Conformal Cloak Research Articles

Conformal Volumetric Grayscale Metamaterials.

Conformal artificial electromagnetic media that feature tailorable responses as a function of incidence wavelength and angle represent universal components for optical engineering. Conformal grayscale metamaterials are introduced as a new class of volumetric electromagnetic media capable of supporting highly multiplexed responses and arbitrary, curvilinear form factors. Subwavelength-scale voxels based on irregular shapes are designed to accommodate a continuum of dielectric values, enabling the freeform design process to reliably converge to exceptionally high figures of merit (FOMs) for a given multi-objective design problem. Through additive manufacturing of ceramic-polymer composites, microwave metamaterials, designed for the radio-frequency range of 8-12GHz, are experimentally fabricated and devices with extreme dispersion profiles, an airfoil-shaped beam-steering device, and a broadband, broad-angle conformal carpet cloak, are demonstrated. It is anticipated that conformal volumetric metamaterials will lead to new classes of compact and multifunctional imaging, sensing, and communications systems.

Topology optimization of thermal cloaks in euclidean spaces and manifolds using an extended level set method

Thermal cloaks are devices designed to shield an object against thermal detection, which have attracted growing interest in research. This paper proposes to design thermal cloaks using the level-set-based shape and topology optimization in the context of pure heat conduction. The cloaking effect is achieved by optimizing the distribution of two bulk heat conductive materials to eliminate the temperature disturbance induced by the introduction of the insulator (cloaking region) into a homogeneous thermal conduction medium. The optimized thermal cloaks are free of high anisotropy and nonhomogeneity commonly seen in the popular transformation thermotics or scattering cancellation methods. Due to the clear boundary characteristic of the level set representation, no sophisticated filtering techniques are required to suppress the appearance of ”gray regions” as opposed to the density-based topology optimization methods. Considering the fact that the device components that need to be thermally cloaked, e.g., sensors, can take an arbitrary free-form shape, a conformal thermal cloak on the manifold is also topologically optimized using the extended level set method (X-LSM), which has not been reported in the literature. The structural boundary is evolved by solving the (modified) Hamilton-Jacobi equation. The feasibility and robustness of the proposed method to design thermal meta-devices with cloaking functionality are demonstrated through a number of 2D and 3D (solid and shell) numerical examples with different cloaking regions (circular, human-shaped, spherical, and curved circular). This work may shed light on further exploration of the thermal meta-devices in the heat flux manipulation regime.

3D Printing of A Thermally Programmable Conformal Metasurface (Adv. Mater. Technol. 7/2022)

Curved Metasurfaces In article number 2101479, Qingxuan Liang and co-workers demonstrate a thermally programmable conformal metasurface carpet cloak printed by the composite fused deposition molding. The thermal programming method effectively reduces the complexity of conformal manufacturing and ensures the electromagnetic performances of the metasurface. This work provides a viable implementation strategy for complex curved metasurface and will substantially promote the applications of the conformal invisibility cloaks.

3D Printing of A Thermally Programmable Conformal Metasurface

AbstractThe curved surfaces conformality has become the coming barrier to the implementation of the metasurface carpet cloaks. A curved conformal strategy that can balance the electromagnetic performances and the manufacturing challenges of metasurface simultaneously is highly in demand, but yet underexplored. Herein, a novel thermal programming 3D‐printing method for curved conformal metasurface is proposed. Owing to the glass‐rubber transition characteristics of thermoplastic polymers, the advantages of rigid substrate and flexible substrate are fully utilized to achieve the conformality of metasurface, which ingeniously reduces the manufacturing complexity and ensures the electromagnetic performances. As a proof, an arched metasurface carpet cloak composed of the easy‐bending unit cells is designed and fabricated by the composite fused deposition molding of polylactic acid and Sn‐Bi materials with the thermal programming process. Experiments prove that the maximum reduced total radar cross section of the conformal cloak reaches about −9.4 dB while the 3 dB reduction bandwidth is ≈26.6%. The excellent cloaking performance of the metasurface sample demonstrates the effectiveness of this curved conformal method. This work provides a viable implementation strategy for complex curved metasurface and will substantially promote the applications of the conformal invisibility cloaks.

