Design and free-space measurements of a simple electromagnetic cloak for conducting cylindrical objects Open Access

Recently a new approach to electromagnetic cloaking of long, cylindrical, conducting objects in free space was proposed.^1–3 With the term free-space cloak we mean that an isolated object placed in free space (in practice vacuum or air)can be cloaked with such a device. This approach^1–3 uses conventional dielectric materials(dielectric materials that are homogeneous, isotropic and have relative permittivity larger than unity) to cover a conducting cylindrical object so that the total scattering width of the object is minimized. The unique feature of this particular free-space cloaking method is that it does not require any complex materials (metamaterials) as do most other known cloaking methods such as plasmonic cloaking,^4,5transformation-optics,^6,7 and many others.⁸ A clear distinction should be made between free-space cloaks and so-called ground-plane cloaks,^9–11 as the previous ones are capable of cloaking isolated objects in free space and the latter are capable to cloak objects placed on a reflecting surface (for example, to hide a bump or some other discontinuity on the surface). In general, the material complexity required of ground-plane cloaks is considerably alleviated as compared to the free-space cloaks.

The obvious drawback of the free-space cloaking method studied here is that the electrical size of the object to be cloaked is limited: The cloaking performance inevitably deteriorates quite rapidly with increasing electrical diameter of the cloaked object. This disadvantage exists of course also in most other practical realizations of any cloak. The most similar cloaking method that we can compare the current one is plasmonic cloaking, where a homogeneous dielectric or magnetodielectric cover is used to cancel some of the scattering harmonics (usually the omnidirectional one) of the object placed inside this cladding.⁴ The difference between plasmonic cloaking and the device studied in this work is that plasmonic cloaking cannot be used to cloak conducting cylindrical objects for the polarization where the electric field is parallel to the axis of the cylinder.¹² Indeed, the polarization that we concentrate on in this work is exactly that one, which causes the most significant scattering from a thin, conducting cylinder (i.e., the electric field is parallel to the axis of the cylinder, see Fig. 1).

The theoretical background of the phenomenon that we are employing here for cloaking has already been elaborated and explained by an analytical model describing the cloaked and uncloaked cylinders with electric and magnetic dipoles.³ In this work,we therefore concentrate on the design of a practical free-space cloaking device, its realization and experimental verification of operation at microwaves. The experimental setup used in this work has already been used in the study of two other types of cloaks, namely, a transmission-line cloak¹³ and a metal-plate cloak.¹⁴ 

It should also be noted that although ideally a cloak should remove all scattering from an object, in practice we can only try to get as close as possible to this ideal condition, usually having to make a compromise between cloaking efficiency and bandwidth. Therefore, we should compare the results of this work mainly to other experimental results of total scattering cross section or width obtained for free-space microwave cloaks that have been presented in several occasions.^13–18 The recently presented work of cloaking a conducting cylinder with single-layer dielectric² is a preliminary study of the concept studied in this paper. In that work the cloaking of a conducting cylinder was demonstrated with a rectangular waveguide setup,where illuminating the object with a $TE 10$ mode of the waveguide effectively emulates an infinite array of similar objects illuminated by two obliquely incident plane waves.² From such a measurement the total scattering caused by an isolated object in free space, which is obviously the most important figure of merit in view of most practical applications of the device, cannot be analyzed. The numerical results presented in the same paper illustrated a good cloaking performance also in a free space scenario, but for an electrically much smaller cylinder than the one studied in this paper.

Although even a single dielectric layer can be used to strongly mitigate the total scattering width of a conducting cylinder,^1–3 a multilayer structure has been shown to be more effective.¹ The multilayer structure should be designed so that the layer permittivityincreases from the outside towards the inside of the structure.¹ However, it is important to clarify that the performance enhancement due to the use of several layers instead of just one was shown to be very modest when compared to the increased material complexity and cost.¹ For example, previously it was shown that the normalized total scattering width of a cloaked conducting cylinder with diameter 0.2λ₀ was decreased from about 0.4 to about 0.25 when changing from a single-layer cloak made of a dielectricwith ɛ_r = 5.42 to a 5-layer cloak of the same thickness but having a hyperbolic permittivity profile with material propertiesɛ_r = 128 (innermost layer), 4.85, 2.47, 1.66 and 1.25 (outermost layer).¹ Indeed, such improvement in cloaking efficiency requires materialswith huge permittivitieswhich may not be readily available.

