Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting $Ω$ particles
An analytical model is presented for a rectangular lattice of isotropic scatterers with electric and magnetic resonances. Each isotropic scatterer is formed by putting appropriately 6 $Ω$-shaped perfectly conducting particles on the faces of a cubic unit cell. A self-consistent dispersion equation is derived and then used to calculate correctly the effective permittivity and permeability in the frequency band where the lattice can be homogenized. The frequency range in which both the effective permittivity and permeability are negative corresponds to the mini-band of backward waves within the resonant band of the individual isotropic scatterer.
Negative real parts of the permittivity and permeability lead an isotropic chiral medium to exhibit circular dichroism that is reversed with respect to that exhibited by an identical medium but the real parts of whose permittivity and permeability are positive.
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…
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 present a solitary wave solution of the generalized nonlinear Schrodinger equation for dispersive permittivity and permeability using a scaling transformation and coupled amplitude-phase formulation. We have considered the third-order dispersion effect (TOD) into our model and show that soliton shift may be suppressed in a negative index material by a judicious choice of the TOD and self-steepening parameter.
Two results about the planewave response of an isotropic, dielectric--magnetic, homogeneous, planar slab are deduced when the real parts of both the permittivity and the permeability are altered from positive to negative. First, the reflection and the transmission coefficients suffer phase reversals without change in their respective magnitudes. Second, the Goos-Haenchen shifts experienced by beams on total reflection reverse their directions.
The reflection of a normally incident wideband pulse by a half-space whose permittivity and permeability obey the one-resonance Lorentz model is calculated. The results are compared with those from frequency-domain reflection analysis. In the spectral regime wherein the real parts of the permittivity and the permeability are negative, as well as in small adjacent neighborhoods of that regime, the time-domain analysis validates the conclusion that it is sufficient to ensure that the imaginary part of the refractive index is positive - regardless of the sign of the real part of the refractive in…
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…
If all space is occupied by a linear bianisotropic material--whether homogeneous or not--then the concurrent replacements of the permittivity and the impermeability tensors by the negatives of their respective complex conjugates and of the magnetoelectric tensors by their respective complex conjugates (in the Boys-Post representation) imply the conjugation of both E and H, in the absence of externally impressed sources. This conjugation symmetry in linear electromagnetism has observable consequences when the linear bianisotropic material occupies a bounded region.
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 …
In order to reduce the difficulties in the experimental realizations of the cloak but still keep good performance of invisibility, we proposed a perfect cylindrical invisibility cloak with spatially invariant axial material parameters. The advantage of this kind of TE (or TM) cloak is that only rho and phi components of mu (or epsilon) are spatially variant, which makes it possible to realize perfect invisibility with two-dimensional (2D) magnetic (or electric) metamaterials. The effects of perturbations of the parameters on the performance of this cloak are quantitatively analyzed by scatteri…
Magnetic permeabilities derived for infinite, periodic media are used in the Fresnel equation to calculate the reflection from corresponding semi-infinite media. By comparison to finite-difference-time-domain (FDTD) simulations, we find that the Fresnel equation gives accurate results for 2D metamaterials which mimic natural magnetism, in a frequency range where the magnetic moment density dominates the $\mathcal O(k^2)$ part of the total Landau--Lifshitz permittivity. For a 1D layered structure, or for large frequencies, the correspondence is poor. We also demonstrate that even if a medium is…
The effects of electric and magnetic loss factors on zero-mu and zero-epsilon gaps in a one-dimensional lossy photonic crystal composed of double-negative and double-positive materials are theoretically investigated by employing the characteristic matrix method. This study contradicts the previous reports as it indicates that by applying the inevitable factors of electric and magnetic losses to the double-negative material, the zero-mu and zero-epsilon gaps appear simultaneously in the transmission spectrum, being independent of the incidence angle and polarizations. Moreover, the results show…
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, …
We show that resonant tunneling of electromagnetic fields can occur through a three-layer structure composed of a single-negative (i.e., either negative-permittivity or negative-permeability) slab paired with bi-layer made of double-positive (i.e., positive permittivity and permeability) media. In particular, one of the two double-positive media can be chosen arbitrarily (even vacuum), while the other may exhibit extreme (either near-zero or very high) permittivity/permeability values. Our results on this counterintuitive tunneling phenomenon also demonstrate the possibility of synthesizing do…
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.
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 propose a composite optical transformation to design an illusion device which can move the image of a target from one place to another place. Enclosed by such an illusion device, an arbitrary object located at one place appears to be at another place virtually. Different from the published shifted-position cloak which is composed of the left-handed materials with simultaneously negative permittivity and permeability, the illusion device proposed in this letter has positive permittivity and permeability. Hence proposed illusion device could be realized by artificial metamaterials.