Designing conformal cloaks by manipulating structures directly in the physical space.

The method to elaborately design the refractive index profile in the lower Riemann sheet of Zhukovski transformation plays an important role in the performance of this kind of conformal cloaks. However, for most proposed schemes, the mathematical calculations are complex. Here, we propose a more convenient method to design conformal cloaks by manipulating structures directly in the physical space. The designed cloak only needs symmetrical metal boundaries filled with normal dielectrics (refractive index ranges from 1 to 2) in the 'circular branch cut', which would be more feasible for future experimental implementation. Numerical simulations are performed by using the finite element method to validate our theoretical analysis.

Composite Strategy for Backward-Scattering Reduction of a Wavelength-Scale Cylindrical Object by an Ultrathin Metasurface

Ultrathin electromagnetic cloaks to reduce backward scattering at microwave wavelengths are in demand, for their promise in $e.g.$ radar detection, as well as concealment. Concealing wavelength-scale objects with sufficient bandwidth at tiny cloak thicknesses is still challenging, though. This study experimentally demonstrates a composite strategy to design an ultrathin microwave conformal metasurface cloak for efficiently reducing backscattering from a wavelength-scale cylinder, with improved bandwidth. These results will have an impact on many applications, such as electromagnetic isolation and camouflage.

Omnidirectional Conformal Cloak Without Geometrical Dispersion

Invisibility cloaks designed by optical conformal mapping work only at some discrete frequencies, due to the phase-delay problem. The present work solves the phase-delay problem by using an optical null medium in the lower Riemann sheet. This approach has many advantages, such as a continuous working-frequency band (without geometrical dispersion), omnidirectionality, robustness under frequency shift, and no need for complex materials that are anisotropic and inhomogeneous. The technique offers a realistic means to an omnidirectional conformal cloak.

Conformal optical devices based on geodesic lenses.

Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann sheets, hence compromising the functionalities. To deal with that, we present a special method for conformal transformation optics based on geodesic lenses with special closed surfaces. The requirement is a continuous refractive index profile of dielectrics, which shows the almost perfect performance of designed devices. We demonstrate such a proposal by achieving conformal transparency (invisibility without cloaking region) and reflection. We can further achieve conformal invisible cloaks by two methods with perfect conductors. The conformal transformation optics method based on geodesic lenses may also find applications in other waves that obey the Helmholtz wave equation in two dimensions.

Isotropic polar solids for conformal transformation elasticity and cloaking

The paper initiates a constitutive theory of isotropic linear elastic solids where Cauchy’s stress tensor is not necessarily symmetric thus earning them the attribute “polar”. Mainly, expressions for the fourth-order elasticity tensors of isotropic polar solids in two and three space dimensions are derived. It is found that the constitutive tensors feature, in addition to the usual bulk and shear moduli, one extra independent elastic constant in 3D, and two extra constants in 2D. In the latter case, the new constants quantify to which degree stress and mirror symmetries are broken. Indeed, it turns out that in 2D, stress asymmetry enables isotropic yet chiral behaviors and the interplay between chirality and polarity is subsequently investigated.To motivate the theory, it is shown that 2D isotropic polar solids naturally arise in the application of the transformation method when the background medium is isotropic and when the underlying spatial transformation is conformal (i.e., angle-preserving). Accordingly, isotropic polar solids, in conjunction with conformal transformations, can simplify the design of invisibility cloaks and other wave-steering devices by circumventing the need for anisotropic behaviors. As a demonstration, a conformal carpet cloak is designed out of graded hexachiral lattices and numerically tested. The cloaking performance is shown to be satisfactory over a range of pressure-shear coupled dynamic loadings.

Mantle Cloaks Based on the Frequency Selective Metasurfaces Designed by Bayesian Optimization

We propose a full optimization procedure for designing mantle cloaks enclosing arbitrary objects, using sub-wavelength conformal frequency selective surface (FSS). Rely on the scattering cancellation principle of mantle cloak characterized by an average surface reactance, a personal computer can achieve this design procedure. By combing a Bayesian optimization (BO) with an electromagnetic solver, we can automatically find the optimal parameters of a conformal mantle cloak which can nearly cancel the scattering from the enclosed objects. It is shown that the results obtained by our method coincide with those from a rigorous analytical model and the numerical results by full parametric scanning. The proposed methodology opens up a new route for realizing ultra-wideband illusion scattering of electromagnetic wave, which is important for stealth and microwave applications.

