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 20.03.2009   Карта сайта     Language По-русски По-английски
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Электротехника и обработка материалов
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Electromagnetic cloaking with metamaterials

Pekka Alitalo1, b and Sergei Tretyakova, E-mail The Corresponding Author

1Department of Radio Science and Engineering / SMARAD Center of Excellence, TKK Helsinki University of Technology, FI-02015 TKK, Finland

bLaboratory of Electromagnetics and Acoustics (LEMA), Ecole Polytechnique Fédérale de Lausanne (EPFL) Bâtiment ELB, Station 11, CH-1015 Lausanne, Switzerland

Available online 19 March 2009.

Electromagnetic cloaking has aroused increasing interest in the scientific community, especially amongst researchers who are developing so-called metamaterials - artificial composites having exotic electromagnetic properties. In this paper we review the basic principles of metamaterials, especially those for cloaking applications, and describe the recent developments in the field of electromagnetic cloaking. Attention is given also to the recently proposed cloaking technique which is based on networks of transmission lines.

Article Outline

What is cloaking and invisibility
Scattering cancellation technique
Coordinate transformation technique
Transmission-line technique
Experimental results on cloaking with volumetric transmission-line cloaks
Other cloaking techniques

The idea of a device which makes objects invisible to the eye has a very long history, starting from folklore of many nationalities: we all have heard about various “invisibility hats” or “invisibility cloaks”, such as the cloak of Harry Potter, a character in J. K. Rowling's novels, but can such a device be practically realized, at least in some limited frequency range? Can a finite-size physical body be made invisible for electromagnetic radiation? Scientists have been thinking about these questions for a long time. Dollin published a paper in 1961, where he described an inhomogeneous and anisotropic magneto-dielectric structure, such that a plane wave falling from infinity on this body “passes through it without distortions1”. Apparently independent from that early work, similar structures were more recently described in a series of papers by Leonhardt, Pendry, Greenleaf, et al.[2], [3], [4] and [5]. As another example, Kerker published a paper entitled “Invisible bodies” in 19756, and that was a precursor of another recent series of publications by Alù and Engheta on invisible structures based on cancellation of scattering[7], [8] and [9].

Here we will review cloaking techniques based on scattering cancellation, on coordinate transformations, and on the use of artificial materials realized as dense meshes of transmission lines10. There are some other techniques, like the use of artificial electromagnetic surfaces, which allow to hide objects of certain special shapes for a single direction of illumination11 or the use of plasmonic resonant structures12, which unfortunately can be only briefly touched in this paper.

At the very core of cloaking techniques is the use of materials with very specific and often quite exotic properties. Because nature does not provide us with ready-to-use materials with the necessary properties, the only possibility is to realize them as artificial materials (metamaterials).


The European Virtual Institute for Artificial Electromagnetic Materials and Metamaterials13 defines the metamaterial as “an arrangement of artificial structural elements, designed to achieve advantageous and unusual electromagnetic properties”. If certain electromagnetic properties of a material (usually measured in terms of its permittivity var epsilon and permeability μ) are needed for an application in a certain range of the wavelengths of electromagnetic radiation, this material should appear homogeneous at the scale of this wavelength. This means that the size of its molecules as well as the distance between molecules should be much smaller than the wavelength. If the application is, for instance, in the microwave frequency range, where the wavelength is of the order of centimeters, the size of a single “molecule” can be of the order of millimeters, and it can be engineered and manufactured from ordinary materials consisting of usual, negligibly small at this wavelength scale, molecules. This is one of the origins of the term “metamaterial”: it is an artificial material with unusual properties made of usual materials with usual properties[14] and [15]. Of course, if the desired application is at very high frequencies, such as in the visible range, the size of these artificial molecules should be of the order of tens of nanometers or even smaller, which makes the actual realization a serious technological challenge.

The effective properties of metamaterials are defined by the (ordinary) materials from which the metamaterial inclusions are made, by their shape, mutual orientation and concentration of inclusions, and so on. This means that there are very many degrees of freedom in the design of the desired electromagnetic response, allowing for realization of artificial media with quite exotic and extreme properties16, such as required for realization of cloaking devices. Although the metamaterial research activities started only quite recently, the results have been already covered in a number of monographs[17], [18], [19], [20], [21], [22], [23], [24], [25], [26] and [27].

What is cloaking and invisibility

What is an electromagnetic cloak? This is a device which makes an object “invisible” for electromagnetic radiation in a certain frequency range. Of course, the most exciting applications can be envisaged for cloaks working in the visible part of the spectrum. An object is invisible if it does not reflect waves back to the source and in addition, it does not scatter waves in other directions, and, furthermore, it does not create any shadow (the last means that there is no scattering in the forward direction). From these conditions it follows that the object should not absorb any power. Put in other words, the object should not disturb the fields existing outside the object.

