We propose an illusion device which transforms a perfectly-electric-conducting (PEC) object into a virtual dielectric object with arbitrary material parameters. Such an illusion device has unconventional electromagnetic properties as verified by accurate numerical simulations. The presented illusion device is composed of inhomogeneous and anisotropic media with finite and positive permittivity and permeability components. Hence the designed device is possible to be realized using artificial metamaterials.
© 2010 Optical Society of America
In the past few years, great attention has been paid to the invisibility cloaks and other optical transformation devices due to their interesting behaviors [1–18]. More recently, Lai et al. have proposed a general concept of illusion device: making an object appear exactly like another one . Using the methodology of transformation optics, they designed an illusion device consisting of two separate pieces of metamaterials, one of which is called as the complementary medium [20, 21]. The complementary medium for the natural matter is composed of left-handed materials with simultaneously negative permittivity and permeability. Hence such an illusion device was extremely demanding of medium properties, and the applications are possible to stay in the realm of theory .
In this work, we propose another illusion device which transforms a perfectly-electric-conducting (PEC) object into a virtual dielectric object with the desired size and material parameters. The proposed illusion device has unconventional electromagnetic (EM) behaviors as verified by accurate numerical simulations. Unlike the previous illusion device which is composed of left-handed materials , all principal values of the permittivity and permeability of the proposed illusion media are finite and positive. Hence the presented method makes it feasible to realize the illusion device using artificial materials. The principle behind such an illusion device is not only bending EM waves around the PEC object, but also generating a virtual dielectric object within the virtual boundary.
An intuitive schematic diagram to show the proposed idea is illustrated in Fig. 1. A PEC sphere (the actual object) is enclosed by an metamaterial layer, the illusion medium layer. Such a layer of illusion medium makes any external detector perceive the scattering fields of a dielectric sphere (the virtual object) instead of the original PEC sphere. In another word, the illusion medium makes the field distribution outside the virtual boundary in both the physical and virtual spaces be exactly the same, regardless the direction of incident fields. Generally, the illusion medium has two functions, concealing the optical signature of the PEC sphere and generating the image of a dielectric sphere. After constructing a proper coordinate transformation Λ, the permittivity and permeability tensors of the illusion medium are calculated by
in which (ε̿, μ̿) and (ε̿′, μ̿′) are the constitutive tensors in the illusion space and the real space, respectively, and Λ is the Jacobian matrix with components Λij = ∂x ′ i/∂xj, corresponding to the transformation from the illusion space to the material space. In the following discussions, we assume that the illusion objects are isotropic, i.e., ε̿ = εr I̿ and μ̿ = μr I̿. We remark that, in the design of invisibility cloaks, the virtual space is just the free space. Hence one usually selected εr = 1, μr = 1, and there were almost no scattered fields from a perfect cloak. For the illusion device, however, the virtual space may contain a lot of illusion objects as our choice. Thus the scattered fields are the same as those from the virtual objects.
The cross section of an illusion medium which transforms a PEC sphere to a dielectric sphere virtually is shown in Fig. 2. The inner and outer radii of the illusion medium layer are r 1 and r 3, respectively. The radius of the dielectric sphere in the illusion space is r 0. We can construct a coordinate transformation in the spherical system as
in which k 1 = (r 2 − r 1)/r 0 and k 2 = (r 3 − r 2)/(r 3 − r 0). In order to demonstrate the function of the illusion device clearly, we divide the device into two layers. Based on the above transformation and Eq. (1), we can obtain the permittivity and permeability tensors as
Equation (3) provide the full design parameters for the permittivity and permeability in the spherical illusion medium layers. Clearly, the illusion medium is composed of inhomogeneous and anisotropic metamaterials with finite and positive parameters. This kind of metamaterials have been extensively studied and fabricated in the microwave frequencies [2,5,9,10, 22].
Equation (3) is not only valid to the three-dimensional (3D) spherical illusion medium, but also valid to two-dimensional (2D) cylindrical illusion medium. For the sake of perspicuity, we focus our demonstration on 2D illusion devices, which are more feasible for realization. In order to validate the formula, Eq. (3), for the 2D case, we make full-wave simulations on a cylindrical illusion medium by using the finite element method (FEM). In the following simulations, we consider the case when a transverse-electric (TE) polarized plane wave is incident upon an illusion medium layer, in which there exists only z component of electric field. Then only μr, μϕ and εz are of interest and must satisfy the request of Eq. (3).