A mass-independent conformal quantum cloak

An obstacle to constructing a quantum cloak with the transformation design method for steering a matter wave is the device involving the anisotropic modulation of the particle mass. It is the purpose of this paper to show that a narrow-acceptance-angle quantum cloak generated by a kind of conformal mapping could be mass-independent. This greatly simplifies the construction of the device since it can now be finished only by applying a potential field to a region of the shell. As demonstrations of the conclusion, an elliptical and a parabolic conformal quantum cloak are designed from the elliptical and parabolic coordinate systems. Their performance is inspected by probability currents. It is shown that the conformal devices can serve as novel splitters for a 2D matter wave. Finally, we discuss the difficulty of constructing a steering device from the hyperbolic coordinate system.

Conformal cloaks from a function composition

Since the beginning of transformation optics, invisibility cloaks have been attracting lots of attention, most of which however are usually too complex to realize. Here we propose a conformal cloak by using two mappings in a function composition. The required isotropic refractive index distribution is optimized to a range from 0 to 7.55, which is more feasible than previous designs. Numerical calculations have been performed to verify the cloaking effect.

Design and research of three-dimensional thermal cloak with arbitrary shape based on the transformation thermodynamics

Based on the form-invariance of the thermal conduction equation different from wave equation, transformation thermodynamics has opened up a new area for the arbitrarily manipulating of heat fluxes at discretion by using thermal metamaterials. Moreover, it can help researchers to design different kinds of thermal devices with many unique properties that cannot be simply realized by natural materials, such as thermal cloaking, thermal concentrating, thermal rotating and thermal illusion. Among these devices, the conventional thermal cloak enabling heat fluxes to travel around the inner region, has attracted the most significant attention so far. At the present time, the studies of the thermal cloak mainly focus on two-dimensional space with arbitrary shape and three-dimensional space with regular shape, which appear to be far from enough to meet the engineering requirements. In this paper, we derive the general expression of the thermal conductivity for three-dimensional thermal cloak with arbitrary shape according to the transformation thermodynamics. In this paper, the thermal conductivity in the polar coordinate system is transformed into that in the Cartesian coordinate system by means of coordinate transformation. On the basis of the expression of the thermal conductivity, we adopt full-wave simulation by using the software COMSOL Multiphysics to analyze the cloaking performances of five designed thermal cloaks, i.e., spherical thermal cloak, ellipsoidal thermal cloak, three-dimensional conformal thermal cloak with arbitrary shapes, non-conformal thermal cloak with the sphere outside the ellipsoid, and three-dimensional non-conformal thermal cloak with arbitrary shapes. The results show that the heat fluxes travel around the protection area, and eventually return to their original paths. The temperature profile inside the thermal cloak keeps unchanged, and the temperature field outside the thermal cloak is not distorted, which proves that the cloak has a perfect thermal invisible effect. Both the conformal and non-conformal thermal cloak have perfect thermal protection and invisible function. In this paper, the transformation thermodynamics is extended from two-dimensional thermal cloak to three-dimensional thermal cloak with better universality. At the same time, this technology provides more flexibility in controlling heat flow and target temperature field, which will have potential applications in designing microchip, motor protection and target thermal stealth. It is believed that the method presented here can be applied to other branches of physics, such as acoustics, matter waves and elastic waves.

Perfect conformal invisible device with feasible refractive indexes

Optical conformal mapping has been used to construct several isotropic devices with novel functionalities. In particular, a conformal cloak could confer omnidirectional invisibility. However, the maximum values of the refractive indexes needed for current designs are too large to implement, even in microwave experiments. Furthermore, most devices designed so far have had imperfect impedance matching and therefore incomplete invisibility functionalities. Here we describe a perfect conformal invisible device with full impedance matching everywhere. The maximum value of refractive index required by our device is just about five, which is feasible for microwave and terahertz experiments using current metamaterial techniques. To construct the device, we use a logarithmic conformal mapping and a Mikaelian lens. Our results should enable a conformal invisible device with almost perfect invisibility to be made soon.