It has been shown that a high-permittivity dielectric is preferable in order to obtain a good cloaking efficiency (in case of a multilayer cloak, the layer closest to the object to be cloaked should have the highest permittivity).^1,3 From the practical point of view, it is best to first choose the materials that will be used for the realization of the cloak. Since we want to carry out our measurementswith the setup operating in the X-band,^13,14we choose our design frequency to be 10 GHz. The object to be cloaked is chosen to be a long aluminum cylinder. Easily available, cheap, and low-loss materials for a high-permittivity dielectric are not many, so we have chosen acetone[ɛ_r = 21(1 − j 0.17)] for this purpose. In order to keep the liquid acetone in a specified volume around the object to be cloaked, we add another dielectric layer to the cloak. This dielectric with a lower permittivity therefore needs to be a material which is chemically resistant to acetone. We have chosen here Polyoxymethylene (POM) [ɛ_r = 3(1 − j 0.04)] which is a common plastic polymer. Based on the previous studies comparing single and multilayerdielectriccloaks,¹ adding this second dielectric layer will give only a minor improvement in the cloaking efficiency, so it is there mainly for the practical purpose of keeping the liquid in place. However, to illustrate the difference between using two layers instead of one, we will later compare the results of this dual-layer cloak to the cases where there is only one layer, made of either acetone or POM, comprising the cloak.

After the material properties of our structure in Fig. 1 have been decided, we should optimize the dimensions in order to achieve cloaking at the frequency of 10 GHz. As discussed in previous publications^1–3 and above, we can reach very effective cloaking only with cylinders having an electrically small diameter. On the other hand, if the structure is electrically too small, then the measurement of the bare metal cylinder, let alone the cloaked metal cylinder, will be more difficult.¹⁴ Here we perform a tradeoff between achievable cloaking performance and the measurement accuracy by using an electrically moderate-sized aluminum cylinder with the radius g = 3.45 mm (i.e., the diameter of the bare metal cylinder is 0.23λ₀ at 10 GHz).

To optimize the dielectric layer thicknesses (b − a and a − g, see Fig. 1), we use the analytical solution of the structure, as was done previously¹ and plot the total scattering width of the cloaked structure, normalized to that of the bare metal cylinder, as functions of a and b. See Fig. 2 for the result, illustrating the local minimum of scattering occurring for a = 4.75 mm and b = 6.5 mm. To further verify the operation of the cloak with these dimensions, i.e., g = 3.45 mm, a= 4.75 mm, and b = 6.5 mm, we solve analytically the normalized total scattering width as a function of frequency and confirm the results with a full-wave simulation software Ansys HFSS.¹⁹ See Fig. 3 for the analytical and numerical results, demonstrating a reduction of about 70 % in the total scattering width of the metal cylinder at around 10 GHz, achieved by the cloak structure. Note that in the analytical and numerical results the structure is considered to be infinitely long and the scattering problem is purely two-dimensional.

Coming back to the discussion regarding the comparison between single-layer and dual-layer cloaks, we can use the analytical model to estimate the benefit of using the proposed two layers instead of one in the cloak. For the considered size of the conducting cylinder, we obtain normalized total scattering widths of 0.312 and 0.447 with single-layer cloaks made of acetone and POM, respectively. For the dual-layer cloak described above the exact analytical value is 0.309,which is only slightly better than with acetone alone. Note that the radius of the innermost dielectric cladding has to be changed from a = 4.75 mm (dual-layer cloak) to a = 4.97 mm (single-layer cloak made of acetone) and a = 7.65 mm (single-layer cloak made of POM) to obtain the optimal cloaking at 10 GHz in all cases. So, as mentioned above, the need to use the second layer in this particular case is due to practical reasons, i.e., we need a solid material layer to keep the liquid acetone in place.

