Elliptical Cloak Research Articles

Design and implementation of elliptical mantle cloaks for polarization decoupling of two tightly spaced interleaved co-frequency patch array antennas

In this paper, we utilized the method of mantle cloaking to decouple/isolate two densely packed interleaved patch array antennas operating at the same frequency but with orthogonal polarizations. To reduce mutual coupling between the adjacent elements, vertical strips, as a type of elliptical mantle cloaks, are located in close proximity to the patches. At the operating frequency of f0 = 3.7 GHz, the edge-to-edge spacing of the elements of the two interleaved arrays is less than λ0/80 (1 mm) and the center-to-center spacing of each array element is 0.7 λ0 (57 mm). The proposed design is implemented using 3D printing technology, and its performance in terms of return loss, efficiency, gain, radiation patterns, and isolation is measured for evaluation. The results show the radiation characteristics of the arrays are perfectly retrieved after cloaking similar to the isolated arrays. Decoupling tightly spaced patch antenna arrays on a single substrate paves the way to achieve miniaturized communication systems with full duplex operation or dual polarization communication.

Cloaking of Slot Antennas at C-Band Frequencies Using Elliptical Metasurface Cloaks

In this letter, we endeavor to curb the adverse effects of mutual coupling between two-slot antennas (operating at C-band frequencies), situated at a subwavelength separation. The effects of mutual coupling become extremely apparent at such close proximity and leads to the deterioration of the radiation aspects of each antenna. To mitigate these detrimental effects, we exploit the concept of mantle cloaking for the design of specialized cloaks, consisting of elliptical dielectric regions integrated with capacitive metallic strips. It is demonstrated through simulation results that by enclosing each radiating edge of the individual slots with these uniquely designed metasurfaces, the slot antennas are decoupled in the near field. Moreover, the metasurface cloaks also facilitate restoration of the far field radiation properties of the slots. In this regard, our cloak design ensures that the slot antennas do not sense the presence of each other, enabling each slot antenna to operate individually, as if they were isolated.

A novel design scheme for acoustic cloaking of complex shape based on region partitioning and multi-origin coordinate transformation

Acoustic cloaking is an important application of acoustic metamaterials. This article proposes a novel design scheme for acoustic cloaking based on the region partitioning and multi-origin coordinate transformation. The cloaked region is partitioned into multiple narrow strips. For each strip, a local coordinate system is established with the local origin located at the strip center, and a coordinate transformation in the local coordinate system is conducted to squeeze the material along the strip length direction to form the cloaked region. To facilitate the implementation of the acoustic cloak, the multilayer effective medium is used to approximate the non-uniform anisotropic material parameters. The effectiveness of the proposed coordinate transformation method is verified by comparing the results from our method with those in the literature. Firstly, the results of a circular acoustic cloak in the literature are reproduced by using our finite element (FE) simulations for validation. Then, a comparison is made between the traditional coordinate transformation scheme and our new scheme for simulating an elliptical acoustic cloak. The results indicate that the proposed multi-origin coordinate transformation method has a better cloaking effect on the incident wave along the ellipse minor axis direction than the traditional method. This means that for the same object, an appropriate transformation scheme can be selected for different incident wave directions to achieve the optimal control effect. The validated scheme is further used to design an arch-shaped cloak composed of an upper semicircular area and a lower rectangular area, by combining the traditional single-centered coordinate transformation method for the semicircular area and the proposed multi-origin method for the rectangular area. The results show that the designed cloak can effectively control the wave propagation with significantly reduced acoustic pressure level. This work provides a flexible acoustic cloak design method applicable for arbitrary shapes and different wave incident directions, enriching the theory of acoustic cloaking based on coordinate transformation.

Optimization Method for Practical Design of Planar Arbitrary-Geometry Thermal Cloaks Using Natural Materials

This study proposes an optimization method for the design of planar arbitrary-geometry thermal cloaks using natural materials based on the bilayer theory in thermal-cloaking studies. Our objective is to provide a practical design method for bilayer thermal cloaks of arbitrary shapes by determining the optimal outer-layer conductivity of the bilayer yielding the best thermal-cloaking performance. The method accounts for a potentially conducting inner layer, which is deemed more realistic from a practical standpoint as opposed to an ideal bilayer having a perfectly insulated inner layer. The proposed method is applied to solve thermal-cloaking problems involving not only conventional circular and elliptical geometries but also arbitrary-geometry thermal cloaks, as well as nonlinear background temperature distributions. For the ideal circular and elliptical bilayer cloaks, the proposed method yields the same analytical results as reported in the literature. For those cases where an analytical solution is not known to exist, the results demonstrate that excellent thermal-cloaking performance can be achieved on the basis of the bilayer design using the optimal outer-layer conductivity determined from the optimization method for a given set of background, inner-layer, and cloaked-region conductivities.

