real p…
We present a metamaterial-based terahertz (THz) sensor for thickness measurements of subwavelength-thin materials and refractometry of liquids and liquid mixtures. The sensor operates in reflection geometry and exploits the frequency shift of a sharp Fano resonance minimum in the presence of dielectric materials. We obtained a minimum thickness resolution of 12.5 nm (1/16000 times the wavelength of the THz radiation) and a refractive index sensitivity of 0.43 THz per refractive index unit. We support the experimental results by an analytical model that describes the dependence of the resonance…
We present a physical explanation of Zitterbewegung-like effect near the zero-refractive-index point in a metamaterial slab in this paper. Between the negative and positive refractive index regions centered at the zero-refractive-index point, the transmittance spectrum distribution of the metamaterial slab is asymmetrical. When a symmetrical pulse propagates through the metamaterial slab, its transmitted spectrum becomes asymmetrical due to the asymmetry of the transmittance spectrum of the slab, leading to a transmitted pulse with an asymmetrical temporal shape. The asymmetry manifests a kind…
We present a general approach for the numerical calculation of the effective dielectric tensor of metamaterials and show that our formalism can be used to study metamaterials beyond the long wavelength limit. We consider a system composed of high refractive index cylindric inclusions and show that our method reproduces the Mie resonant features and photonic band structure obtained from a multiple scattering approach, hence opening the possibility to study arbitrarily complex geometries for the design of resonance-based negative refractive metamaterials at optical wavelengths.
Photonic metamaterials are man-made structures composed of tailored micro- or nanostructured metallo-dielectric sub-wavelength building blocks that are densely packed into an effective material. This deceptively simple, yet powerful, truly revolutionary concept allows for achieving novel, unusual, and sometimes even unheard-of optical properties, such as magnetism at optical frequencies, negative refractive indices, large positive refractive indices, zero reflection via impedance matching, perfect absorption, giant circular dichroism, or enhanced nonlinear optical properties. Possible applicat…
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…
Contrary to conventional wisdom that light bends away from the normal at the interface when it passes from high to low refractive index media, here we demonstrate an exotic phenomenon that the direction of electromagnetic power bends towards the normal when light is incident from arbitrary high refractive index medium to ε-near-zero metamaterial. Moreover, the direction of the transmitted beam is close to the normal for all angles of incidence. In other words, the electromagnetic power coming from different directions in air or arbitrary high refractive index medium can be redirected to the di…
Negative index metamaterials (NIMs) give rise to unusual and intriguing properties and phenomena, which may lead to important applications such as superlens, subwavelength cavity and slow light devices. However, the negative refractive index in metamaterials normally requires a stringent condition of simultaneously negative permittivity and negative permeability. A new class of negative index metamaterials - chiral NIMs, have been recently proposed. In contrast to the conventional NIMs, chiral NIMs do not require the above condition, thus presenting a very robust route toward negative refracti…
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 present a gradient-index (GRIN) metamaterial based on an array of annular slots. The structure allows a large variation of the effective refractive index under normal-to-plane incidence and thus enables the construction of GRIN devices consisting of only a small number of functional layers. Using full-wave simulations, we demonstrate the annular slot concept by means of a 3-unit-cell thin GRIN lens for the terahertz (THz) range. In the presented realizations, we achieved an index contrast of Delta n = 1.5 resulting in a highly refractive lens suitable for focusing THz radiation to a spot si…
This letter discusses the importance of the nature of local fields inside a unit cell of optical metamaterials in developing a valid effective medium theory. In particular, we apply the Meier-Wokaun procedure to derive a corrected version of the Maxwell-Garnett formula for the refractive index of a medium composed by metallic rods with subwavelength cross-section. We compare this result with the values obtained using the full mode analysis calculated via numerical simulations and analyze the impact of surface plasmon polaritons in adequately determining the effective refractive index of the me…
Extreme mid-infrared field enhancement and anapoles in high-index plasmonic metamaterials
School of Physics and Astronomy, University of Birmingham（伯明翰大学物理与天文学学院）；NanoPhotonics Centre, Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室纳米光子学中心）
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…
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…
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…
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
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 report on a method and an associated open source software, Fit@TDS, working on an average personal computer. The method is based on the fitting of a time-trace data of a terahertz time-domain-spectroscopy system enabling the retrieval of the refractive index of a dielectric sample and the resonance parameters of a metasurface (quality factor, absorption losses, etc.). The software includes commonly used methods where the refractive index is extracted from frequency domain data. However, these methods are limited, for instance in case of a high noise level or when an absorption peak saturate…
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.