An aluminum cylinder and a dual-layer dielectric cloak with the aforementioned dimensions were manufactured. To keep the liquid acetone in the structure, the bottom of the cloak was made of a plastic disc, connected tightly to the metal cylinder as well as to the hollow POM cylinder via an elastic sealing. A photograph of the POM cylinder, enclosing the aluminum cylinder is shown in Fig. 4. The height of the structure is 200 mm, much larger than the half-power width of the beam in the measurements¹⁴ so that the edges of the structure are not illuminated in the measurements.

For the bistatic measurements of the scattering widths of uncloaked and cloaked objects we use the same setup as with the previously studied transmission-line¹³ and metal-plate cloaks.¹⁴ A horn antenna with a fixed position in front of the object under test is used to illuminate the object and another one is utilized to measure the transmitted fields at various positions around the object. Dielectric lenses are connected to the horns, creating a focal spot (half-power width 45 mm), at the position of the illuminated object.¹⁴ 

In order to obtain a measured value corresponding to the scattered electric field, also a measurement of the free space case (no object between the antennas) is needed, as has been previously explained in detail.¹⁴ Due to the finite sizes of the antennas, it is not possible to measure the full angular range from 0° to 180° to obtain the whole bistatic scattering pattern, but only a range from 22° to 180° (note that 180° corresponds to the forward scattering direction here, as shown in Fig. 1). However, as was the case in the previous studies,^13,14 the main scattering happens anyway close to the forward direction. Accordingly, the fact that a small part of the backscattering is neglected will have only a minimal effect on the normalized total scattering width. To make sure of this, in Fig. 3 we report the measurement results together with the numerical results concerning both the full angular range (“HFSS #1”) and the limited angular range (“HFSS #2”).

As demonstrated by Fig. 3, the analytical, numerical (both the limited angular range as well as the full angular range), and the experimental results are in fairly good agreement with each other. Most importantly, all the results predict the optimal cloaking effect to be found at around the design frequency of 10 GHz, with the normalized total scattering width reaching the minimum value of about 0.3 at that frequency (corresponding to 70 %reduction in the total scattering width). Moreover, the cloaking bandwidth can be considered to be very wide, especially when compared to most other cloaking techniques. In particular, the relative bandwidth with more than 50% reduction in the total scattering width is numerically and analytically estimated to be about 27%, with the experimental result leading to an even wider bandwidth. Overall,such cloaking performance is comparable and in some cases even better than results obtained with more complicated microwave cloaking devices operating in free space.^{5,13–18,20,21} Of course, direct comparisons are difficult to make as the objects to be cloaked vary significantly in composition and electrical size. However, one of the cloaks studied in Ref. 18 is a metal cylinder with electrical size comparable to the one studied here (both having the diameter of approximately 0.2λ₀). To that case a comparison can be made, and the result is that with a more complicated (anisotropic material) cloak structure a higher optimal cloaking efficiency can be obtained (90% reduction in total scattering width),¹⁸ but the cloak studied in the current paper has much wider cloaking bandwidth:more than 50% scattering reduction is obtained here in a bandwidth of 27%, as in Ref. 18 the bandwidth is 20%.

To this end, we study the scattering intensity patterns at fixed frequencies, comparing numerical results to the experimental ones. See Fig. 5 for the results at 10 GHz and 11 GHz. As in the cases of the previously studied cloaks,^13,14 we employ here also the monostatic measurement that provides the backscattering intensity (circles and squares in Fig. 5). The angular dependencies of the measured scattered field intensities are in good agreement with the numerical results, thus providing further evidence of the accuracy of the measurement method.

In conclusion, we have experimentally demonstrated the reduction of the total scattering width of a metal cylinder, using a bistatic free space measurement setup operating in the X-band. The scattering reduction is accomplished with an electromagnetic cloak comprised of two readily available dielectric materials.Measurement results have been compared with numerical and analytical ones and they all are in good agreement with each other.

This work was supported in part by the Academy of Finland and Nokia through the centre-of-excellence program. The work of P. Alitalo and C. A. Valagiannopoulos has been supported by the Academy of Finland via post-doctoral project funding. The authors thank Mr. Stefan Thurner for conducting the measurements.