Ideal Cloak Research Articles

Bandwidth evaluation of dispersive transformation electromagnetics based devices

In this paper, the transient responses of some devices which are based on transformation electromagnetics are studied, such as invisible cloaks and concentrators, by using the Finite-Difference Time-Domain (FDTD) numerical technique. In particular, effects of the inherent losses as well as the coating size of the ideal cylindrical cloak on its bandwidth and cloaking performance are examined. In addition, it is demonstrated that the performance of transformation electromagnetics based devices is affected by the material parameters in the design, although they may behave nicely under monochromatic plane wave illuminations. The obtained results are of interest for the future practical implementation of these structures.

Dynamic study and applications of metamaterial systems

We investigate the dynamic characteristics of metamaterial systems, such as the temporal coherence gain of the superlens, the causality limitation on the ideal cloaking systems, the relaxation process and essential elements in the dispersive cloaking systems, and the extending of the working frequency range of cloaking systems. The key point of our study is the physical dispersive properties of metamaterials, which are well-known to be intrinsically strongly dispersive. With physical dispersion, new physical pictures can be obtained for the waves propagating inside metamaterial, such as the “group retarded time” for waves inside the superlens and cloak, the causality limitation on real metamaterial systems, and the essential elements for design optimization. Therefore, we believe the dynamic study of metamaterials will be an important direction for further research. All theoretical derivations and conclusions are demonstrated by powerful finite-difference time-domain simulations.

Isotropic non-ideal cloaks providing improved invisibility by adaptive segmentation and optimal refractive index profile from ordering isotropic materials

Mimicking the ideal cloak, which is anisotropic and inhomogeneous, can be achieved by alternating homogeneous isotropic materials, whose permittivity and permeability of each isotropic coating can be determined from effective medium theory. An improved two-fold method is proposed by optimally discretizing the cloak and re-ordering the combination of the effective parameters of each layer to form a smooth step-index profile. The roles of impedance matching and index matching are investigated for cloaking effects. Smoothing the index profile leads to better invisibility than that obtained by smoothing the impedance profile, since the forward scattering can be further diminished. Nonlinear-transformationbased spherical ideal cloaks are studied, and improved design method is explored together with different segmentation schemes. Significant improvement in invisibility is always observed for the optimal segmentation in virtual space with the proposed two-fold design method no matter how nonlinear the coordinate transformation is.

Minimizing the scattering of a nonmagnetic cloak

Nonmagnetic cloak offers a feasible way to achieve invisibility at optical frequencies using materials with only electric responses. In this letter, we suggest an approximation of the ideal nonmagnetic cloak and quantitatively study its electromagnetic characteristics using a full-wave scattering theory. It is demonstrated that the forward scattering of the impedance matched cloak increases dramatically as the thickness of the cloak decreases. Nevertheless, it is still possible to effectively reduce the total scattering cross section with a very thin cloak whose impedance is not matched to the surrounding material at the outer boundary. Our analysis also provides the flexibility of reducing the scattering in an arbitrary direction.

Cloaking a metal object from an electromagnetic pulse: A comparison between various cloaking techniques

Electromagnetic cloaks are devices that can be used to reduce the total scattering cross section of various objects. An ideal cloak removes all scattering from an object and thus makes this object “invisible” to the electromagnetic fields that impinge on the object. However, ideal cloaking appears to be possible only at a single frequency. To study cloaking from an electromagnetic pulse, we consider propagation of a pulse inside a waveguide with a cloaked metal object inside. There are several ways to achieve cloaking, and in this paper, we study three such methods, namely, the coordinate-transformation cloak, the transmission-line cloak, and the metal-plate cloak. In the case of the two last cloaks, pulse propagation is studied using experimental data, whereas the coordinate-transformation cloak is studied with numerical simulations. The results show that, at least in the studied cases where the cloaked object’s diameter is smaller than the wavelength, the cloaks based on transmission-line meshes and metal plates have wider bandwidth than the coordinate-transformation cloak and are thus more efficient in hiding objects from electromagnetic pulses.