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…
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…
Drug metabolites usually have structures of split-ring resonators (SRRs), which might lead to negative permittivity and permeability in electromagnetic field. As a result, in the UV-vis region, the latent fingermarks images of drug addicts and non drug users are inverse. The optical properties of latent fingermarks are quite different between drug addicts and non-drug users. This is a technic superiority for crime scene investigation to distinguish them. In this paper, we calculate the permittivity and permeability of drug metabolites using tight-binding model. The latent fingermarks of smoker…
A system of periodic poly-disperse coated nano-rods is considered. Both the coated nano-rods and host material are non-magnetic. The exterior nano-coating has a frequency dependent dielectric constant and the rod has a high dielectric constant. A negative effective magnetic permeability is generated near the Mie resonances of the rods while the coating generates a negative permittivity through a field resonance controlled by the plasma frequency of the coating and the geometry of the crystal. The explicit band structure for the system is calculated in the sub-wavelength limit. Tunable pass ban…
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…
The Lorentz transformations for the optical constants (electric permittivity, magnetic permeability and index of refraction) of moving media are considered.
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 theoretically study negative refraction of inhomogeneous waves at the interface of lossy isotropic media. We obtain explicit (up to the sign) expressions for the parameters of a wave transmitted through the interface between two lossy media characterized by complex permittivity and permeability. We show that the criterion of negative refraction that requires negative permittivity and permeability can be used only in the case of a homogeneous incident wave at the interface between a lossless and lossy media. In a more general situation, when the incident wave is inhomogeneous, or both media …
Some kinds of psychoactive drugs have the structures which are called split-ring resonators (SRRs). SRRs might result in negative permittivity and permeability simultaneously in electromagnetic field. Simultaneous negative indexes can lead to the famous phenomenon of negative refraction. This optical property makes it possible to distinguish synthetic cannabinoids from other abusive psychoactive drugs in the UV-vis region. This optical method is non-damaged and superior in forensic science. In this paper, we use tight-binding model calculating the permittivity and permeability of the main ingr…
The implications of causality are examined in detail for the permittivity, permeability, and refractive index of passive and active media. Particular attention is given to negative index media.
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…
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 extend designs of perfect lenses to the focussing of surface plasmon polaritons (SPPs) propagating at the interface between two anisotropic media of opposite permittivity sign. We identify the role played by the components of anisotropic and heterogeneous tensors of permittivity and permeability, deduced from a coordinate transformation, in the dispersion relation governing propagation of SPPs. We illustrate our theory with three-dimensional finite element computations for focussing of SPPs by perfect flat and cylindrical lenses.
The three-dimensional Gaussian beam transmission through a ferrite-semiconductor finely-stratified structure being under an action of an external static magnetic field in the Faraday geometry is considered. The beam field is represented by an angular continuous spectrum of plane waves. In the long-wavelength limit, the studied structure is described as a gyroelectromagnetic medium defined by the effective permittivity and effective permeability tensors. The investigations are carried out in the frequency band where the real parts of the on-diagonal elements of both effective permittivity and e…
We find the analytical expression for the threshold intensity necessary to launch ultra-slow light pulses in a metamaterial with simultaneous cubic electric and magnetic nonlinearity. The role played respectively by the permittivity, the permeability, the electric cubic nonlinearity, the magnetic cubic nonlinearity and the pulse duration is clearly identified and discussed.
We theoretically investigate the intra-band transitions in Möbius molecules. Due to the weak magnetic response, the relative permittivity is significantly modified by the presence of the medium while the relative permeability is not. We show that there is hyperbolic dispersion relation induced by the intra-band transitions because one of the eigen-values of permittivity possesses a different sign from the other two, while all three eigen-values of permeability are positive. We further demonstrate that the bandwidth of negative refraction is 0.1952~eV for the $H$-polarized incident light, which…
We investigate the prospect of achieving negative permittivity and permeability at optical frequencies in a dielectric crystal containing stoichiometric rare-earth ions. We derive the necessary transition linewidth, ion density and electric and magnetic oscillator strengths using a simplified model of non-interacting dipoles. We identify Erbium crystals in a magnetically ordered phase as the most promising material to meet these conditions, and describe initial optical measurements of two potential candidates, \ercl{} and ${}^7$\lierf{}, which display linewidths of 3~GHz and 250~MHz, respectiv…
We present the first dual-band negative index metamaterial that operates in the visible spectrum. The optimized four-functional-layer metamaterial structure exhibits the first double-negative (i.e., simultaneously negative permittivity and permeability) band in the red region of the visible spectrum with a figure of merit of 1.7 and the second double-negative band in the green region of the visible spectrum with a figure of merit of 3.2. The optical behavior of the proposed structure is independent of the polarization of the incident field. This low-loss metamaterial structure can be treated a…
We propose a design for optical-frequency double-negative metamaterials (DMNs) in which the unit cell is formed by a single-layer plasmonic inclusion. By introducing some properly arranged stepwise modulations onto the inclusions, the effective permittivity and permeability of the material may become simultaneously negative due to the excitation of higher-order multipole plamonic (electrostatic) resonances. The approach opens a possibility to construct low-loss optical DNMs with great engineering simplicity.
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 derive the expression for the anisotropic heterogeneous matrices of permittivity and permeability associated with two-dimensional polygonal and star shaped cloaks. We numerically show using finite elements that the forward scattering worsens when we increase the number of sides in the latter cloaks, whereas it improves for the former ones. This antagonistic behavior is discussed using a rigorous asymptotic approach. We use a symmetry group theoretical approach to derive the cloaks design.
