Broadband electromagnetic cloaking with smart metamaterials. Published Journal Article The ability to render objects invisible with a cloak that fits all objects and sizes is a long-standing goal for optical devices. Invisibility devices demonstrated so far typically comprise a rigid structure wrapped around an object to which it is fitted. Here we demonstrate smart metamaterial cloaking, wherein the metamaterial device not only transforms electromagnetic fields to make an object invisible, but also acquires its properties automatically from its own elastic deformation. The demonstrated device is a ground-plane microwave cloak composed of an elastic metamaterial with a broad operational band GHz and nearly lossless electromagnetic properties.
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Transformation optics Abstract The ability to render objects invisible with a cloak that fits all objects and sizes is a long-standing goal for optical devices. Invisibility devices demonstrated so far typically comprise a rigid structure wrapped around an object to which it is fitted.
Here we demonstrate smart metamaterial cloaking, wherein the metamaterial device not only transforms electromagnetic fields to make an object invisible, but also acquires its properties automatically from its own elastic deformation.
The demonstrated device is a ground-plane microwave cloak composed of an elastic metamaterial with a broad operational band 10—12 GHz and nearly lossless electromagnetic properties.
The metamaterial is uniform, or perfectly periodic, in its undeformed state and acquires the necessary gradient-index profile, mimicking a quasi-conformal transformation, naturally from a boundary load. This easy-to-fabricate hybrid elasto-electromagnetic metamaterial opens the door to implementations of a variety of transformation optics devices based on quasi-conformal maps.
Amongst the celebrated applications of these emerging design approaches is cloaking: making objects of various shapes invisible by implementing coordinate transformations from the physical to a virtual space, in which the concealed object appears to have zero volume 3 , 4 , 5.
Owing to the difficulty of constructing metamaterials with such extreme properties, only a few experimental demonstrations of omnidirectional cloaks exist so far 6 , 7. The reduced dimensionality of the compression transformation allows one to select transformations whose implementations require only modest ranges of permittivity, permeability and refractive index 8. Such devices have been demonstrated to have a large operational bandwidth, the benefit originating from the reduced range of required material properties 9 , 10 , 11 , 12 , 13 , 14 , 15 , One of the most notoriously difficult properties to achieve without significant dispersion is magnetic permeability.
Devices have been proposed for two-dimensional 2D wave propagation of transverse magnetic waves that use special coordinate transformations combined with eikonal-limit approximations that is, neglecting the impedance gradient that allow elimination of the out-of-plane magnetic response, and thus remove the need for any magnetic response Such approaches are not applicable to transverse electric TE wave devices, as TO recipes typically require in-plane magnetic response that cannot be eliminated in the eikonal limit.
Fortunately, a special class of transformations exists, known as quasi-conformal maps QCMs , which minimize or even eliminate deviations of in-plane magnetic permeability from unity. This is achieved by minimizing the degree of anisotropy in the metric tensor of the transformation.
A ground-plane cloak is one of the TE-polarization TO devices that can be constructed entirely from dielectric materials as long as a quasi-conformal transformation for a given boundary shape can be found.
Because of their ability to realize a much broader range of constitutive properties with considerable control, artificially structured metamaterials have been preferentially used to implement the complex gradient permittivity and permeability distributions required by cloaks and other TO media.
In all previously proposed cloaking schemes, the spatial distribution of constitutive parameters is derived assuming interior and exterior cloak boundaries of fixed and known shapes to be hidden. Any deviation in the shape of the hidden object requires a complete redesign of the cloak, and thus a redesign of the metamaterial implementation.
In addition, the performance of a TO cloak also degrades with deformations of its exterior boundary, which is exposed to an ambient medium, typically air. Practically unavoidable mechanical loads at the exterior boundary caused, for example, by aerodynamic pressure, can deform conventional metamaterial cloaks beyond the tolerance of their unit cells 18 , In a smart TO device, the boundary deformation should create a distribution of unit cell deformations that leads to a new distribution of electromagnetic properties that still implements a desired coordinate transformation.
That such a behaviour is extremely difficult to achieve in general can be easily understood by considering that the stress and strain distributions of a loaded structure in mechanical equilibrium are solutions of rather complicated equations.
Although the strain profiles are uniquely determined by the boundary conditions, obtaining the desired strain distribution throughout the entire volume of the device is very challenging as, in general, this requires knowing the solution to the corresponding inverse problem.
An implementation of a given strain profile for a given boundary deformation would require a custom distribution of elastic properties in the entire volume of the device. As difficult as it is to construct such a graded distribution of elastic properties, this resulting distribution of mechanical properties does not solve the smart TO problem; such a distribution would, in general, depend on the type of boundary deformation, meaning, the device would only operate subject to one specific boundary load.
