Cylindrical Cloak Research Articles

Two-dimensional cylindrical thermal cloak designed by implicit transformation method

As a new-type technology of heat management, thermal metamaterials have attracted more and more attentions recently and thermal cloak is a typical case. Thermal conductivity of thermal cloak designed by coordinate transformation method is usually featured by inhomogeneity, anisotropy and local singularity. Explicit transformation method, which is commonly used to design thermal cloak with the coordinate transformation known in advance, has insufficient flexibility, making it hard to proactively reduce the difficulty of device fabrication. In this work, we designed the thermal conductivity of two-dimensional (2D) cylindrical thermal cloak using the implicit transformation method without knowledge of the coordinate transformation in advance. With two classes of generation functions taken into consideration, this study adopted full-wave simulations to analyze the thermal cloaking performances of designed thermal cloaks. Material distributions and simulation results showed that the implicit transformation method has high flexibility. The form of coordinate transformation not only influences the homogeneity and anisotropy but also directly influences the thermal cloaking performance. An improved layered structure for 2D cylindrical thermal cloak was put forward based on the generation function g ( r ) = r 15 , which reduces the number of the kinds of constituent materials while guaranteeing good thermal cloaking performance. This work provides a beneficial guidance for reducing the fabrication difficulty of thermal cloak.

Optimization of multilayer cylindrical cloaks using genetic algorithms and NEWUOA

The problem of minimizing the scattering from a multilayer cylindrical cloak is studied. Both TM and TE polarizations are considered. A two-stage optimization procedure using genetic algorithms and NEWUOA (new unconstrained optimization algorithm) is adopted for realizing the cloak using homogeneous isotropic layers. The layers are arranged such that they follow a repeated pattern of alternating DPS and DNG materials. The results show that a good level of invisibility can be realized using a reasonable number of layers. Maintaining the cloak performance over a finite range of frequencies without sacrificing the level of invisibility is achieved.

Scattering reduction of an acoustically hard cylinder covered with layered pentamode metamaterials.

Transformational acoustics offers the theoretical possibility of cloaking obstacles within fluids, provided metamaterials having continuously varying bulk moduli and densities can be found or constructed. Realistically, materials with the proper, continuously varying anisotropies do not presently exist. However, discretely layered cloaks having constant material parameters within each layer may be a viable alternative in practice. The present work considers a range of cloaks, from those comprised of fluid layers that are isotropic in bulk moduli with anisotropic density (inertial cloaks) to those having anisotropic bulk moduli and isotropic density (pentamode cloaks). In this paper an analytical solution is obtained for the case of plane wave scattering from a submerged rigid cylinder covered with a multilayered cylindrical cloak composed of discrete anisotropic fluid layers. An investigation of the parameter space defining such cloaks is undertaken with the goal of minimizing the far-field scattered pressure, using layer constituent anisotropic properties (density and bulk modulus) constrained to lie within reasonable ranges relative to those of water.

Influence of nonlinear coordinate transformation on thermal cloaking performances of multilayered cylindrical thermal cloaks

Layered discretization is an efficient way of realizing thermal cloaks. The aim of this paper is to investigate the effect of nonlinear coordinate transformation on the thermal cloaking performance of multilayered cylindrical thermal cloak. Two indexes are defined to quantify the thermal cloaking performance. Nonlinear coordinate transformations with different forms are established to design the multilayered structures and the thermal cloaking performances are analyzed by full-wave simulations. The results show that the thermal cloaking performances of multilayered structures are directly influenced by the form of coordinate transformation which determines the distributions of heat flows in the cloak region. Through the active changing of the form of coordinate transformation, the thermal cloaking performance of multilayered structure can be controlled and optimized. In addition, a three-piecewise linear coordinate transformation is designed to concentrate the heat flux into the middle region of the cloak and the corresponding multilayered structure is demonstrated to have near-perfect thermal cloaking performance. These results may provide a beneficial guidance to achieve performance improvements for multilayered structures of thermal cloaks.

The refractive index of reciprocal electromagnetic media

We study the electromagnetics of media described by identical inhomogeneous relative dielectric and magnetic tensors, Such media occur generically as spatial transformation media, i.e. electromagnetic media that are defined by a deformation of space. We show that such media are completely described by a refractive index that depends on position and direction but is independent of polarization. The phase surface is always ellipsoidal, and is therefore represented by the radius vector to the surface of the ellipsoid. We apply our method to calculate the angular dependence of the refractive index in the well-studied cylindrical cloak and to a new kind of structurally chiral medium induced by a twist deformation. By way of a simple example we also show that media for which do not in general preserve the impedance properties of vacuum. The implications of this somewhat surprising conclusion for the field of transformation optics are discussed.