Electromagnetic Detection of a Perfect Invisibility Cloak

A perfect invisibility cloak is commonly believed to be undetectable from electromagnetic (EM) detection because it is equivalent to a curved but empty EM space created from coordinate transformation. Based on the intrinsic asymmetry of coordinate transformation applied to motions of photons and charges, we propose a method to detect this curved EM space by shooting a fast-moving charged particle through it. A broadband radiation generated in this process makes a cloak visible. Our method is the only known EM mechanism so far to detect an ideal perfect cloak (curved EM space) within its working band.

A Rigorous Analysis of Plane-Transformed Invisibility Cloaks

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 still be achieved along the direction parallel to the major axis of the cloak for transverse magnetic illumination. Another plane-transformed cloak with a conical geometry is also proposed. The advantage of this cloak is that all the permittivity and permeability elements are spatially invariant while none of them is singular. Hence, it is easily realizable with artificially structured metamaterials. Finally, we show that this kind of cloak can also be used to cloak objects on a flat ground plane.

Importance of the singular constitutive parameters of cylindrical cloaks: illustration on the anticloak concept

Two-dimensional electromagnetic cloaking devices with infinite optic constants at the inner boundary are investigated. Numerical simulations of this class of ideal cloak, performed with the transmission line modeling method, confirm the fundamental importance of such extreme values in the efficiency of the cloak in some situations. This is illustrated by using the concept of the anticloak, which was shown to be capable of defeating the non-ideal cloak. We numerically show that the presence of a layer with extreme constitutive parameters renders the anticloak unable to produce its effect. Furthermore, we propose a simple theoretical model that leads to the same conclusion if the cloak is slightly dissipative.

General transformation for the reduced invisibility cloak

We present a generalized perspective for ``reduced'' invisibility cloaks, which formulates a general way to ``reduce'' the cloak so that it can be realized more easily. We show explicitly that several published reduced cloak designs are in fact special cases of a more general transformation. Furthermore, we showed that a cylindrical reduced cloak is linked to a cylindrical isotropic inhomogeneous object by exactly the coordinate transformation that one applies on an ideal cloak. This perspective also suggests an alternative but easier way to calculate the scattering properties of the reduced cloaks.

Lorentz force and radiation pressure on a spherical cloak

The mechanical behavior of a transformation based spherical cloak under wave illumination is derived. We show that the equatorial region of the cloak is subject to much higher stress than the polar regions, where the polar axis is defined along the wave propagation direction. These forces do not exist before transformation but stem from the squeezed electromagnetic space. The trajectory of the ray can be interpreted as a result of the recoil force that the cloak exerts upon the ray. The total radiation pressure on an ideal cloak is shown to be exactly zero, effecting a stationary cloak. It is well known that electromagnetic waves carry both momentum and energy 1,2. When light impinges onto a dielectric particle, part of the optical momentum will transfer to it 3‐6, and the radiation pressure will accelerate the particle. That is the reason why we can see the comet’s tail, which results from the radiation pressure of the sunlight pushing particles of the tail away from the comet. The recently proposed invisibility cloak 7‐9, which neither absorbs nor reflects light, will be immune to the light radiation pressure. The idea of cloak has been proposed based on the coordinate transformation method, where a hole is created in the transformed space and an object in the hole can be concealed from detection 7‐9. Compared with the cloak design based on other approaches, such as the scattering cancellation method 10‐12, the anti-object method 13, and the dipole moment cancellation method using anomalous localized resonance 14,15 etc., the transformation based design has advantages that it does not depend on the parameters of the hidden object. The ray tracing method 7,16 and the full wave method 17‐22 have both shown that light can be smoothly guided around the transformation based cloak. Such interesting phenomena have been experimentally demonstrated by a two-dimensional cylindrical cloak with simplified parameters 23, a ground-plane cloak 24,25, and dielectric optical cloaks 26,27. The reason that the rays are guided around the invisibility cloak can be interpreted as a result of the bending of electromagnetic space, which is always associated with some force appearance, such that the gravity is the appearance of the bent time and space. Therefore, a bent electromagnetic space must exhibit certain force properties and affect the mechanical behavior of light in physical space. Such mechanical behavior is a very fundamental physical problem associated with the transformed invisibility cloak but has not been revealed. In this Rapid Communication, the mechanical behavior of a general transformation based spherical cloak under planewave illumination is revealed based on Lorentz force, which links the Maxwell equations to mechanics in the theory of electromagnetics. We show that the equatorial region of the cloak is subject to much higher stress than the polar regions, where the polar axis is defined along the wave propagation direction. These forces do not exist before transformation but stem from the squeezed electromagnetic space and are one of the ways that it appears in physical space. In addition, the force distribution exhibits a symmetric pattern in the cross section perpendicular to the wave propagation direction, therefore the total radiation pressure on an ideal cloak is exactly zero. The trajectory of the ray inside of the cloak can be interpreted vividly as a result of the recoil force that the cloak exerts upon the ray. The three-dimensional spherical cloak we consider here has an inner radius R1 and outer radius R2. The cloak shell within R1rR2 is a radially uniaxial and inhomogeneous

