The design of metamaterial cloaks embedded in anisotropic medium

By using coordinate transformation method, this paper obtains an useful equation of designing meta-material cloaks embedded in anisotropic medium. This equation is the generalization of what was introduced early by Pendry et al (2006 \textit{Science} {312 1780) and can be more widely used. As an example of its applications, this paper deduces the material parameter equation for cylinder cloaks embedded in anisotropic medium, and then offers the numerical simulation. The results show that such a cylinder cloak has perfect cloaking performance and therefore verifies the method proposed in this paper.     

Examination of the Thermal Cloaking Effectiveness with Layered Engineering Materials

The concentrically layered thermal cloaks with isotropic materials could realize the equivalent thermal cloaking effect with Pendry's cloak,while the effectiveness is scarcely investigated quantitatively.Here we examine the cloaking effectiveness quantitatively by evaluating the standard deviation of the temperature difference between the simulated plane with the layered thermal cloak and Pendry's thermal cloak.The design rules for the isotropic materials in terms of thermal conductivity and layer thickness are presented.The present method could quantitatively evaluate the cloaking effectiveness,and could open avenues for analyzing the cloaking effect,detecting the(anti-) cloaks,etc.     

Two-Dimensional （2D） Polygonal Electromagnetic Cloaks

Transformation optics offers remarkable control over electromagnetic fields and opens an exciting gateway to design ＇invisible cloak devices＇ recently. We present an important class of two-dimensional （2D） cloaks with polygon geometries. Explicit expressions of transformed medium parameters are derived with their unique properties investigated. It is found that the elements of diagonalized permittivity tensors are always positive within an irregular polygon cloak besides one element diverges to plus infinity and the other two become zero at the inner boundary. At most positions, the principle axes of permittivity tensors do not align with position vectors. An irregular polygon cloak is designed and its invisibility to external electromagnetic waves is numerically verified. Since polygon cloaks can be tailored to resemble any objects, the transformation is finally generalized to the realization of 2D cloaks with arbitrary geometries.     

Acoustic elliptical cylindrical cloaks

By making a comparison between the acoustic equations and the 2-dimensional (2D) Maxwell equations, we obtain the material parameter equations (MPE) for acoustic elliptical cylindrical cloaks. Both the theoretical results and the numerical results indicate that an elliptical cylindrical cloak can realize perfect acoustic invisibility when the spatial distributions of mass density and bulk modulus are exactly configured according to the proposed equations. The present work is the meaningful exploration of designing acoustic cloaks that are neither sphere nor circular cylinder in shape, and opens up possibilities for making complex and multiplex acoustic cloaks with simple models such as spheres, circular or elliptic cylinders.     

Three dimensional multilayered acoustic cloak with homogeneous isotropic materials

A three-dimensional (3D) spherical acoustic cloak is designed using an acoustic layered system, which can hide an object from the detection of acoustic wave in arbitrary direction. The cloak is constructed from multilayered concentric spherical shells filled with homogeneous isotropic materials. Based on spherical wave expansion method, we confirm that significant low-reflection, acoustic-shadow-reducing, and wavefront-bending effects in 3D space can be achieved by the proposed cloak. The angle distribution of the scattered wave is further evaluated by the far-field scattering pattern. In addition, the cloak is demonstrated to work efficiently in a wide bandwidth in which the cloaking efficiency decreases with increasing frequency. This study may be helpful to design high-performance 3D acoustic cloaks for broadband acoustic waves in all incidence directions.     

Debye Series of Scattering by a Multi-Layered Cylinder in an Off-Axis 2D Gaussian Beam

The Debye series of light scattering by an infinite multi-layered cylinder in an off-axis 21） Gaussian beam is studied. A simplified but rigorous iterative formula for scattering coefficients is presented. The numerical calculations of scattering intensity by a cylinder in on-axis and off-axis beams are developed. It is indicated that the results of Debye series reach an agreement with those of generalized Lorenz-Mie theory and the off-axis distances vary the results to a great extent. The Debye series components of a two-layered cylinder are further discussed. The relations between them with rainbow phenomena are analysed.     

Super-thin cloaks mediated by spoof surface plasmons

We demonstrated the possibility of designing super-thin electromagnetic cloaks based on spoof surface plasmon (SSP). Using a metamaterial layer, incident waves can be coupled into SSP efficiently at the air/metamaterial interface. Due to the strong surface confinement of SSP, EM waves are squeezed into and propagate in deep sub-wavelength scales. Implementation of an 8.2 GHz cloak less than 1/50 the cloaking diameter was presented using split ring resonator (SRR). Excellent cloaking effect was verified by simulations. Rather than isolating objects from the background, such cloaks can drastically enhance the field intensity around the cloaked object. This is of particular importance in applications such as weak wave detection and near-field sensing.     

Acoustic cloaking by a superlens with single-negative materials

We propose a specific transformation in cloaking to make an acoustic sensor undetectable, in which the cloaking shell consists of complementary media with single-negative acoustic parameters instead of double-negative ones, and is proved to be a magnifying superlens. Moreover, the acoustical parameters of the cloak are completely independent of those of the host material as well as the cloaked object. This may significantly facilitate the experimental realization of acoustic cloaks and is of fundamental importance in a wide range of acoustics, optics, and engineering applications.     