Superluminal media formed by photonic crystals for transformation optics-based invisibility cloaks

We have developed an approach to building superluminal medium for transformation optics‐based devices, including invisibility cloaks, from photonic crystals. Analysis of dispersion diagrams of 2D arrays composed from dielectric rods has shown that at frequencies corresponding to the second bands formed due to bandgap opening at increase of rod permittivity, the medium formed by arrays exhibits refractive indices providing for superluminal phase velocities of propagating waves. It is further demonstrated that rod arrays with various lattice constants could be used for realizing a range of superluminal index values prescribed by transformation optics for cylindrical cloaks at arbitrary chosen operating frequency. The performed studies allowed for solving a row of problems with employment rod arrays in the cloak medium: in particular, formulating transformation optics‐based prescriptions for refractive index dispersion in the cloaking shell, defining the dimensions of array fragments capable of responding similar to infinite arrays, finding optimal distribution of linear arrays sets at their coiling to form concentric material layers in the cloaking shell, and employing interaction between neighboring array sets with various lattice constants to assist the realization of prescribed index dispersion. The performance of the superluminal medium formed by rod array sets was demonstrated on an example of a cloaking shell developed for microwave frequency range. In contrast to metamaterial-based cloak media, the developed media requires neither material homogenization, nor obtaining the effective parameters with peculiar values and Lorentz’s type resonances in rods. Combination of these advantages and low losses makes photonic crystals perspective materials for invisibility cloaks operating in THz and optical ranges.

2D Electromagnetic Wave Scattering Problem for Cylindrical Cloak Incorporating PEMC-Layer

The 2D scattering problem is studied for the case of a two-dimensional cylindrical invisibility cloak, incorporating a tiny layer of perfect electromagnetic conductor (PEMC). The solution of the corresponding Helmholtz equation with variable coefficients is seeked as cylindrical functions Fourier series. The coefficients of these series are determined by solving the system of four linear algebraic equations with respect to four unknown coefficients with badly-conditioned matrix. The Singular Value Decomposition (SVD) method is applied for solving the system. Based on this idea the efficient numerical method is developed for solving the cloaking problem under study. The properties of this algorithm are studied and some results of numerical experiments are discussed.

The effect of coordinate transformation function on scattering characteristics of cylindrical cloaks with a quantity of discrete layers

We studied the electromagnetic scattering from cylindrical cloaks with a quantity of discrete homogeneous layers. The scattering cross sections (SCS) of electromagnetic cloaks designed by different coordinate transformation function are discussed by using a polynomial transform function. The results show that besides the inner boundary, the interfaces between the adjacent discrete anisotropic layers inside the cloak also affect its performance. Through the proper design of the coordinate transformation order, the electromagnetic field distribution insides the cloak can be optimized and the invisible performance of the cloak could be improved with minimization of SCS. These results provide a better way of designing the cloak to achieve low scattering with only a few layers of anisotropic metamaterials.

Full wave finite-difference time-domain study of lossless acoustic bipolar cylindrical cloak with compressed geometry and complementary media

Full-wave finite-difference time-domain analysis of a lossless acoustic cloak with complementary media is studied for bipolar cylindrical geometry. The material parameters for the acoustic cloak are obtained by comparing two-dimensional Maxwell's equations in the transverse magnetic polarization and acoustic field equations for general curvilinear coordinates. The permittivity and permeability tensors for the corresponding electromagnetic fields are then obtained by using an effective medium approach in general relativity. The complementary media cancels the phase vectors across the boundaries of the illuminated acoustic waves. It is shown that for the lossless cloak the broadband and illumination direction independent cloaking can be achieved with the proposed structure.

Molding acoustic, electromagnetic and water waves with a single cloak

We describe two experiments demonstrating that a cylindrical cloak formerly introduced for linear surface liquid waves works equally well for sound and electromagnetic waves. This structured cloak behaves like an acoustic cloak with an effective anisotropic density and an electromagnetic cloak with an effective anisotropic permittivity, respectively. Measured forward scattering for pressure and magnetic fields are in good agreement and provide first evidence of broadband cloaking. Microwave experiments and 3D electromagnetic wave simulations further confirm reduced forward and backscattering when a rectangular metallic obstacle is surrounded by the structured cloak for cloaking frequencies between 2.6 and 7.0 GHz. This suggests, as supported by 2D finite element simulations, sound waves are cloaked between 3 and 8 KHz and linear surface liquid waves between 5 and 16 Hz. Moreover, microwave experiments show the field is reduced by 10 to 30 dB inside the invisibility region, which suggests the multi-wave cloak could be used as a protection against water, sonic or microwaves.

Electromagnetic detection of a perfect carpet cloak.