Analysis of elliptical thermal cloak based on entropy generation and entransy dissipation approach**Project supported by the National Natural Science Foundation of China (Grant Nos. 51606074 and 51625601) and the Fund from the Ministry of Science and Technology of China (Grant No. 2017YFE0100600).

In this work, we designed the elliptical thermal cloak based on the transformation thermotics. The local entropy generation rate distribution and entransy dissipation rate distribution were obtained, and the total entropy generation and entransy dissipation of different types of elliptical cloaks were evaluated. We used entropy generation approach and entransy dissipation approach to evaluate the performance of the thermal cloak, and heat dissipation analysis was carried out for models with different parameters. Finally, the optimized elliptical thermal cloak with minimum entropy generation and minimum entransy dissipation is found, and some suggestions on optimizing the structure of elliptical thermal cloak were given.

Complementary elliptical cloak with arbitrary axial ratio

Complementary elliptical cloak with arbitrary axial ratio

Optimized cloaks made of near-zero materials for different-sized concealed targets

The optimized cloaking design for conducting cylinders of different sizes is studied based on the Mie scattering theory. We construct a concentric multi-layered cloak made of alternating materials with isotropic dielectrics and epsilon-near-zero (ENZ) material, the thickness of which can be determined through genetic algorithm. As the radius of the conducting cylinder increases, high order scattering contributions are becoming evident, and more layers are needed. The scattering cross sections of three different radii of PEC cylinders are minimized by utilizing different numbers of multi-layers respectively. We find that eight or less optimized layers can cancel most of the scattering from a conducting cylinder with its dimension compared to wavelength, and more effectively when taking the ENZ material as the inner starting shell. The frequency dependence of total scattering is also studied, leading to the result that the bandwidth decreases as the size of concealed PEC cylinder increases. Furthermore, it is shown that the cloaking efficiency is less sensitive to the permittivity and thickness of the ENZ material, due to the small phase variation in the ENZ material. The multi-layered cloak designed for a PEC target can also be used to evidently reduce the scattering of a dielectric core and design a multi-layered elliptical cloak.

Design of elliptic cylindrical thermal cloak with layered structure

Thermal cloak has potential applications in thermal protection and sensing. Based on the theories of spatial transformation and effective medium, layered structure of elliptic cylindrical thermal cloak was designed. According to theoretical analysis and numerical simulation, the layered structure has typical characteristics of perfect thermal cloak. The external temperature field remains unchanged, while the internal temperature gradient decreases obviously. Meanwhile, the cloaking effect is stable in any direction. The cloaking effect can be improved by increasing the number of discretization layers or reducing the cloak thickness. The elliptic cylindrical cloak can be considered as cylindrical cloak when the focal distance is close to zero. This study has provided an effective way for realizing thermal cloak with more complex shapes.

Three-dimensional elliptical cloak by impedance design of meta-composite cloak shell structure

Research into metamaterials with unique material properties has led to the development of acoustic cloaks. The use of a spatially transformed space makes it possible to change (i.e. redirect) the propagating path of an acoustic wave using an anisotropic shell material as a cloak. However, the cloak of an acoustic wave in air, based on spatial transformation, requires an anisotropic cloak shell with unique properties, such as a mass density less than air that is not found in nature and is hard to be realized. We overcome the difficulties by providing a new concept in acoustic metamaterial design based on the impedance of the cloak shell. Using this method, we propose a new meta-composite material structure and further, design an elliptic meta-composite cloak shell complying with a three-dimensional space transformation. The new meta-composite material comprises a specially designed structure of layered plastic block elements forming cavities and pipes, respectively. Analysis of acoustic waves passing through the cloak shell demonstrates the effectiveness of acoustic cloaking performance over a frequency range of 800 to 1250 Hz in a 1/3 octave band. The anisotropic properties of the proposed cloak make it possible to alter the direction of the acoustic waves propagating from the original path and direct them to travel along a pre-determined path. This meta-composite material design accomplishes the goal of realizing an invisible elliptical acoustic cloak in the air.

