A novel electromagnetic energy squeezing mechanism is proposed based on the special properties of permeability-near-zero metamaterials. Nearly no energy stream can enter a conventional dielectric region positioned inside a permeability-near-zero material. When a source is surrounded by a dielectric split ring (encloser with a gap opened), the electromagnetic energy generated by the source is forced to propagate through the gap. When the gap is narrow, the energy stream density becomes very large and makes the magnetic field enhanced drastically in the gap. The narrow gap can be long and bended. This provides us a method to obtain strong magnetic field without using resonance enhancement.
We show that any pair of real symmetric tensors $\BGve$ and $\BGm$ can be realized as the effective electric permittivity and effective magnetic permeability of a metamaterial at a given fixed frequency. The construction starts with two extremely low loss metamaterials, with arbitrarily small microstructure, whose existence is ensured by the work of Bouchitt{é} and Bourel and Bouchitté and Schweizer, one having at the given frequency a permittivity tensor with exactly one negative eigenvalue, and a positive permeability tensor, and the other having a positive permittivity tensor, and a permeab…
Metamaterials with artificial optical properties have attracted significant research interest. In particular, artificial magnetic resonances in non-unity permeability tensor at optical frequencies in metamaterials have been reported. However, only non-unity diagonal elements of the permeability tensor have been demonstrated to date. A gyromagnetic permeability tensor with non-zero off-diagonal elements has not been observed at the optical frequencies. Here we report the observation of gyromagnetic properties in the near-infrared wavelength range in a magneto-plasmonic metamaterial. The non-zer…
In this work, we present a simple method for the direct retrieval of the effective permittivity and permeability of a bulk semi-infinite metamaterial from variable-angle spectroscopic ellipsometry measurements. Starting from the well-known Fresnel equations, we derive an analytical expression in which unknown coefficients are fitted to the experimental data using a linear regression model. The effective permittivity and permeability are then determined by solving a simple system and the correct solution is selected based on physical criteria. As an example, the method is applied to the case of…
We consider layered heterostructures combining ordinary positive index materials and dispersive metamaterials. We show that these structures can exhibit a new type of photonic gap around frequencies where either the magnetic permeability μor the electric permittivity εof the metamaterial is zero. Although the interface of a semi-infinite medium with zero refractive index (a condition attained either when μ= 0 or when ε= 0) is known to give full reflectivity for all incident polarizations, here we show that a gap corresponding to μ= 0 occurs only for TE polarized waves, whereas a gap correspond…
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.
It is shown that perfect absorption and giant amplification can be realized when a wave impinges on a special metamaterial layer with zero real parts of the permittivity and permeability. The imaginary parts of the permittivity and permeability remain nonzero, corresponding to finite loss or gain. Perfect absorption and giant magnification can still be achieved even if the thickness of the metamaterial layer is arbitrarily thin and the absolute imaginary parts of the permittivity and permeability are very small. The metamaterial layer needs a total-reflection substrate for perfect absorption, …
Practical design parameters of resonant metamaterials, such as loss tangent, are derived in terms of the quality factor $Q$ of the resonant effective medium permeability or permittivity. Through electromagnetic simulations of loop-based resonant particles, it is also shown that the $Q$ of the effective medium response is essentially equal to the $Q$ of an individual resonant particle. Thus, by measuring the $Q$ of a single fabricated metamaterial particle, the effective permeability or permittivity of a metamaterial can be calculated simply and accurately without requiring complex simulations,…
We present an effective-medium model for calculating the frequency-dependent effective permittivity $ε(ω)$ and permeability $μ(ω)$ of metamaterial composites containing spherical particles with arbitrary permittivity and permeability. The model is derived from the zero-scattering condition within the dipole approximation, but does not invoke any additional long-wavelength approximations. As a result, it captures the effects of spatial dispersion and predicts a finite effective refractive index and antiresonances in $ε(ω)$ and $μ(ω)$, in agreement with numerical finite-element calculations.
A scheme of left-handed metamaterial (LHM) composed of superconducting quantum interference devices (SQUIDs) and conducting wires is proposed. The permeability of a probe field can be smoothly tuned over a wide range with another electromagnetic (coupling) field due to quantum interference effect. Similar to electromagnetically induced transparency (EIT) of atomic systems, the absorption of the probe field can be strongly suppressed even in the case of negative permeability. There are two passbands of negative refractive index with low loss, which can be tuned with the coupling field.