Logarithm conformal mapping brings the cloaking effect.

Over the past years, invisibility cloaks have been extensively discussed since transformation optics emerges. Generally, the electromagnetic parameters of invisibility cloaks are complicated tensors, yet difficult to realize. As a special method of transformation optics, conformal mapping helps us design invisibility cloak with isotropic materials of a refractive index distribution. However, for all proposed isotropic cloaks, the refractive index range is at such a breadth that challenges current experimental fabrication. In this work, we propose two new kinds of logarithm conformal mappings for invisible device designs. For one of the mappings, the refractive index distribution of conformal cloak varies from 0 to 9.839, which is more feasible for future implementation. Numerical simulations by using finite element method are performed to confirm the theoretical analysis.

Transformation optics with artificial Riemann sheets

The two original versions of ‘invisibility’ cloaks (Leonhardt 2006 Science 312 1777–80 and Pendry et al 2006 Science 312 1780–2) show perfect cloaking but require unphysical singularities in material properties. A non-Euclidean version of cloaking (Leonhardt 2009 Science 323 110–12) was later presented to address these problems, using a very complicated non-Euclidean geometry. In this work, we combine the two original approaches to transformation optics into a more general concept: transformation optics with artificial Riemann sheets. Our method is straightforward and can be utilized to design new kinds of cloaks that can work not only in the realm of geometric optics but also using wave optics. The physics behind this design is similar to that of the conformal cloak for waves. The resonances in the interior region make the phase delay disappear and induce the cloaking effect. Numerical simulations confirm our theoretical results.

Transmutation of planar media singularities in a conformal cloak

Invisibility cloaking based on optical transformation involves materials singularity at the branch cut points. Many interesting optical devices, such as the Eaton lens, also require planar media index singularities in their implementation. We show a method to transmute two singularities simultaneously into harmless topological defects formed by anisotropic permittivity and permeability tensors. Numerical simulation is performed to verify the functionality of the transmuted conformal cloak consisting of two kissing Maxwell fish eyes.

Conformal cloaks at eigenfrequencies

(Chen et al 2011 Phys. Rev. A 83 055801) show that conformal cloak can not only work in geometrical optics limit but also in wave optics, if the working frequency is at the eigenfrequencies of the refractive index profile applied in the lower Riemann sheet (the profile is a special one that pushes light rays to propagate in close orbits). In this paper, we propose a more general concept of conformal cloaks for waves. We find that simply with a cavity set in the lower sheet, can the devices perform as good cloaking effect if the cavity mode can be excited out. The effect is not valid in geometrical optics limit but only for waves. Numerical simulations are performed to verify our findings.

Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space

We present the first experimental realization and verification of a three-dimensional stand-alone mantle cloak designed to suppress the total scattering of a finite-length dielectric rod of moderate cross-section. Mantle cloaking has been proposed to realize ultralow-profile conformal covers that may achieve substantial camouflage, transparency and high-performance non-invasive near-field sensing. Here, we realize and verify a mantle cloak for radio-waves. We report an extensive campaign of far- and near-field free-space measurements demonstrating that conformal cloaks can indeed produce strong scattering suppression in all directions and over a relatively broad bandwidth of operation.

Conformal cubical 3D transformation-based metamaterial invisibility cloak

A conformal cubical transformation-based metamaterial invisibility cloak is presented and verified, in the near and the far field, by a rigorous full-wave numerical technique based on a higher-order, large-domain finite element method, employing large anisotropic, continuously inhomogeneous generalized hexahedral finite elements, with no need for discretization of the permittivity and permeability profiles of the cloak. The analysis requires about 30 times fewer unknowns than with commercial software. To our knowledge, this is the first conformal cubical cloak and the first full-wave computational characterization of such a structure with sharp edges. The presented methodology can also be used in development of conformal, transformation-based perfectly matched layers.