Loss of Invisibility in Metamaterials under Thermal Fluctuation Induced Radiation

Metamaterials have been extensively investigated for the development of invisibility cloaks; however, the role of nonequilibrium thermal fluctuations in the operation of metamaterial‐based cloaking remains an unexplored avenue. Here, an analytical study on nonequilibrium thermal fluctuations induced charges and currents in metamaterials which generate electromagnetic modes is presented. It is argued that thermally induced charges in metamaterials cannot remain shielded from incoming electromagnetic radiation and excitation of such charges, by incoming electromagnetic waves, can enhance specific modes, whose radiation limits the invisibility effects associated with metamaterial‐based cloaking. The analysis leads to the conclusion that thermodynamic equilibrium is an essential condition of the invisibility of metamaterial‐based cloaking.     

Acoustic cloaking using layered pentamode materials

While receiving less attention in the literature than electromagnetic cloaking, theoretical efforts to define and create acoustic cloaks based upon mimicking coordinate transformations through use of metamaterials is of interest. The present work extends recent analysis of Norris [Proc. R. Soc. London, Ser. A 464, 2411-2434 (2008)] by considering a range of cloaks, from those comprised of fluid layers which are isotropic in bulk moduli with anisotropic density to those having anisotropic bulk moduli and isotropic density. In all but pure inertial varieties, fluid layers comprising the cloaks are pentamode materials governed by a special scalar acoustic equation for pseudopressure derived by Norris. In most cases presented, material properties of the fluid/pentamode layers are based upon target values specified by continuously varying properties resulting from theoretical coordinate transformations geared to minimize scattered pressure limited by realistic goals. The present work analyzes such cloaks for the specific case of plane wave scattering from an acoustically hard sphere. An initial exploration of the parameter space defining such cloaks (for example, material properties of its constituent layers, and operating frequency) is undertaken with a view toward "optimal" design.     

A revisit to imperfect acoustic cloak of multi-layered shell structures considering sound speed and impedance matching

An imperfect multi-layered acoustic cloak is proposed for a two-dimensional cloaking zone based on feasible material properties. In this model, the matching of sound speed and acoustic impedance has been investigated, and the effects of material and geometric properties on the imperfect cloak have been studied for better design of the imperfect cloak. The imperfect cloak could be improved using appropriate changes in the design parameters. By increasing the thickness of the high density layer and with some changes in the sound speeds between the high density and the low density layers, the imperfect cloaking model showed better cloaking performance than Cummer–Schurig cloak. Also, present results show that the sound speed matching is more important for acoustic cloaking than the impedance matching. These results can be applied as a practical design guide for two-dimensional cloaks using multilayered structures composed of naturally existing materials.     

Broadband cross-circular polarization carpet cloaking based on a phase change material metasurface in the mid-infrared region

In view of the fact that most invisibility devices focus on linear polarization cloaking and that the characteristics of mid-infrared cloaking are rarely studied, we propose a cross-circularly polarized invisibility carpet cloaking device in the mid-infrared band. Based on the Pancharatnam–Berry phase principle, the unit cells with the cross-circular polarization gradient phase were carefully designed and constructed into a metasurface. In order to achieve tunable cross-circular polarization carpet cloaks, a phase change material is introduced into the design of the unit structure. When the phase change material is in amorphous and crystalline states, the proposed metasurface unit cells can achieve high-efficiency cross-polarization conversion, and reflection intensity can be tuned. According to the phase compensation principle of carpet cloaking, we construct a metasurface cloaking device with a phase gradient using the designed unit structure. From the near- and far-field distributions, the cross-circular polarization cloaking property is confirmed in the broadband wavelength range of 9.3–11.4 µm. The proposed cloaking device can effectively resist detection of cross-circular polarization.     

Remote acoustic cloaks

Due to the correspondence of the acoustic equations to Maxwell??s equations of one polarization in two dimensions, we exploit theoretically the acoustic counterpart of the recently proposed remote invisibility cloak. The cloak consists of a circular cylindrical core with designed bulk moduli, and an ??anti-object?? embedded inside a shell with anisotropic mass densities. The material parameters of the cloaking shells are obtained by using the coordinate transformation method. The essence of the new design of cloaks relies on the ability that the cloaked object is no longer deafened by the cloaking shell, which is verified by both the far-field and near-field full-wave finite-element simulations in two dimensions.     

Mathematical Simulation of Cloaking Metamaterial Structures

In this paper we present a rigorous derivation of the material parameters for both the cylinder and rectangle cloaking structures. Numerical results using these material parameters are presented to demonstrate the cloaking effect.     

Material parameter equation for rotating elliptical spherical cloaks

By using the coordinate transformation method, we have deduced the material parameter equation for rotating elliptical spherical cloaks and carried out simulation as well. The results indicate that the rotating elliptical spherical cloaking shell, which is made of meta-materials whose permittivity and permeability are governed by the equation deduced in this paper, can achieve perfect invisibility by excluding electromagnetic fields from the internal region without disturbing any external field.     