It has been shown that a spherical invisibility cloak originally proposed by Pendry et al. can be electromagnetically detected by shooting a charged particle through it, whose underlying mechanism stems from the asymmetry of transformation optics applied to motions of photons and charges [PRL 103, 243901 (2009)]. However, the conceptual three-dimensional invisibility cloak that exactly follows specifications of transformation optics is formidably difficult to implement, while the simplified cylindrical cloak that has been experimentally realized is inherently visible. On the other hand, the recent carpet cloak model has acquired remarkable experimental development, including a recently demonstrated full-parameter carpet cloak without any approximation in the required constitutive parameters. In this paper, we numerically investigate the electromagnetic radiation from a charged particle passing through a perfect carpet cloak and propose an experimentally verifiable model to demonstrate symmetry breaking of transformation optics.

Manipulation of the propagation of out-of-plane shear waves

For a given elastic medium, there is a one-to-one correspondence relation between material properties (elastic moduli and density) and the propagation path of elastic waves. Based on this idea, we propose a new method for designing a cylindrical cloak invisible to out-of-plane shear waves. We begin by writing the Hamiltonian governing the path trajectory of out-of-plane shear waves in an inhomogeneous orthotropic medium. Based on Hamilton’s equations of motion, we derive the ray equation for out-of-plane shear waves and the differential equation that describes the optimal spatial distribution of material properties in the cylindrical cloak. To solve these two differential equations, two boundary conditions are imposed in terms of the continuity conditions of displacement and traction on the outer boundary of the cylindrical cloak. The two differential equations and two boundary conditions constitute a solvable system from which various cloak profiles can be designed. The proposed approach, which differs from the transformation optics approach, provides an intuitive and flexible design platform and allows considerable freedom to construct invisibility cloaks with a specific spatial distribution of material properties. The effects of the material properties and boundary conditions on cloak invisibility are analyzed in detail. Numerical simulations show that optimized cylindrical cloaks with finite material properties can be easily constructed.

Accurate Simulation of Circular and Elliptic Cylindrical Invisibility Cloaks

AbstractThe coordinate transformation offers a remarkable way to design cloaks that can steer electromagnetic fields so as to prevent waves from penetrating into thecloaked region(denoted by Ω0, where the objects inside are invisible to observers outside). The ideal circular and elliptic cylindrical cloaked regions are blown up from a point and a line segment, respectively so the transformed material parameters and the corresponding coefficients of the resulted equations are highly singular at the cloaking boundary ∂Ω0. The electric field or magnetic field is not continuous across ∂Ω0. The imposition of appropriatecloaking boundary conditions(CBCs) to achieve perfect concealment is a crucial but challenging issue.Based upon the principle that a well-behaved electromagnetic field in the original space must be well-behaved in the transformed space as well, we obtain CBCs that intrinsically relate to the essential “pole” conditions of a singular transformation. We also find that for the elliptic cylindrical cloak, the CBCs should be imposed differently for the cosine-elliptic and sine-elliptic components of the decomposed fields. With these at our disposal, we can rigorously show that the governing equation in Ω0can be decoupled from the exterior region, and the total fields in the cloaked region vanish under mild conditions. We emphasize that our proposal of CBCs is different from any existing ones.Using the exact circular (resp., elliptic) Dirichlet-to-Neumann (DtN) non-reflecting boundary conditions to reduce the unbounded domainto a bounded domain, we introduce an accurate and efficient Fourier-Legendre spectral-element method (FLSEM) (resp., Mathieu-Legendre spectral-element method (MLSEM)) to simulate the circular cylindrical cloak (resp., elliptic cylindrical cloak). We provide ample numerical results to demonstrate that the perfect concealment of waves can be achieved for the ideal circular/elliptic cylindrical cloaks under our proposed CBCs and accurate numerical solvers.

Cylindrical Thermal Cloak Based on the Path Design of Heat Flux

When heat flux flows in a given medium, its path will solely be determined. This implies that material parameters determined by the predesigned path of heat flux will guide heat to flow along the designed path. Based on this idea, we develop a new method for the design of the cylindrical thermal cloak which can make heat flux detour the cloaked object. For the inhomogeneous anisotropic medium, we derive the relation between the path trajectory of heat flux and material parameters and obtain two differential equations and one boundary condition which are used to determine material parameters in the cylindrical cloak. The transient behavior on the flow of heat flux is simulated by Comsol Multiphysics and the transient thermal protection of the cylindrical cloak for the cloaked object is examined. The effect of the product of density and specific heat on the dynamic diffusion process of heat flux is analyzed. Since one can flexibly design the path of heat flux in the cloak, it has the large degree of freedom to construct thermal cloaks with the specific distributions of material parameters. The present method provides a new blue print for the transient thermal protection of a specific target.

