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 scattering theory. Our work provides a simple and feasible solution to the experimental realization of cloaks with ideal parameters.
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…
By investigating wave properties at cloak boundaries, invisibility cloaks with arbitrary shape constructed by general coordinate transformations are confirmed to be perfectly invisible to the external incident wave. The differences between line transformed cloaks and point transformed cloaks are discussed. The fields in the cloak medium are found analytically to be related to the fields in the original space via coordinate transformation functions. At the exterior boundary of the cloak, it is shown that no reflection is excited even though the permittivity and permeability do not always have a…
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…
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 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.
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 …
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 develop and apply an optimization method to design invisibility cloaks. Our method is based on minimizing the forward scattering amplitude of the cloaked object, which by the optical theorem, is equivalent to the total cross section. The use of the optical theorem circumvents the need to evaluate and integrate the scattering amplitude over angle at each iteration, and thus provides a simpler, more computationally efficient objective function for optimizing structures. We implement the approach using gradient descent optimization and present several gradient-permittivity cloaks that reduce s…
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…
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 …
Permittivity tensors of arbitrary shaped invisibility devices are obtained using effective medium approach in general relativity. As special cases, analytical expressions for the permittivity tensors of invisibility cloaks for the elliptic cylinder, prolate spheroid, and the confocal paraboloid geometry are derived. In the case of elliptic cylinder, we found that the point of infinite light speed in the electromagnetic space becomes two points in the physical space in the zz component of the permittivity tensor. This result is different from the case of perfect cylinder in which there is a lin…
The method of coordinate transformation offers a way to realize perfect cloaks, but provides less ability to characterize the performance of a multilayered cloak in practice. Here, we propose an analytical model to predict the performance of a multilayered cylindrical cloak, based on which, the cloak in practice can be optimized to diminish the intrinsic scatterings caused by discretization and simplification. Extremely low scattering or "quasi-perfect invisibility" can be achieved with only a few layers of anisotropic metamaterials without following the transformation method. Meanwhile, the p…
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, …
Is it possible to actually make Harry's invisibility cloaks? The most promising approach for realizing such magical cloaking in our real world would be to use transformation optics, where an empty space with a distorted geometry is imitated with a non-distorted space but filled with transformation medium having appropriate permittivity and permeability. An important requirement for true invisibility cloaks is nonreciprocity; that is, a person in the cloak should not be seen from the outside but should be able to see the outside. This invisibility cloak, or a nonreciprocal shield, cannot be cre…
We investigate the scattering of 2D cylindrical invisibility cloaks with simplified constitutive parameters with the assistance of scattering coefficients. We show that the scattering of the cloaks originates not only from the boundary conditions but also from the spatial variation of the component of permittivity/permeability. According to our formulation, we propose some restrictions to the invisibility cloak in order to minimize its scattering after the simplification has taken place. With our theoretical analysis, it is possible to design a simplified cloak by using some peculiar composite…
The electromagnetic characteristics of plane-transformed invisibility cloaks are quantitatively studied in this paper. We take elliptical cylindrical cloak as the example, and use an elliptical cylindrical wave expansion method to obtain the scattered field. It is demonstrated that an ideal elliptical cylindrical cloak is inherently visible. Noticeable field scattering and penetration will be induced when the cloak is exposed directly to an electromagnetic wave. However, as long as the cloak consists of a perfect electric conducting lining at the interior surface, perfect invisibility can stil…
The straightforward method of transformation optics implies that one starts from the coordinate transformation, determines the Jacobian matrix, the fields and material parameters of the cloak. However, the coordinate transformation appears as an optional function: it is not necessary to know it. We offer the solution of some sort of the inverse problem: starting from the fields in the invisibility cloak we directly derive the permittivity and permeability tensors of the cloaking shell. The approach can be useful for finding material parameters for the specified electromagnetic fields in the cl…
Electromagnetic invisibility cloak requires material with anisotropic distribution of the constitutive parameters deduced from a geometrical transformation as first proposed by Pendry et al. [Science 312, 1780 (2006)]. In this paper, we proposed a useful method to realize the required radius-dependent, anisotropic material parameters and to construct an electromagnetic cloak through concentric layered structure of thin, alternating layers of homogeneous isotropic materials. With proper design of the permittivity or the thickness ratio of the alternating layers, we demonstrated the low-reflecti…
Beginning with a straightforward formulation of electromagnetic cloaking that reduces to a boundary value problem involving a single Maxwell first-order differential equation, explicit formulae for the relative permittivity-permeability dyadic and fields of spherical and circular cylindrical annular cloaks are derived in terms of general compressed radial coordinate functions. The general formulation is based on the requirements that the cloaking occurs for all possible incident fields and that the cloaks with frequency w > 0 have continuous tangential E and H fields across their outer surface…
The concept of an invisibility cloak is a fixture of science fiction, fantasy, and the collective imagination. However, a real device that could hide an object from sight in visible light from absolutely any viewpoint would be extremely challenging to build. The main obstacle to creating such a cloak is the coupling of the electromagnetic components of light, which would necessitate the use of complex materials with specific permittivity and permeability tensors. Previous cloaking solutions have involved circumventing this obstacle by functioning either in static (or quasi-static) fields where…
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 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 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…
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 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.
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…
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 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…
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…
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…
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…
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 reveal extraordinary electromagnetic properties for a general class of uniaxially polarizable media. Depending on parameters, such metamaterials may have wide range of nontrivial shapes of isofrequency contours including lemniscate, diamond and multiply connected curves with connectivity number reaching five. The possibility of the dispersion engineering paves a way to more flexible manipulation of electromagnetic waves. Employing first-principle considerations we prove that uniaxially polarizable media should be described in terms of the nonlocal permittivity tensor which by no means can b…