We propose a class of optical transformation media, illusion media, which render the enclosed object invisible and generate one or more virtual objects as desired. We apply the proposed media to design a microwave device, which transforms an actual object into two virtual objects. Such an illusion device exhibits unusual electromagnetic behavior as verified by full-wave simulations. Different from the published illusion devices which are composed of left-handed materials with simultaneously negative permittivity and permeability, the proposed illusion media have finite and positive permittivit…
Achieving zero backward scattering (ZBS) and zero forward scattering (ZFS), i.e., the so-called the first and second Kerker's conditions respectively, by sphere spherical particles is considered to be impossible due to the unavailability of naturally occurring magnetic materials in the visible frequency range. We report theoretical modeling to design composite metamaterials that present large optical magnetic permeability in the visible frequency range by employing Mie scattering theory and extended Maxwell Garnett theory. We numerically show that a careful selection of constituents of a compo…
A moving medium drags light along with it as measured by Fizeau and explained by Einstein's theory of special relativity. Here we show that the same effect can be obtained in a situation where there is no physical motion of the medium. Modulations of both the permittivity and permeability, phased in space and time in the form of travelling waves, are the basis of our model. Space-time metamaterials are represented by effective bianisotropic parameters, which can in turn be mapped to a moving homogeneous medium. Hence these metamaterials mimic a relativistic effect without the need for any actu…
We use the theory of inhomogeneous waves to study the transmission of light in $μ$-near-zero metamaterials. We find the effect of all-angle collimation of incident light, which means that the vector of energy flow in a wave transmitted to a $μ$-near-zero metamaterial is perpendicular to the interface for any incident angles if an incident wave is s-polarized. This effect is similar to the all-angle collimation of incident light recently found through a different theoretical framework in $\varepsilon$-near-zero metamaterials for a p-polarized incident wave [S. Feng, Phys. Rev. Lett. 108, 193904…
In this article, we report the growth of gold nanorods on glass substrates and copper nanoparticle thin films by cylindrical direct current magnetron sputtering (CDCMS) at room temperature. The grown gold nanorods have short lengths of < 20nm and show negative optical parameters in UV-Vis region. So far negative permittivity and permeability were only shown for complex artificial structures. In a case of simple structures like gold nanorods, the negative optical parameters were only predicted by simulation methods and considering ideal structures and they were not yet reported by experimental …
We propose that macroscopic objects built from negative-permeability metamaterials may experience resonantly enhanced magnetic force in low-frequency magnetic fields. Resonant enhancement of the time-averaged force originates from magnetostatic surface resonances (MSR) which are analogous to the electrostatic resonances of negative-permittivity particles, well known as surface plasmon resonances in optics. We generalize the classical problem of MSR of a homogeneous object to include anisotropic metamaterials, and consider the most extreme case of anisotropy where the permeability is negative i…
We discuss electromagnetic modes in cavities formed by metamaterials with negative refraction and demonstrate that the straightforward approach to substitute negative values of the electric permittivity and the magnetic permeability leads to quasi-bound states with a negative quality factor. To ensure positive quality factors and a consistent physical interpretation of the quasi-bound states it is essential to include the frequency dispersion of the permittivity and the permeability, as required by positive field energy and causality. The basic mode equation and the boundary conditions includi…
Artificial magnetism, negative permeability and negative refractive index are demonstrated in 3D-chiral metamaterial that shows giant polarization rotation and circular dichroism.
Using detailed simulations we investigate the magnetic response of metamaterials consisting of pairs of parallel slabs or combinations of slabs with wires (including the fishnet design) as the length-scale of the structures is reduced from mm to nm. We observe the expected saturation of the magnetic resonance frequency when the structure length-scale goes to the sub-micron regime, as well as weakening of the effective permeability resonance and reduction of the spectral width of the negative permeability region. All these results are explained by using an equivalent resistor-inductor-capacitor…
We demonstrate that metamaterial devices requiring anisotropic dielectric permittivity and magnetic permeability may be emulated by specially designed tapered waveguides. This approach leads to low-loss, broadband performance. Based on this technique, we demonstrate broadband electromagnetic cloaking in the visible frequency range on a scale ~100 times larger than the wavelength.
It is commonly assumed that the long-wavelength limit of a metamaterial can always be described in terms of effective permeability and permittivity tensors. This assumption holds true in all metamaterials considered up to now. Here we report that this assumption is false--there exist an entirely new class of metamaterials consisting of multiple interlocking disconnected metal networks, for which the effective long-wavelength theory is local, but the effective field is non-Maxwellian, and possesses much more internal degrees of freedom than effective Maxwellian fields in a homogeneous medium.