This idea can be quickly grasped from Fig. This paper provides the first experimental demonstration of a self-adjustable elastic metamaterial for broadband electromagnetic cloaking composed of two triangular regions with a silicone rubber tube array. In the undeformed initial state the tube array is perfectly periodic, with uniform electromagnetic properties homogenized over each unit cell.
Both materials involved—silicone rubber and air—are virtually lossless and dispersion-free at microwave frequencies, and the unit cells are electromagnetically non-resonant, which allows broadband operation of the demonstrated device. The uniformity of the array in its initial state and the simplicity of the identical metamaterial elements enable low-cost mass fabrication of large-area devices.
Because of its general ability to mimic QCMs, this hybrid elasto-electromagnetic smart metamaterial should have applications in various TO devices not limited to cloaks, as long as they can be implemented with QCMs.
Figure 1: Smart cloaking in accordance with the elastic deformation of the cloak boundary. Arrows indicate the propagation behaviour of incident and reflected beams through cloak, which resembles reflection from a flat reflector. Frame is incompressible dielectric materials and empty spaces indicate air. When we upwardly compress a square dashed line into a half size in y direction, the deformed shape solid line and Jacobian J are calculated if PRs are e 0. Results Quasi-conformal transformations with dielectric metamaterials To explain the operation principle of the smart metamaterial cloak, we begin by reviewing general TO theory for TE-polarization devices whose operation is limited to in-plane propagation.
A conformal transformation derives its name from the fact that it conforms to the angle preservation requirement. As any transformation can be seen locally as a combination of a rotation and simultaneous stretching in two orthogonal directions, the conformal requirement thus corresponds to isotropic stretching of a grid element.
Thus, by restricting the general coordinate transformations to the subset based on conformal maps, one can come up with implementations of TE-polarization devices not requiring a non-trivial magnetic permeability.
However, if the transformation was not conformal, magnetic permeability would also transform in a non-trivial fashion as equation 1 and become anisotropic.
To eliminate the performance limitations arising from the use of non-unity permeability, we thus want to use conformal or close to conformal quasi-conformal rather than general coordinate transformations. Design of auxetic smart metamaterials Now, we find a class of electromagnetic metamaterials for TE-polarization problems whose dielectric constant changes as prescribed by the TOs rule of equation 2 as a function of elastic strain.
For an elastic deformation, which transforms from X1, X2 to in Fig. Next, we consider what happens to this effective permittivity after an elastic deformation that does not preserve the volume of the metamaterial elements.
The ratio of effective permittivity after and before the deformation is. An elastic and electromagnetic metamaterial makes it possible to perform smart cloaking by this accordingly changing permittivity distribution under the change of the cloak boundary. Note that this equation matches precisely to the TO rule of equation 2 , and it does so regardless of the type of transformation used.
As described above, this behaviour is needed to maintain a unity permeability in equation 1. One can easily see that an elastic deformation of a homogeneous medium that possesses a negative PR with very large absolute value creates a deformed grid in precise agreement with the conformal transformation requirement. To illustrate this, we compress a square dashed line of different PRs of 0.
Therefore, we can have both ingredients to achieve smart cloaking in a single elasto-electromagnetic metamaterial; the deformed grid closely resembles a quasi-conformal transformation, and the dielectric constant transformation rule matches the one prescribed by TO. This can be seen as the limiting case of a hidden object of zero height. Then, we increase the height of the object, h, to 10 mm and carry out solid mechanics simulations assuming several different, and progressively lower, PR: 0.
We calculate the changes of the angle between lines and within the dashed line rectangle after the deformation; Figure 2: Theoretical demonstrations of smart metamaterial cloaking. A triangle patch with mm base and mm height is attached to the bottom of the rectangle. Full size image which is supposed to be zero for a precisely conformal mapping Fig. If we use a typical material with positive PR of 0.
Figure 2b show that a strongly scattered secondary beam is produced and a power gap from the primary scattered beam appears as a result of the bump on the reflector. As a result of a very close match between the transformed permittivity map and the one prescribed by the carpet cloak design, the power gap an indication of the bump on the reflector is no longer present Fig. Therefore, auxetic materials provide a smart way to deliver angle-preserving coordinate transformations needed for quasi-conformal TO.
The theoretical results shown in Figs 1 — 2 clearly demonstrate that the elastic deformation becomes progressively closer to an exact conformal map as the absolute value of a negative PR increases.
To achieve the desired range of variation for effective permittivity, we attach an additional triangular patch of material with a mm base and mm height to the bottom of the sample Fig. In both cases of our simulations, the cloaked bumps with different cloak boundaries produce a single specularly reflected beam that would be produced by a perfectly flat ground plane, which implies invisibility of the bump underneath the metamaterial structure.