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 me…
This work is concerned with the experimental demonstration of a dual-band negative index metamaterial. The sample is double-negative (showing both a negative effective permeability and a negative effective permittivity) for wavelengths between 799 and 818 nm of linearly polarized light with a real part of refractive index of about -1.0 at 813 nm; the ratio -Re(n)/Im(n) is close to 1.3 at that wavelength. For an orthogonal polarization, the same sample also exhibits a negative refractive index in the visible (at 772 nm). The spectroscopic measurements of the material are in good agreement with …
We demonstrate experimentally and numerically that metamaterials based on bilayer cross wires give giant optical activity, circular dichroism, and negative refractive index. The presented chiral design offers a much simpler geometry and more efficient way to realize negative refractive index at any frequency. We also developed a retrieval procedure for chiral materials which works successfully for circularly polarized waves.
Artificial magnetism, negative permeability and negative refractive index are demonstrated in 3D-chiral metamaterial that shows giant polarization rotation and circular dichroism.
A well-established, silver fishnet design has been further miniaturized to function as a negative-index material at the shortest wavelength to date. By studying the transmittance, reflectance, and corresponding numerical simulations of the sample, we report in this paper a negative refractive index of -0.25 at the yellow-light wavelength of 580 nm.
The Bruggeman formalism is implemented to estimate the refractive index of an isotropic, dielectric, homogenized composite medium (HCM). Invoking the well--known Hashin--Shtrikman bounds, we demonstrate that the group velocity in certain HCMs can exceed the group velocities in their component materials. Such HCMs should therefore be considered as metamaterials.
Planar metamaterials with tailorable electromagnetic properties in the terahertz domain offer customized optics solutions that are needed for the development of imaging and spectroscopy systems. In particular, metamaterials carry the potential to substitute conventional bulky optics or can be basic building blocks for completely novel devices. In this respect it is advantageous that metamaterials can be devised to be impedance-matched to another material regarding their electromagnetic properties. Here, we design, fabricate and investigate a metamaterial with tailorable refractive index and im…
A new class of artificially structured materials called metamaterials makes it possible to achieve electromagnetic properties that do not exist in nature. In this paper we review the recent progress made in the area of optical metamaterials. It was predicted that nanostructured metamaterials could provide us with artificial magnetic response and negative refractive index at optical frequencies. To date, optical metamagnetics have been already fabricated to demonstrate artificial magnetic response in the infrared and across the entire visible spectrum, while metamaterials showing negative refra…
We introduce a class of metamaterials with uniformly balanced gain and loss associated with complex permittivity and permeability constants. The refractive index of such a balanced pseudo-passive metamaterial is real. An unbounded uniform pseudo-passive medium has transport characteristics similar to those of its truly passive and lossless counterpart with the same real refractive index. However, bounded pseudo-passive samples show some unexpected scattering features which can be further emphasized by including such elements in a photonic structure.
Here we report the designing of chiral metamaterial with metallic helix array. The effective electric and magnetic dipoles, which originate from the induced surface electric current upon illumination of incident light, are collinear at the resonant frequency. Consequently, for the circularly polarized incident light, negative refractive index is realized. Our design provides a unique approach to tune the optical properties by assembling helices, and demonstrates a different approach in exploring three- dimensional chiral metamaterial.
We present the blueprint for a novel negative-index metamaterial. This structure is fabricated via three-dimensional two-photon direct laser writing and silver shadow evaporation. The comparison of measured linear optical spectra with theory shows good agreement and reveals a negative real part of the refractive index at around 3.85 micrometer wavelength - despite the fact that the metamaterial structure is bi-anisotropic due to the lack of inversion symmetry along its surface normal.
Increasing the refractive index available for optical and nanophotonic systems opens new vistas for design: for applications ranging from broadband metalenses to ultrathin photovoltaics to high-quality-factor resonators, higher index directly leads to better devices with greater functionality. Although standard transparent materials have been limited to refractive indices smaller than 3 in the visible, recent metamaterials designs have achieved refractive indices above 5, accompanied by high losses, and near the phase transition of a ferroelectric perovskite a broadband index above 26 has been…