In this work, we investigate wave transmission through an epsilon-near-zero metamaterial waveguide embedded with defects. We show that by adjusting the geometric sizes and material properties of the defects, total reflection and even transmission can be obtained, despite the impedance mismatch of epsilon-near-zero material with free space. Our work can greatly simplify the design of zero-index material waveguide applications by removing the dependence on permeability.
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…
In this paper, mu-near-zero (MNZ) metamaterials are utilized to achieve an ultrathin absorber with a thickness of only about one percent of the operating wavelength. The metamaterial absorber (MA) is made of double-layered metallic spiral arrays designed to have a large purely imaginary permeability at low microwave frequencies (~ 1.7 GHz). An absorption efficiency above 90% is demonstrated at illumination angles up to 60 degrees. A polarization-insensitive MA implemented by 2D isotropic metamaterials is also studied. Our designs have great application potential as compared with the traditiona…
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.
Metamaterials-or artificial electromagnetic materials-can create media with properties unattainable in nature, but mitigating dissipation is a key challenge for their further development. Here, we demonstrate a low-loss metamaterial by exploiting dark bound states in dielectric inclusions coupled to the external waves by small nonresonant metallic antennas. We experimentally demonstrate a dispersion-engineered metamaterial based on a meta-atom made from alumina, and we show that its resonance has a much larger quality factor than metal-based meta-atoms. Finally, we show that our dielectric met…
In this paper the design for an absorbing metamaterial with near unity absorbance in terahertz region is presented. The absorber's unit cell structure consists of two metamaterial resonators that couple to electric and magnetic fields separately. The structure allows us to maximize absorption by varying dielectric material and thickness and, hence the effective electrical permittivity and magnetic permeability.
Electromagnetic field propagation through a transition layer between the positive-index and negative-index materials with linearly changing dielectric permittivity and magnetic permeability was investigated. It is shown that at oblique incidence, the components of both TE- and TM-waves exhibit singular behavior in the vicinity of the point where both dielectric permittivity and magnetic permeability are equal to zero. In this case, finite dissipation of electromagnetic field energy takes place even at infinitesimally small values of losses. These results are applicable to a broader class of in…
Electromagnetic localization and existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band - where the magnetic permeability $μ(ω)$ is positive and the dielectric permittivity $ε(ω)$ is negative - is described by a nonlinear Klein-Gordon equation with a dispersive nonlinear term. A family of standing and moving localized waves for both electric and magnetic fields is found, and the rol…
We have experimentally realized Brewster's effect for transverse-electric waves with metamaterials. In dielectric media, Brewster's no-reflection effect arises only for transverse-magnetic waves. However, it has been theoretically predicted that Brewster's effect arises for TE waves under the condition that the relative permeability r is not equal to unity. We have designed an array of split-ring resonators as a metamaterial with mu_r 1 using a finite-difference time-domain method. The reflection measurements were carried out in a 3-GHz region and the disappearance of reflected waves at a part…
The behavior of strongly coupled Radial Photonic Crystals shells is investigated as a potential alternative to transfer electromagnetic energy wirelessly. These sub-wavelength resonant microstructures, which are based on anisotropic metamaterials, can produce efficient coupling phenomena due to their high quality factor. A configuration of selected constitutive parameters (permittivity and permeability) is analyzed in terms of its resonant characteristics. The coupling to loss ratio between two coupled resonators is calculated as a function of distance, the maximum (in excess of 300) is obtain…
In this paper we explored the scattering behavior of thin cylinders made of LHM and coated by a monoatomic graphene layer. A spectral tunability of the resonance peaks is evidenced by altering the chemical potential of the graphene coating, a fact that occurs at any state of polarization of the incident plane wave in opposition to the case of scatterers of dielectric core. On the contrary, no invisibility condition can be satisfied for dielectric environments. A singular performance is also found for cylinders with permittivity and permeability near zero. Practical implementations of our resul…
A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the metamaterial as a cubic arrangement of coupled LC circuits, giving the relation between currents and local magnetic field. The second equation comes from macroscopic Maxwell equations, and gives the relation between the macroscopic magnetic field and the average magnetization of the metamaterial. It is shown that electromagnetic and magnetoinductive waves propag…
Anomalous field enhancement accompanied by resonant absorption phenomenon was originally discussed in the context of plasma physics and in applications related to radio-communications between the ground and spacecraft returning to Earth. Indeed, there is a critical period of time when all communications are lost due to the reflection/absorption of electromagnetic waves by the sheath of plasma created by a high speed vehicle re-entering the atmosphere. While detailed experimental studies of these phenomena in space are challenging, the emergence of electromagnetic metamaterials enables research…
We consider the interaction between a particle beam and a propagating electromagnetic wave in the presence of a metamaterial. We show that the introduction of a metamaterial gives rise to a novel dispersion curve which determines a unique wave particle relationship, via the frequency dependence of the metamaterial and the novel ability of metamaterials to exhibit simultaneous negative permittivity and permeability. Using a modified form of Madey's theorem we find that the novel dispersion of the metamaterial leads to a amplification of the EM wave power.