Cancellation of acoustic scattering from an elastic sphere

Recent research has suggested the possibility of creating acoustic cloaks using metamaterial layers to eliminate the acoustic field scattered from an elastic object. This paper explores the possibility of applying the scattering cancellation cloaking technique to acoustic waves and the use of this method to investigate its effectiveness in cloaking elastic and fluid spheres using only a single isotropic elastic layer. Parametric studies showing the influence of cloak stiffness and geometry on the frequency dependent scattering cross-section of spheres have been developed to explore the design space of the cloaking layer. This analysis shows that an appropriately designed single isotropic elastic cloaking layer can provide up to 30 dB of scattering reduction for ka values up to 1.6. This work also illustrates the importance of accounting for the elasticity of the object and the relevant limitations of simplistic quasi-static analyses proposed in recent papers.     

Cloaks,editors, and bubbles: applications of spacetime transformation theory

Spacetime or ‘event’ cloaking was recently introduced as a concept, and the theoretical design for such a cloak was presented for illumination by electromagnetic waves [McCall et al., J. Opt. 2011]. Here it is described how event cloaks can be designed for simple wave systems, using either an approximate ‘speed cloak’ method, or an exact full‐wave one. Further, details of many of the implications of spacetime transformation devices are discussed, including their (usually) directional nature, spacetime distortions (as opposed to cloaks), and how leaky cloaks manifest themselves. More exotic concepts are also addressed, in particular concepts that follow naturally on from considerations of simple spacetime transformation devices, such as spacetime modeling and causality editors. A proposal for implementing an interrupt‐without‐interrupt concept is described. Finally, the design for a time‐dependent ‘bubbleverse’ is presented, based on temporally modulated Maxwell's Fisheye transformation device (T‐device) in a flat background spacetime.     

While rotating while cloaking

Invisible optical and thermal cloaking have been explored as the typical demonstrations of the transformation optics and thermotics theory. However, the existing cloaks are realized by only one-coordinate transformation, and the cloaking layout, i.e. the form of electromagnetic wave/heat passing around the invisible region, is single for a long time. Here, we propose a new rotated thermal cloak which can unify the conventional cloaking and rotating together, and realize the while-rotating–while-cloaking effect. The required anisotropic thermal conductivity tensor is deduced from the new geometric mapping. Though rotated, the heat flux can be tuned around the central invisible region perfectly by the proposed rotated thermal cloak. The underlying physics is explored by comprehensive analysis of the distribution of the thermal conductivity tensor, which is further compared with those of the conventional cloak and rotator. The experimental feasibility is also discussed by validating the practical while-rotating–while-cloaking effect through a proof-of-concept design. The proposed rotated thermal cloak is expected to extend the possibility of cloaking scheme, and open avenues for the multiple coordinate transformation in counterpart physical fields, like optics, electrics, acoustics, magnetics, mechanics, etc.     

Physical bounds on electromagnetic invisibility and the potential of superconducting cloaks

The possibility of suppressing the scattering cross section of an object is subject to fundamental physical bounds imposed by causality and passivity. Global cloaking limitations have been recently derived, which imply that any linear, causal and passive cloak necessarily increases the global scattering, integrated over the whole electromagnetic spectrum, compared to the uncloaked object. Here, we expand on this topic, discussing in detail an interesting exception to this limit represented by cloaks with static diamagnetism. In this context, we explore the potential of superconducting materials to realize global and local reduction of the scattering cross section. The concepts of plasmonic and mantle cloaking are extended to superconductors, realizing strong and tunable invisibility, with some unique properties stemming from the peculiar electrodynamics of superconductors. We conclude by qualitatively discussing a possible method to derive more stringent local bounds on cloaking.     

Finite elements modelling of scattering problems for flexural waves in thin plates: Application to elliptic invisibility cloaks,rotators and the mirage effect

We propose a finite elements algorithm to solve a fourth order partial differential equation governing the propagation of time-harmonic bending waves in thin elastic plates. Specially designed perfectly matched layers are implemented to deal with the infinite extent of the plates. These are deduced from a geometric transform in the biharmonic equation. To numerically illustrate the power of elastodynamic transformations, we analyze the elastic response of an elliptic invisibility cloak surrounding a clamped obstacle in the presence of a cylindrical excitation i.e. a concentrated point force. Elliptic cloaking for flexural waves involves a density and an orthotropic Young’s modulus which depend on the radial and azimuthal positions, as deduced from a coordinates transformation for circular cloaks in the spirit of Pendry et al. [Science 312, 1780 (2006)], but with a further stretch of a coordinate axis. We find that a wave radiated by a concentrated point force located a couple of wavelengths away from the cloak is almost unperturbed in magnitude and in phase. However, when the point force lies within the coating, it seems to radiate from a shifted location. Finally, we emphasize the versatility of transformation elastodynamics with the design of an elliptic cloak which rotates the wavevector of a flexural wave within its core.