Cylindrical Cloak Research Articles

Non singular material parameters for arbitrarily elliptical–cylindrical invisibility cloaks

Simple general expressions for an important class of invisibility cloaks with less radial symmetry are derived by using transformation optics theory. Material parameters of arbitrarily elliptical–cylindrical invisibility cloak are obtained using a transformation in the elliptical–cylindrical coordinate system. It is explicitly shown that the azimuthal terms of material parameters in ideal case, like circular-cylindrical cloaks, are infinite at the whole interior surface of the cloak which makes ideal cloak impractical. Maxwell's equations are obtained in arbitrarily elliptical–cylindrical coordinate system and then the reduced material approximation is expanded to eliminate such singularities in the cylindrical cloaks with arbitrarily elliptical cross sections. The impedance of the cloak is derived and the cloak with reduced material approximation is designed so that the cloak's impedance at outer boundary experiences no change. An approximated 8 layer practical cloak is proposed such that each layer is divided to 32 slices azimuthally. Functionality of the proposed cloaks are numerically confirmed by two-dimensional finite element simulations where we illustrated that both layered and reduced cloaks with no singularities in their material parameters and therefore much easier realization possibility, show very good cloaking performance.

Experimental Characterization of a Broadband Transmission-Line Cloak in Free Space

The cloaking efficiency of a finite-size cylindrical transmission-line cloak operating in the X-band is verified with bistatic free space measurements. The cloak is designed and optimized with numerical full-wave simulations. The reduction of the total scattering width of a metal object, enabled by the cloak, is clearly observed from the bistatic free space measurements. The numerical and experimental results are compared resulting in good agreement with each other.

Analytical modeling of conformal mantle cloaks for cylindrical objects using sub-wavelength printed and slotted arrays

Following the idea of “cloaking by a surface” [A. Alù, Phys. Rev. B 80, 245115 (2009); P. Y. Chen and A. Alù, Phys. Rev. B 84, 205110 (2011)], we present a rigorous analytical model applicable to mantle cloaking of cylindrical objects using 1D and 2D sub-wavelength conformal frequency selective surface (FSS) elements. The model is based on Lorenz-Mie scattering theory which utilizes the two-sided impedance boundary conditions at the interface of the sub-wavelength elements. The FSS arrays considered in this work are composed of 1D horizontal and vertical metallic strips and 2D printed (patches, Jerusalem crosses, and cross dipoles) and slotted structures (meshes, slot-Jerusalem crosses, and slot-cross dipoles). It is shown that the analytical grid-impedance expressions derived for the planar arrays of sub-wavelength elements may be successfully used to model and tailor the surface reactance of cylindrical conformal mantle cloaks. By properly tailoring the surface reactance of the cloak, the total scattering from the cylinder can be significantly reduced, thus rendering the object invisible over the range of frequencies of interest (i.e., at microwaves and far-infrared). The results obtained using our analytical model for mantle cloaks are validated against full-wave numerical simulations.

Numerical simulations of cloaking problems using a DPG method

The paper reviews the construction of cloaks for 2D acoustic or electromagnetic waves using the Piola transform, and shows how the knowledge of the transform leads to the construction of a quasi-optimal test norm for the Discontinuous Petrov---Galerkin (DPG) method with optimal test functions for this class of problems. Numerical experiments for cylindrical and square cloaks illustrate the discussed concepts and demonstrate the effectiveness of the DPG method in cloak simulations.

Complementary cloak based on conventional cloak with axial symmetrical cloaked region

Based on the concept of complementary medium, a method which can make the conventional cylindrical cloak with axial symmetrical cloaked region to be not blind by filling the isotropic complementary in inner cloaked region is proposed. Firstly, the perfect electric conductor cylindrical shell was removed. Secondly, the symmetrical cloaked region was separated into two symmetrical regions along the symmetry axis and filled with isotropic complementary medium according to folding transformation. Full wave simulations are performed to confirm the effectiveness of the proposed method. The simulation results show that the converted cloak not only can exchange information with the outside, but also its presence cannot be detected.

FDTD Study on the Invisibility Performance of Two-Dimensional Cylindrical Cloak With Off-Plane Incidence

In this paper, we derive a theory for the modeling of 3-D cylindrical cloak based on 2-D finite-difference time-domain method, which is less time consuming and memory saving. By using the method, we develop the concept of invisibility angle and investigate the invisibility performance of the 3-D cylindrical cloak with 2-D constitutive parameters under off-plane incident waves. The bistatic radar cross sections as well as the scattered fields are calculated to evaluate the scatterings, from which the invisibility performance is observed to get worse with the increase in the incident angle, while the defined invisibility angle diminishes with the decrease in the cloak thickness and wavelength. The deterioration of the invisibility performance is mainly caused by the scatterings of TM wave defined in the study. The present results point out a possible way to evaluate the 2-D cloak on 3-D applications.