We study the propagation of electromagnetic waves in the limit of geometrical optics for a class of nearly transparent nonlinear uniaxial metamaterials for which their permittivity tensors present a negative principal component. Their permeability are assumed positive and dependent on the electric field. We show that light waves experience triple refraction -- trirefringence. Additionally to the ordinary wave, two extraordinary waves propagate in such media.
We demonstrate theoretically that electromagnetically induced transparency can be achieved in metamaterials, in which electromagnetic radiation is interacting resonantly with mesoscopic oscillators rather than with atoms. We describe novel metamaterial designs that can support full dark resonant state upon interaction with an electromagnetic beam and we present results of its frequency-dependent effective permeability and permittivity. These results, showing a transparency window with extremely low absorption and strong dispersion, are confirmed by accurate simulations of the electromagnetic f…
Graphene exhibits unique material properties and in electromagnetic wave technology, it raises the prospect of devices miniaturized down to the atomic length scale. Here we study split-ring resonator metamaterials made from graphene and we compare them to gold-based metamaterials. We find that graphene's huge reactive response derived from its large kinetic inductance allows for deeply subwavelength resonances, although its resonance strength is reduced due to higher dissipative loss damping and smaller dipole coupling. Nevertheless, tightly stacked graphene rings may provide for negative perm…
Light propagation in all-dielectric rod-type metamaterials is studied theoretically. The electric and magnetic dipole moments of the rods are derived analytically in the long-wavelength limit. The effective permittivity and permeability of a square lattice of rods are calculated by homogenizing the corresponding array of dipoles. The role of dipole resonances in the optical properties of the rod array is interpreted. This structure is found to exhibit a true left-handed behavior, confirming previous experiments [L. Peng \textit{et al.}, Phys. Rev. Lett. \textbf{98}, 157403 (2007)]. A scaling a…
We solve the nonlinear Maxwell equations in an InP-based dielectric metamaterial, considering both two-photon absorption and photo-induced free-carrier absorption. We obtain the intensity-dependent reflection, absorption, and effective permittivity and permeability of the metamaterial. Our results show that nonlinear absorption dampens both the electric and magnetic Mie resonance, although the magnetic resonance is more affected because it occurs at longer wavelengths where the free-carrier absorption cross section is larger. Owing to field concentration in the metamaterial at resonance, the t…
Zero-index (ZI) materials are synthetic optical materials with vanishing effective permittivity and/or permeability at a given design frequency. Recently, it has been shown that the permeability of a zero-index host material can be deterministically tuned by adding photonic dopants. Here, we apply metal-induced crystallization (MIC) in quasi-random metal-semiconductor composites to fabricate large-area zero-index materials. Using Ag-Si as a model systems, we demonstrate that the localized crystallization of the semiconductor at the metal/semiconductor interface can be used as design parameter …
Forward models for the Mueller Matrix (MM) components of materials with relative magnetic permeability tensor μ \neq 1 are studied. 4x4 matrix formalism is employed to produce general solutions for the complex reflection coefficients and MMs of dielectric-magnetic materials having arbitrary crystal symmetry and arbitrary laboratory orientation. For certain orientations of materials with simultaneously diagonalizable ε and μ tensors (with coincident principal axes), analytic solutions to the Berreman equation are available. For the single layer thin film configuration of these materials, analyt…
Metamaterials are artificially created media, which allow introducing additional degrees of freedom into electromagnetic design by controlling constitutive material parameters. Reconfigurable time-dependent metamaterials can further enlarge those capabilities by introducing a temporal variable as an additional controllable parameter. Here we demonstrate a first-of-its-kind reconfigurable volumetric metamaterial-based scatterer, wherein the electromagnetic properties are controlled dynamically with light. In particular, hybridized resonances in arrays of split ring resonators give rise to a col…
Several results concerning active media or metamaterials are proved and discussed. In particular, we consider the permittivity, permeability, wave vector, and refractive index, and discuss stability, refraction, gain, and fundamental limitations resulting from causality.