Cloaking radiation of moving electron beam and relativistic energy loss spectra

The interaction of ideal and nonideal metamaterial cylindrical cloaks with an electron beam has been studied. The exact solution for energy loss suffered by a fast electron moving inside or outside a cylindrical cloak has been established within a fully relativistic approach. The effect of various imperfect parameters on the efficiency of the cloak has been discussed. It is shown that radiation can be shielded very well by such cloaks when an electron moves either inside or outside of them. The efficiency of nonideal cloaks and the effect of various nonideal parameters on cloak invisibility can be exhibited in the spectra of electron energy loss and radiation emission. This means that the property of a cylindrical cloak can be explored by means of scanning transmission electron microscopy.

Improvement of Cylindrical Cloak by Layered Structure of Homogeneous Isotropic Materials

The perfect cylindrical cloak requires three spatial variant material parameters, which is very difficult to realize in practice [Science 312, 1780 (2006)]. The approach of realizing the electromagnetic cloaking by concentric layered structures instead of using the metamaterial was presented [Optics Express, Vol. 15, No. 18 (2007)]. We use the concentric layered structures to realize a simplified cylindrical cloak with improved parameters and an ideal cylindrical cloak with spatially invariant axial material parameters. Numerical simulation results validate that cloaking performance is significantly improved compared with previously proposed multilayered cloak.

Extraordinary Resonant Scattering in Imperfect Acoustic Cloak

We present a systematic study on the extraordinary resonant scattering in imperfect acoustic cloak by means of acoustic scattering theory. Analysis results demonstrate that the resonances are inevitable due to the perturbation to the ideal cloak, and specific resonance modes are excited by specific order waves. The strength of resonance is determined by the magnitude of perturbation and each order wave's sensitivity to the perturbation. Further studies reveal the unique scattering characters of different resonance modes.

Ideal and nonideal invisibility cloaks

We employ the analytical solutions for the spatial transformation of the electromagnetic fields to obtain and analyze explicit expressions for the structure of the electromagnetic fields in invisibility cloaks. Similar approach can be also used for analyzing beam splitters and field concentrators. We study the efficiency of nonideal electromagnetic cloaks and discuss the effect of scattering losses on the cloak invisibility.

Approximate Quantum Cloaking and Almost-Trapped States

We describe potentials which act as approximate cloaks for matter waves. These potentials are derived from ideal cloaks for the conductivity and Helmholtz equations. At most energies E, if a potential is surrounded by an approximate cloak, then it becomes almost undetectable and unaltered by matter waves originating externally to the cloak. For certain E, however, the approximate cloaks are resonant, supporting wave functions almost trapped inside the cloaked region and negligible outside. Applications include dc or magnetically tunable ion traps and beam switches.