Infrared cylindrical cloak in nanosphere dispersed liquid crystal metamaterial

We present a design of an infrared cylindrical cloak using nanosphere dispersed nematic liquid crystal (NLC) metamaterial following the approach of Smith's group [Science 314, 977 (2006)]. Cloaking conditions require spatial distribution of liquid crystal birefringence with constant extraordinary index of refraction and radially dependent ordinary index of refraction. An approximate analytical formula for the latter is derived. Finite element (FE) simulations confirm the cloaking effect. Owing to the tunable birefringence of the liquid crystal component, such cloaking material offers the interesting possibilities of real-time control of invisibility. The possibility of experimental realization is briefly discussed.

Metal–dielectric metamaterials for transformation-optics and gradient-index devices in the visible regime

We investigate the application of metamaterials made of dielectrics with embedded metal nanoparticles for transformation-optics and gradient-index devices. We demonstrate that the permittivity and permeability distribution required for cylindrical cloaking at optical frequencies can be obtained by a composite material made of silver spheres embedded in a PMMA host. We show that this approach can be applied also to devices with an isotropic permittivity distribution and illustrate this for the optical black hole. The key ingredient of our system is the tunability of the plasmonic interactions between the metallic nanoparticles, depending on distance and size. In addition, we discuss possible realizations of the proposed structures.

Dispersive finite-difference time-domain (FDTD) analysis of the elliptic cylindrical cloak

A dispersive full-wave finite-difference time-domain (FDTD) model is used to calculate the performance of elliptic cylindrical cloaking devices. The permittivity and the permeability tensors for the cloaking structure are derived by using an effective medium approach in general relativity. The elliptic cylindrical invisibility devices are found to show imperfect cloaking, and the cloaking performance is found to depend on the polarization of the incident waves, the direction of the propagation of those waves, the semi-focal distances and the loss tangents of the meta-material. When the semi-focal distance of the elliptic cylinder decreases, the performance of the cloaking becomes very good, with neither noticeable scatterings nor field penetrations. For a larger semi-focal distance, only the TM wave with a specific propagation direction shows good cloaking performance. Realistic cloaking materials with loss still show a cloak that is working, but attenuated back-scattering waves exist.

Toward a cylindrical cloak via inverse homogenization

An effective cylindrical cloak may be conceptualized as an assembly of adjacent local neighborhoods, each of which is made from a homogenized composite material (HCM). The HCM is required to be a certain uniaxial dielectric-magnetic material, characterized by positive-definite constitutive dyadics. It can arise from the homogenization of component materials that are remarkably simple in terms of their structure and constitutive relations. For example, the components can be two isotropic dielectric-magnetic materials, randomly distributed as oriented spheroidal particles. By carefully controlling the spheroidal shape of the component particles, a high degree of HCM anisotropy may be achieved which is necessary for the cloaking effect to be realized. The inverse Bruggeman formalism can provide estimates of the shape and constitutive parameters for the component materials, as well as their volume fractions.

Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates

A cylindrical cloak is designed to control the bending waves propagating in isotropic thin plates. This is achieved through homogenization of a multiply perforated coating of isotropic homogeneous elastic material, which greatly simplifies the design of the multilayered cloak we proposed [Phys. Rev. Lett. 103, 024301 (2009)]. We first derive the homogenized biharmonic equation, which involves an anisotropic Young's modulus and an isotropic mass density. We then numerically show that a clamped obstacle is cloaked over a finite range of frequencies for an acoustic source located a couple of wavelengths away from its surrounding cloak. The reduced backward and forward scattering is confirmed by both the profile of the total field computed along a line passing through the source and the center of the cloak (near field confirmation), and the computation of the scattered far field.

Developing a time-domain finite-element method for modeling of electromagnetic cylindrical cloaks

In this paper we propose a time-domain finite element method for modeling of electromagnetic cloaks. The permittivity and permeability of the cloak model are described by the Drude dispersion model. The model to be solved is quite challenging in that we have to solve a coupled problem with different partial differential equations given in different regions. Our method is based on a mixed finite element method using edge elements with different types of meshes in different regions. Numerical results demonstrate that our algorithm is quite effective for simulating cloaks in time-domain. To our knowledge, this is the first cloak simulation carried out by the time-domain finite element method.

Design and study of elliptical cylinder external cloak based on line-transformation

Electromagnetic external cloak is an important device, which can make an object outside its domain invisible, meanwhile the object can exchange information with the outer region. Based on line-transformation and the concept of complementary medium, an elliptical cylindrical external cloak with only axial parameter changed is designed in this paper. The expressions of material parameters are derived, and then the performance of the elliptical cylindrical external cloak is simulated using the full wave simulation software. The results obtained confirm the correctness of constitutive parameters tensor. In addition, the effects of loss on performation of external cloak are investigated. Finally, the distribution of constitutive tensors is also investigated. This work provide a feasible way to fabricate matematerial-assisted elliptical cylindcial external cloak.