Acoustic cloak constructed with thin-plate metamaterials

We propose a strategy for designing the cylindrical acoustic cloak with thin-plate metamaterials. The inhomogeneous cloaking shell as derived by transformation acoustics is first discretized into a three-layer anisotropic metafluid, and their material parameters are optimized by minimizing the external scatterings. Then these metafluids are practically realized by thin-plate structures according to the metamaterial concept. As an example, an acoustic cloak is designed with nine layers of thin plate and totally 900 plate units. Numerical simulations are performed to assess the cloaking performance of the designed structure.

Theoretical and numerical analysis of layered cylindrical pentamode acoustic cloak

As a newly-developed method, acoustic cloak made of pentamode materials is on its speedway to the promising potential application. However, physical fabrication of pentamode cloak with continuously varying material parameters can be a tough work, if not totally impossible. Layering is a natural compromise to bypass this quandary. Researches on layering effects of inertial cloak are ample. However, researches on layering pentamode acoustic cloak are relatively limited. Among these researches Scandrett extends the effective bandwidth through optimization of material parameters[2010 J. Acoust. Soc. Am. 127 2856, 2011 Wave Motion. 48 505].#br#The present work concerns the layering effects of pentamode acoustic cloak. By comparing with precedent results, the present paper has two major innovations: Firstly, cylinder is chosen to be the basic geometry. This is of obvious advantage since cylinder is the basic geometry of acoustic cloak's important potential host. Secondly, effects of layers' number and thickness distribution on the stealth effect are analyzed. The two are key parameters to be determined in the layering process. This paper is organized as follows: Firstly, analytical expression of the scattering pressure field of layered cloak is deduced by means of variables separation. In this process Fourier expansion plays a key role. And the harmonic assumption of the incident acoustic wave is made. Secondly, typical cases are calculated to verify the validation of the theoretical analysis. First let material parameters tend towards that of water, and compare the scattering field with that of the bare rigid object when the cloak is replaced by water. Second let the layering number goes to infinity, and compare the scattering field with that of the continuous cloak. Phenomena conforming with basic physical laws are observed. And validity of the theory and codes is confirmed. Thirdly, effects of layers' number and thickness distribution on the stealth character are theoretically and numerically analyzed. One can easily see from the computational results that a critical number N exists. When layers' number exceeds N, improvement of the stealth effect becomes less efficient by further adding layers' number. One can also see from the computational results that a wise distributional strategy that helps improve the stealth effect indeed exists. And the optimization iteration can be utilized to further improve it.#br#As a summary, the present paper concerns the layering process of cloaking. Qualitatively and quantitatively, several significant results are obtained. This paper offers a useful reference for future fabrication of realistic acoustic pentamode cloak.

Design of Cylindrical Metamaterial Invisible Cloak with Non-Singular Electromagnetic Tensors

Based on line transformation, cylindrical metamaterial invisible cloak with non-singular electromagnetic tensors is designed. The results of simulation software based on finite element methods (FEM) show that the singularity in the electromagnetic tensors of the cloak has been eliminated, comparing with the cylindrical cloak with ideal tensors. From the simulation results, although there is electromagnetic perturbation in the free-space of the solution region, this cloak exhibits nice electromagnetic invisible performance. The bending wave front is clearly seen when the incoming wave transmits into the cloak region. Because of the non-singular electromagnetic tensors, the designed cloak may have more engineering application than the cloak with idea tensors.

Morphing for faster computations in transformation optics

We propose to use morphing algorithms to deduce some approximate wave pictures of scattering by cylindrical invisibility cloaks of various shapes deduced from the exact computation (e.g. using a finite element method) of scattering by cloaks of two given shapes, say circular and elliptic ones, thereafter called the source and destination images. The error in L(2) norm between the exact and approximate solutions deduced via morphing from the source and destination images is typically less than 2 percent if control points are judiciously chosen. Our approach works equally well for rotators and concentrators, and also unveils some device which we call rotacon since it both rotates and concentrates electromagnetic fields. However, it breaks down for superscatterers (deduced from non-monotonic transforms): the error in L(2) norm is about 25 percent. We stress that our approach might greatly accelerate numerical studies of 2D and 3D cloaks.

Well-posedness study and finite element simulation of time-domain cylindrical and elliptical cloaks

Well-posedness study and finite element simulation of time-domain cylindrical and elliptical cloaks

Bicephalous transformed media: concentrator versus rotator and cloak versus superscatterer.

Transformational optics allows for unprecedented control of light with cylindrical cloaks, concentrators, rotators and superscatterers. These are made of different heterogeneous anisotropic media. Can one cloak an s-polarized field and concentrate (or rotate) a p-polarized field with the same metamaterial (or vice versa)? We show the answer is positive provided the geometric transforms underpinning these functionalities take the same values on the outer boundary of what we call a bicephalous metamaterial. In this way, one can also make a metallic cylinder appear invisible for one light polarization, and larger for the other.