Isotropic transformation optics: approximate acoustic and quantum cloaking

Transformation optics constructions have allowed the design of electromagnetic, acoustic and quantum parameters that steer waves around a region without penetrating it, so that the region is hidden from external observations. The material parameters are anisotropic, and singular at the interface between the cloaked and uncloaked regions, making physical realization a challenge. We address this problem by showing how to construct isotropic and nonsingular parameters that give approximate cloaking to any desired degree of accuracy for electrostatic, acoustic and quantum waves. The techniques used here may be applicable to a wider range of transformation optics designs. For the Helmholtz equation, cloaking is possible outside a discrete set of frequencies or energies, namely the Neumann eigenvalues of the cloaked region. At these frequencies or energies the ideal cloak supports trapped states, vanishing outside of the cloaked region; near these energies, an approximate cloak supports almost trapped states. This is in fact a useful feature, and we conclude by giving several quantum mechanical applications.

Controlling the transmitted field into a cylindrical cloak's hidden region

Constitutive parameters for simplified cylindrical cloaks have been developed such that epsilon(z)micro(theta) and epsilon(z)micro(r) match those of the ideal cylindrical cloak. Although they are not perfect, simplified cylindrical cloaks have been shown to inherit many of the power-bending properties of the ideal cloak. However, energy is transmitted into simplified cloaks hidden regions. Here, we develop a constraint equation that can be used to determine how closely field behavior within the simplified cylindrical cloak matches that of the ideal cloak. The deviation from this controlling equation can be reduced by controlling the cloaks parameter value, microtheta. As the deviation from our constraint equation is decreased, the field transmitted into the cloaks hidden region is reduced, resulting in less energy impinging on the cloaked object. This results in a smaller scattered field due to the presence of the cloaked object. However, the resulting impedance mismatch at r = b results in a significant scattered field by the cloak itself. Thus, we have found when using cylindrical cloaks that satisfy the ideal values of epsilon (z)micro(theta)and epsilon(z)micro(r) for scattering width reduction, it is more important to have a matched impedance at r = b than to have a smaller field transmitted into the cloaks hidden region. However, such cloaks scattering widths can vary significantly as a function of the object in the hidden region. A cloak with a matched impedance at r = b and that satisfies specific values for epsilon(z)micro(theta) and micro'theta performs reasonably well in terms of scattering width reduction in certain angular regions while being independent of the object in the hidden region.

Electromagnetic interactions between a fast electron beam and metamaterial cloaks

Relativistic energy loss and photon emission in the interaction of ideal and nonideal metamaterial cloaks with an external electron beam are studied based on the classical electrodynamics. The effects of various imperfect parameters on the efficiency of the cloak are emphasized. The energy-loss spectra and the photon emission for such structures with the different combinations of electron velocity and impact parameter are calculated. It is shown that the efficiency of nonideal electromagnetic cloaks and the effect of various nonideal parameters on the cloak invisibility can be exhibited in the electron energy loss spectroscopy. This means that the properties of cloak can be explored by scanning transmission electron microscopy.

The effect of transformation order on the invisibility performance of a practical cylindrical cloak

A class of polynomial coordinate transformation functions with an arbitrary order number is used to design cylindrical invisibility cloaks. Since an ideal cylindrical cloak is inevitably unphysical at its inner boundary, our investigation involves the replacement of a thin layer of material at the cloak's inner surface by a homogeneous material layer. This approach effectively avoids the infinities in the material parameters, and at the same time produces practical near-ideal invisibility cloaks. The cloaks obtained are perfectly matched in impedance at the outer boundary. We quantitatively show the effect of the transformation order on the proposed cloak's scattering coefficients.

Time delays and energy transport velocities in three dimensional ideal cloaking devices

We obtain the energy transport velocity distribution for a three dimensional ideal cloak explicitly. Near the operation frequency, the energy transport velocity has a rather peculiar distribution. The transport velocity along the direction pointing at the center of the cloak is found to be a constant, while the transport velocity approaches zero at the inner boundary of the cloak. A ray pointing right into the center of the cloak will experience abrupt changes in velocities when it impinges on the inner surface of the cloak. This peculiar distribution causes long time delays for beams passing through the ideal cloak within a geometric optics description.