First, we consider an illusion medium layer which realizes the virtual conversion from a PEC cylinder to a dielectric cylinder. Figure 3 illustrates the numerical results of electric fields for the illusion device. The plane waves are incident horizontally from the left to the right at 2 GHz. In this example, we select r 1 = 0.4 m, r 2 = 0.6 m, r 3 = 0.8 m, and r 0 = 0.4 m. Figures 3(a) and 3(c) show the scattered patterns of a bare PEC cylinder without the illusion medium layer and a dielectric cylinder with εr = 3 and μr = 1, respectively. When enclosed by the illusion medium layer, the scattered pattern from the PEC cylinder will be changed as if there were a dielectric cylinder. This can be clearly observed by comparing the near-field pattern of the PEC cylinder coated by the illusion medium layer shown in Fig. 3(b) with that of the dielectric cylinder shown in Fig. 3(c). The near-field distributions are exactly the same outside the virtual boundary. Inside the virtual boundary, the field distributions in Figs. 3(b) and 3(c) are different.
In the above example, we have considered an illusion device which transforms a PEC cylinder to a dielectric cylinder. For the inner illusion medium layer shown in Fig. 3(b), εr = 3 and μr = 1, which generates the illusion of the dielectric cylinder; for the outer layer, εr = 1 and μr = 1, which generates the illusion of free space. Here we consider another illusion device which transforms a PEC cylinder to a dielectric hollow pipe. In such a case, we choose εr = 1 and μr = 1 in the inner layer and εr = 3 and μr = 1 in the outer layer. Figure 4(b) illustrates the electric-field distribution for such an illusion medium layer, which is very similar to that of the dielectric hollow pipe with εr = 3 and μr = 1, as shown in Fig. 4(a). In this case, the inner layer with εr = 1 and μr = 1 generates an illusion of free space inside the dielectric pipe; while the outer layer with εr = 3 and μr = 1 generates an illusion of the outer dielectric pipe. Hence the illusion medium layer renders the enclosed PEC cylinder invisible and projects the illusion of a dielectric hollow pipe as shown in Fig. 4(b).
Next we consider a more complicated illusion device: a bronze of a woman model is enclosed by an illusion medium layer, which transforms the bronze into a dielectric women model with material parameters εr = 3 and μr = 1. To present the illusion function better, we divide the illusion medium into two layers. The inner and outer layers together make the bronze invisible, and the inner layer projects a virtual dielectric woman. In the inner layer, εr = 3 and μr = 1; in the outer layer, εr = 1 and μr = 1. Within such illusion medium layers, a woman bronze could appear to be a woman model with arbitrary predefined material parameters.
To calculate the permittivity and permeability of the illusion medium layers, we first consider a three-dimensional problem obtained by rotating the mirror-symmetric women model around the y-axis . Then we can obtain two-dimensional parameters by setting z = 0. Again, all medium parameters are finite and positive, and hence the illusion medium could be realized with the development of metamaterial technique for the complicated device. Figure 5 demonstrates the numerical simulation results of the scattered electric fields when the plane waves are incident horizontally from the left to the right at 2 GHz, in which Figs. 5(a) and 5(c) give the scattered-field distributions of the woman bronze and the dielectric woman in the computational domain, respectively, and Fig. 5(b) gives the scattered-field pattern of the woman bronze enclosed by the illusion medium layers. Comparing Figs. 5(b) and 5(c), we observe that the scattered-field patterns are completely identical outside the illusion medium layers. Thus, an observer outside the virtual boundary will see the metal woman as if a dielectric woman at the working frequency of the illusion medium.
In summary, we have presented a kind of new illusion media, which can transform a PEC object to a dielectric object by using artificial metamaterials. In such illusion devices, all principal values of the constitutive parameters are finite and positive. Hence the illusion device could be realizable using artificial structures.
This work was supported in part by the National Science Foundation of China under Grant Nos. 60990320, 60990324, 60871016, 60921063 and 60901011, in part by the National Key Preliminary Research Foundation for Weapons and Equipment, in part by the Natural Science Foundation of Jiangsu Province under Grant No. BK2008031, and in part by the 111 Project under Grant No. 111-2-05. WXJ acknowledges the support from the Graduate Innovation Program of Jiangsu Province under No. CX08B_074Z and the Scientific Research Foundation of Graduate School of Southeast University under No. YBJJ0816.
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