These results demonstrate that the smart cloak gives the observer the impression of looking at a flat surface for a variety of shapes and heights of the physical bump on the bottom plane. As the bump is covered with a reflector that shields electromagnetic fields from its interior, the volume of its interior can be used as an invisible cavity. Fabrication of smart metamaterials Auxetic materials with very high dielectric constant and negative PR are difficult to realize, and we performed a more feasible experiment using a lower dielectric constant material.
The structure is made of a square lattice array of flexible silicone rubber tube with 10 mm outer diameter and 10 mm lattice constant inset of Fig. The empty air space has two regions: the inside tube region with 9 mm inner diameter and interstitial regions between unit rubber tubes. The smart carpet cloak is composed of two triangular regions marked as C1, C2 made of uniform tube array, serving as a homogeneous medium with an effective index of 1. The lower triangular region marked as C1 is elastically compressed to a curved surface with maximum height of h, resulting in a spatially varying density of silicone rubber, embedded in the empty air space Fig.
The spatial distribution of silicone rubber causes a variation of the effective index of refraction across the surface. As we appropriately achieve a smart cloaking device out of a uniform elastic crystal structure, this self-adjustable cloak facilitates easy fabrication in large area and potential applications. By changing the Jacobian J , we are able to span the required effective permittivity range of 1.
Figure 3: Experimental sample of non-auxetic smart metamaterial cloak. Photographs of the sample used in our experiment with an additional triangle patch of mm base and mm height.
Images of the sample a before and b after the deformation. The inset in a is a diagram of elastic crystal structure and the inset in b is the effective permittivity curve versus Jacobian values. To prevent refraction at air-sample interface, upper part of cloak has a right-angled triangle shape. Full size image The size of the unit cell, 10 mm, is substantially less than the wavelength of microwave radiation at 10 GHz.
We place and reversibly compress the smart metamaterial cloak made of an initially homogeneous medium by pushing it with a triangular bump made of nearly perfect electric conductors. As explained above, the deformation in a specific range always results in some effective permittivity profile that mimics a quasi-conformal coordinate transformation; thanks to the properly chosen elastic properties of the elastic tube array. To observe the smartness of the self-adjustable carpet cloak, we place and reversibly compress the smart metamaterial cloak by pushing it with a metallic bump.
Without a cloak, as shown in Fig. The reflecting scattered wave interferes with the incident wave and the fringe patterns, shown in the electric field map of Fig. To remove the interference effects between incident and scattered waves, we average the field map over the region of a wavelength distance to obtain the beam profiles at the reflecting output region as shown in Fig.
Figure 4: Experimentally measured E-field mapping of the smartly cloaked perturbations and non-cloaked perturbation at 10 GHz. The triangle in red dashed line presents the size of sample. Full size image Figure 5: Averaged beam profiles of the reflecting scattered waves at the output plane.
Without a cloak, a strongly scattered secondary beam appears. The dispersion curve of silicone rubber bulk see Fig. Apparently, the device operates fairly well in this experimental setup in the 8—12 GHz range, especially at the 11 and 12 GHz test frequencies. The observation of Gaussian beam cloaking at 8 GHz is complicated by the dimensions of the experimental setup and the diffraction limit for the Gaussian beam waist Fig.
At the other extreme 14 GHz , the metamaterial unit cell is not small enough relative to the wavelength to be accurately homogenizable. This explains the poor performance observed in Fig. Figure 6: Experimentally measured E-field mapping of smart metamaterial cloaking. Full size image An ideal carpet ground-plane cloak cancels the reflection spectrum of an object illuminated by plane waves incident from any direction, leaving only the specular reflection of the ground plane itself. These results show that the device operates as a carpet cloak for beams incident at various angles.
The demonstrated smart cloak is nearly lossless and broadband 10—12 GHz , can be extended to covering objects of larger area, and is amenable to inexpensive fabrication.
Broadband electromagnetic cloaking with smart metamaterials.
Mujinn The cloak was constructed with the use of artificially structured metamaterials, designed for operation over a band of microwave frequencies. The coordinate transformation transformation optics requires extraordinary material parameters that are only approachable through the use of resonant elements, which are inherently narrow bandand dispersive at resonance. Cloaking across a broad spectrum of frequencies has not been achieved, including the visible spectrum. Theoretical Phenomenology Computational Experimental Applied. Broadband electromagnetic cloaking with smart metamaterials. This means invisibility had not been achieved for the human eyewhich sees only within the visible spectrum. Each component has its own response to the external electric and magnetic fields of the radiated source.
Broadband electromagnetic cloaking with smart metamaterials