Decoupling antennas in printed technology using elliptical metasurface cloaks

In this paper, we extend the idea of reducing the electromagnetic interactions between transmitting radiators to the case of widely used planar antennas in printed technology based on the concept of mantle cloaking. Here, we show that how lightweight elliptical metasurface cloaks can be engineered to restore the intrinsic properties of printed antennas with strip inclusions. In order to present the novel approach, we consider two microstrip-fed monopole antennas resonating at slightly different frequencies cloaked by confocal elliptical metasurfaces formed by arrays of sub-wavelength periodic elements, partially embedded in the substrate. The presence of the metasurfaces leads to the drastic suppression of mutual near-field and far-field couplings between the antennas, and thus, their radiation patterns are restored as if they were isolated. Moreover, it is worth noting that this approach is not limited to printed radiators and can be applied to other planar structures as well.

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.

Analytical Solution for Elliptical Cloaks Based on The Frequency Selective Surface

In this paper the elliptical dielectric cylinder which is covered with FSS cloak is considered. Frequency selective surface cloak which Alu named it mantle cloak is one of the recent techniques for cloaking. In this method an appropriate FSS can act as cloaking device for suppressing the scattering of object in the desired frequency. With using this method the dimension of the cloaks is extremely reduced. By this proposed structure, the RCS of elliptical cylinder is reduced about 10-20 dB and designed cloak has an appropriate performance. The analytical solution for the wave in each layer is presented and with using simulation, the electric field and the scattering pattern has been drawn.

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

Full-wave finite-difference time-domain analysis of the invisibility cloak mapped to a line segment with isotropic complementary media

A dispersive full-wave finite-difference time-domain model is used to study the performance of point mapped and line-segment mapped complementary invisibility cloaking devices. We have used the permittivity and the permeability tensors for conventional elliptic and bipolar cylindrical invisibility cloaks obtained from an effective medium approach in general relativity. In the case of a line-segment mapped cloak we also employ the mapping of the σ-axis in bipolar cylindrical coordinates. In these cloaks, we employ the complementary media both horizontally and vertically. Cloaks with horizontally or vertically arranged complementary media mapped to a point show good performance of cloaking in any case. On the other hand, cloaks with horizontally arranged complementary media mapped to a line-segment, do not show cloaking performance. However, for cloaks with vertically arranged complementary media mapped to a line-segment, cloaking works very well in any cases. These results show improved cloaking performance over the conventional cloaks with perfect electrical conductor mapped to a line-segment. On the other hand, realistic cloaking materials with loss still show cloaking but attenuated backscattering waves exist.

Design and study of the two-dimensional ellptical scattering-shifting cloak

Based on transformation optics theory, an elliptical scattering-shifting cloak is designed and the constitutive parameter tensor expressions are derived. Then full-wave simulations to mimic the ellptical dielectric and conductor cylinder are obtained by using finite-element software. The results of full-wave simulations validate the constitutive parameter tensors we derived and verify that the scattering-shifting cloak can imitate any object including dielectric and conductor: these results provide a new theoretical approach to design cloaks.

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.

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.

Design of electromagnetic cloaks with the same scattering patterns of a reduced perfect electric conducting line or ring

A design method of electromagnetic (EM) cloaks which can change the scattering pattern of the concealed object to that of a reduced perfect electric conducting (PEC) line or ring (two-dimensional case) is proposed in this paper. It is based on the radial transformation method. The boundary of the concealed space is crushed to an arbitrary line or a ring in the designs, and it is thus called the line-projecting or ring-projecting here. When the line or the ring is shrunk to a point, the EM cloak becomes the normally called invisibility cloak. While in the ring-projecting, none of the constitutive parameters of the EM cloaks is singular, so it may be easier to be realized compared with the singular one. Circular, elliptical and diamond cloaks are designed and simulated as examples. Furthermore, the proposed method is also valid in the design of cloaks with three-dimensional structure.

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.

The simplified material parameter equation for elliptical cylinder cloaks

We simplify the material parameter equation for elliptical cylinder cloaks under transverse-electric and transverse-magnetic models, respectively, and confirm these simplified equations by numerical simulations. As a result, the number of the component parameters is reduced from three to two, which simplifies the design of meta-materials and thus opens up the possibility of achieving elliptical cylinder cloaks in an easy way.