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…
Electromagnetic metamaterials are man-made structures that have novel properties such as a negative refraction index, not attainable in naturally occurring materials. Although negative index materials (NIMs) in microwave frequencies were demonstrated in 2001, it has remained challenging to design NIMs for optical frequencies especially those with both negative permittivity and negative permeability [known as left-handed metamaterials (LHMs)]. Here, by going beyond the traditional concept of the combination of artificial electronic and magnetic meta-atoms to design NIMs, we propose a novel LHM …
We consider a boundary problem for 1D electrodynamics modeling of a pulse propagation in a metamaterial medium. We build and apply projecting operators to a Maxwell system in time domain that allows to split the linear propagation problem to directed waves for a material relations with general dispersion. Matrix elements of the projectors act as convolution integral operators. For a weak nonlinearity we generalize the linear results still for arbitrary dispersion and derive the system of interacting right/left waves with combined (hybrid) amplitudes. The result is specified for the popular met…
We investigate numerically the use of a negative-permeability "perfect lens" for enhancing wireless power transfer between two current carrying coils. The negative permeability slab serves to focus the flux generated in the source coil to the receiver coil, thereby increasing the mutual inductive coupling between the coils. The numerical model is compared with an analytical theory that treats the coils as point dipoles separated by an infinite planar layer of magnetic material [Urzhumov et al., Phys. Rev. B, 19, 8312 (2011)]. In the limit of vanishingly small radius of the coils, and large wid…
Metamaterials are patterned metallic structures which permit access to a novel electromagnetic response, negative index of refraction, impossible to achieve with naturally occurring materials. Using the Babinet principle, the complementary split ring resonator (SRR) is etched in a metallic plate to provide negative ε, with perpendicular direction. Here we propose a new design, etched in a metallic plate to provide negative magnetic permeability μ, with perpendicular direction. The combined electromagnetic response of this planar metamaterial, where the negative μcomes from the aperture and the…
Photonic crystals and metamaterials represent two seemingly different classes of artificial electromagnetic media but often they are composed of similar structural elements arranged in periodic lattices. The important question is how to distinguish these two types of periodic photonic structures when their parameters, such as dielectric permittivity and lattice spacing, vary continuously. Here, we discuss transitions between photonic crystals and all-dielectric metamaterials and introduce the concept of a phase diagram and an order parameter for such structured materials, based on the physics …
Artificially created media allow employing material parameters as additional valuable degrees of freedom in tailoring electromagnetic scattering. In particular, metamaterials with either negative permeability or permittivity allow creating deeply subwavelength resonant structures with relatively high scattering crosssections. However, the equivalence principle allows replacing volumetric structures with properly designed curved impedance surfaces, ensuring the same electromagnetic properties. Here, we examine this statement from a practical standpoint, considering two structures, having a dipo…
We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for the nonlinear susceptibilities of the composite metamaterial medium. The expressions are convenient, as they enable inhomogeneous system of scattering elements to be described as a continuous medium using the standard notation of nonlinear optics. We illustrate the validity and accuracy of our theoretical framework by performing measurements on a fabricated …
Frequency upconversion of an electromagnetic wave can occur in ionized plasma with decreasing electric permittivity and in split-ring resonator-structure metamaterials with decreasing magnetic permeability. We develop a general theory to describe the evolution of the wave frequency, amplitude, and energy density in homogeneous media with a temporally decreasing refractive index. We find that upconversion of the wave frequency is necessarily accompanied by partitioning of the wave energy into low-frequency modes, which sets an upper limit on the energy conversion efficiency. The efficiency limi…
Metamaterials are known to exhibit a variety of electromagnetic properties non-existing in nature. We show that an all-dielectric (non-magnetic) system consisting of deep subwavelength, high permittivity resonant spheres possess effective negative magnetic permeability (dielectric permittivity being positive and small). Due to the symmetry of the electromagnetic wave equations in classical electrodynamics, localized "magnetic" plasmon resonances can be excited in a metasphere made of such metamaterial. This is theoretically demonstrated by the coupled-dipole approximation and numerically for r…