In terms of the theory of scattering of electromagnetic waves (including light), to “cloak” an object means to reduce its total scattering cross section (SCS), ideally to zero, since the total scattering cross section is defined as the ratio of the total scattered power to the incident power density. Cloaking should not be confused with the stealth technology. Stealth technologies minimize only the power reflected back to the probing radar (the backscattering cross section or “radar cross section”). This can be done either by covering an object with an absorbing layer or by shaping the object so that the field scattered towards the illumination direction is minimized. Obviously, even an ideal stealth aircraft is visible if observed from the side or from the back. It can be shown that absorbing coverings and object shaping cannot reduce the total scattering cross section by more than 50%28.

The concept of invisibility has been closely related to cloaking in recent literature, the difference is that invisibility means the reduction of the total scattering cross section of a specific object. This can be achieved for example by cancelling radiation from the induced dipole moments of the scatterer by introducing another object, in which dipole moments of the opposite direction are induced7. Thus, the combination of these objects scatters very little, whereas both objects independently scatter strongly. Some invisible structures can also be used as cloaks, if the object to be made invisible consists of, e.g., a perfectly conducting hollow enclosure, since inside this enclosure there are no fields9.

Scattering cancellation technique

It has been known for a long time that scattering from an object can be mitigated by adding to the system another object, the scattering of which is complementary with respect to the principal scatterer[6], [29] and [30]. This type of scattering minimization can be achieved for example with covering the main scattering object by single or multiple layers of dielectric materials[6], [30] and [31]. The recent interest towards this technique has been aroused after the proposal of using plasmonic materials for transparency7 and this technique has been developed further[8], [9], [32], [33], [34], [35], [36], [37] and [38].

Fig. 1 shows an illustration of the principle of scattering cancellation. Here a spherical dielectric object with permittivity larger than in the surrounding medium, is covered with a dielectric shell having the permittivity smaller than in the surrounding medium. The shell diameter can be chosen so that the scattering from the core and the shell cancel each other, since dipole moments of the opposite sign are induced in them. Of course, there may also exist higher modes in addition to the dipolar modes, but it has been shown that efficient invisibility can be achieved even with suppressing just the dipolar scattering9. It is possible to suppress also higher modes, but this obviously makes the design more complicated9. Cloaking of collections of particles and the extension of the scattering cancellation approach to infrared and optical frequencies have also been recently discussed[33], [34], [35] and [36], as well as the effects of material dispersion37.

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Fig. 1. Illustration of the scattering cancellation technique7: the dipole moments induced in the object to be made invisible and in the shell covering this object cancel each other. Reproduced with permission from the American Physical Society.

The problems of utilizing cloaks based on the scattering cancellation technique relate to the realization of materials with the needed type of exotic material parameters (e.g., materials having the relative permittivity var epsilonr < 1). There are some materials readily available in nature that have the property of the desired low permittivity values at THz, infrared or optical frequencies (plasmonic materials such as silver and gold). The utilization of these plasmonic materials is limited by losses and by the fact that their material properties vary significantly as a function of the frequency. Moreover, at a specific frequency of interest there may not be a material with suitable properties available at all.

One recently suggested (practically possible) design of a scattering cancellation cloak consists of metallic parallel-plate implants placed radially around the cylindrical region where a dielectric object (to be made invisible) is located32. This structure is an example of a scattering cancellation device which is composed of an artificial metamaterial, see Fig. 2.

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Fig. 2. An example design of a scattering cancellation device32, composed of metallic parallel plates embedded in a dielectric. The object to be made invisible is a dielectric cylinder. Reproduced with permission from the American Physical Society.

The benefits of the scattering cancellation technique are simple design and structure (assuming that materials with required properties are available) and the possibility to realize invisibility or cloaking with isotropic and homogeneous materials. The drawbacks, depending on what kind of object needs to be made invisible (penetrable or impenetrable object) are realization of metamaterials with required properties if plasmonic materials are not available, bandwidth limitations inherent to many realizable (resonant) metamaterials, and the fundamental limitation on the energy velocity when cloaking impenetrable objects in free space with passive cloaks (for ideal operation the energy of the electromagnetic wave should circle around the cloaked object faster than the speed of light).

Coordinate transformation technique

Cloaking with metamaterials that enable the creation of volumes with zero electromagnetic fields inside a device composed of such materials, has been recently described by Leonhardt2 and Pendry et al.3 Mathematical basis of the coordinate transformation required in such a method has been previously presented[1], [4] and [5]. These techniques rely on the transformation of coordinates, e.g., a point in the electromagnetic space is transformed into a sphere in the physical space, thus leading to the creation of a spherical volume where electromagnetic fields do not exist, but are instead guided around this volume, see Fig. 3. There exist many possibilities to perform coordinate transformations, see recent literature related to the design and analysis of various types of cloaks based on the coordinate transformation technique

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