Research on a cylindrical cloak with active acoustic metamaterial layers

Enlightened by the tunable properties of effective density of the active acoustic metamaterial, we design an active infinite cylinder acoustic cloak according to the idea of the multilayer structured acoustic cloak with homogeneous isotropic materials. Utilizing the electrical analog, the dynamical equation of the acoustic cavity with Piezo-Diaphragm is presented. By analyzing the circuit diagram, the control strategy of achieving various effective densities which are used for constructing the acoustic cloak is given. Based on the necessary parameters such as the wide range values of the relative densities gained by active control, and the acoustic speed of each composite layer, the acoustic pressure field of the plane wave incident on the cloak is calculated, via the FEM model. Also the pressure map of a rigid cylinder scatterer with surrounded fluid is performed for comparison. Results show that outside the cloaking shell, the plane wave field is almost undisturbed. However inside the shell, the plane wavefronts are gradually deflected, and guided around the cloaked domain, returning to the original plane shape with small perturbation. This phenomenon making the cloak acoustically invisible in some frequency ranges has useful values in engineering applications. Finally, the total scattering cross section of the cloak is calculated to investigate the invisible effect according to the frequency domain. The total number of the composite active metamaterial layers is 15, which is much easier to realize in experiment.

Electromagnetic Reciprocal Cloak with Only Axial Material Parameter Spatially Variant

Reciprocal cloak is an intriguing metamaterial device, in which a hidden antenna or a sensor can receive electromagnetic irradiation from the outside but its presence will not be detected. Based on transformation optics, a cylindrical electromagnetic reciprocal cloak with only axial parameter varying with radius is designed and validated by full wave simulation. When two dispersive reciprocal cloaks are put together, they do not interfere with each other. Our work demonstrates the electromagnetic compatibility (EMC) ability of the reciprocal cloak which is very important in multi antenna and sensor design.

Acoustic external cloak with only spatially varying bulk modulus

Acoustic external cloak is an important device, which can cloak an object without encircling it but allows the object to exchange information with the outer region. By choosing appropriate spatial transformation, we design a cylindrical acoustic external cloak with only spatially varying bulk modulus in this paper. The general expressions of material parameters are derived, and then the performance of the external cloak is simulated based on full-wave simulations. The advantage of the cloak is that mass density elements are constants, and only bulk modulus is a function of radius, which make it easier to realize in practice. Besides, the effects of perturbations of parameters on the performance of the cloak are also investigated. This work provides a feasible way for the fabrication of the metamaterial-assisted acoustic external cloak.

Time-of-flight imaging of invisibility cloaks

As invisibility cloaking has recently become experimental reality, it is interesting to explore ways to reveal remaining imperfections. In essence, the idea of most invisibility cloaks is to recover the optical path lengths without an object (to be made invisible) by a suitable arrangement around that object. Optical path length is proportional to the time of flight of a light ray or to the optical phase accumulated by a light wave. Thus, time-of-flight images provide a direct and intuitive tool for probing imperfections. Indeed, recent phase-sensitive experiments on the carpet cloak have already made early steps in this direction. In the macroscopic world, time-of-flight images could be measured directly by light detection and ranging (LIDAR). Here, we show calculated time-of-flight images of the conformal Gaussian carpet cloak, the conformal grating cloak, the cylindrical free-space cloak, and of the invisible sphere. All results are obtained by using a ray-velocity equation of motion derived from Fermat's principle.

Cylindrical electromagnetic external cloak with only axial material parameter spatially variant

Electromagnetic external cloak is an important device, which can make an object outside its domain invisible, meanwhile the object can exchange information with the outer region. Based on optical transformation method, we design a simplified cylindrical electromagnetic external cloak with only axial material parameter spatially variant in this paper. The general expressions of material parameters are derived, and then the performance of the external cloak is simulated using the full wave simulations. The advantage of this external cloak is that transverse material parameters are constants, which makes it easier to realize with two-dimensional metamaterials. Besides, the effects of loss and perturbations of parameters on the performance of the cloak are also investigated. This work provides a feasible way for the fabrication of the metamaterial-assisted external cloak.

Optimized cylindrical invisibility cloak with minimum layers of non-magnetic isotropic materials

We present optimized design of cylindrical invisibility cloak with minimum layers of non-magnetic isotropic materials. Through an optimization procedure based on genetic algorithm, simpler cloak structure and more realizable material parameters can be achieved with better cloak performance than that of an ideal non-magnetic cloak with a reduced set of parameters. We demonstrate that a cloak shell with only five layers of two normal materials can result in an average 20 dB reduction in the scattering width for all directions when covering the inner conducting cylinder with the cloak. The optimized design can substantially simplify the realization of the invisibility cloak, especially in the optical range.

Elastic cloaking theory

Transformation theory is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by selection of the matrix relating displacements in the two descriptions. This gauge matrix can be chosen to make the transformed density isotropic for any transformation although the stress in the transformed material is not generally symmetric. Symmetric stress is obtained only if the gauge matrix is identical to the transformation matrix, in agreement with Milton et al. [1]. The elastic transformation theory is applied to the case of cylindrical anisotropy. The equations of motion for the transformed material with isotropic density are expressed in Stroh format, suitable for modeling cylindrical elastic cloaking. It is shown that there is a preferred approximate material with symmetric stress that could be a useful candidate for making cylindrical elastic cloaking devices.