Abstract

Recently, invisible cloaks have attracted much attention due to their exciting property of invisibility, which are based on a solid theory of transformation optics and quasi-conformal mapping. Two kinds of cloaks have been proposed: free-space cloaks, which can render objects in free space invisible to incident radiation, and carpet cloaks (or ground-plane cloaks), which can hide objects under the conducting ground. The first free-space and carpet cloaks were realized in the microwave frequencies using metamaterials. The free-space cloak was composed of resonant metamaterials, and hence had restriction of narrow bandwidth and high loss; the carpet cloak was made of non-resonant metamaterials, which have broad bandwidth and low loss. However, the carpet cloak has a severe restriction of large size compared to the cloaked object. The above restrictions become the bottlenecks to the real applications of free-space and carpet cloaks. Here we report the first experimental demonstration of broadband and low-loss directive free-space cloak and compact-sized carpet cloak based on a recent theoretical study. Both cloaks are realized using non-resonant metamaterials in the microwave frequency, and good invisibility properties have been observed in experiments. This approach represents a major step towards the real applications of invisibility cloaks.

©2009 Optical Society of America

1. Introduction

Recently, a new theory of transformation optics and quasiconformal mapping has been proposed to design the electromagnetic metamaterials to control the paths of electromagnetic waves [1,2,4]. Based on the Fermat’s principle, an electromagnetic wave will always travel in the quickest route between two points. In a homogeneous and isotropic material, the route is a straight line. In an inhomogeneous material, the route becomes nonlinear to make the total traveling time be minimal because the wave travels at different speeds inside. Hence one can control the route of wave by designing the material parameters, which has found a lot of potential applications such as cloaking objects invisible [17], concentrating of electromagnetic waves [8,9], rotating of electromagnetic waves [10], bending of electromagnetic waves [11], and forming multi-beam antennas [12]. Artificial metamaterials provide flexible choices of the designed parameters.

Among above potential applications, the invisibility cloak is the most attractive. There have been mainly two kinds of invisibility cloaks proposed: free-space cloaks and carpet cloaks. A free-space cloak is a designed material shell covering an object in free space, which can guide the waves to propagate around the shell, making the object inside invisible [1]. The theoretical tool to study invisible cloak is the so-called transformation optics [13], which is based on the coordinate transformation [14]. An optical conformal mapping method was used to design the material parameters that create perfect invisibility [1,2], in which the permittivity tensor ε and the permeability tensor µ are both spatially varying and anisotropic with singular values. By implementing such complicated full material properties, the concealed object and the cloak appear to have the free-space properties exactly when viewed externally, which has been verified by full-wave simulations [15] and analytic solutions [16].

However, the fully inhomogeneous and anisotropic parameters for perfect free-space cloaks require extremely complicated metamaterial design. For a two-dimensional (2D) cylindrical cloak in free space, when the electric field is polarized along the cylinder axis, the full parameters can be greatly simplified [3]. Since the reduced constitutive parameters provide the same dispersion equation as the full parameters for the 2D cloak, the electromagnetic waves have the same trajectory inside the cloak with a penalty of nonzero reflections. Using the reduced parameters, the first practical free-space cloak has been realized in the microwave frequency [3]. In the experiment, a conducting cylinder was hidden inside the cloak, which was constructed with the use of artificially structured metamaterials. Due to the requirement of very large and very small values of refraction index, resonant structures [17] have been applied. This makes the invisible cloak operate in a narrow frequency band with a relatively large loss. The experiment and simulation results have a good match. But notable reflections and shadow of the hidden object were observed due to the use of simplified parameters and relatively large loss [3]. The narrow bandwidth and large loss become the big restriction to real applications of free-space cloaks.

In view of the difficulty to realize the free-space cloaks, a recently published theory has suggested a carpet cloak, or ground-plane cloak, which can hide any objects under a metamaterial carpet [4]. Different from the free-space invisibility cloak, which crushes the cloaked object to a point, the carpet cloak crushes the hidden object to a conducting sheet [4]. In the other word, any objects hidden under the carpet appear as a flat conducting sheet, and hence cannot be detected by any exterior sources. The great advantage of the carpet cloak is that it does not require singular values for the material parameters [1]. By choosing appropriate coordinate transformation, it has been shown that the anisotropy of the cloak can be minimized and the range of the permittivity and permeability is much smaller than that for the free-space cloak [4]. Hence the carpet cloak is easier to be realized using metamaterials.

The carpet cloak has very important applications, especially in the microwave frequencies. For example, it can be used to hide the aircraft on the airport, and the automobile on the ground, etc. The carpet cloaks have been experimentally demonstrated firstly in the microwave frequency [5], and then in the optical frequency [6,18], using non-resonant metamaterials. The non-resonant metamaterials have very low loss and operate in a broad frequency band, hence the carpet cloaks have good invisibility performance [5,6]. However, there are two restrictions in the existing carpet-cloak experiments: 1) the background is not free space to get easily realized material parameters (in the microwave experiment, the refractive index of background material was chosen as 1.331 [5]; in the optical experiment, the refractive index of background material was chosen as 1.58 [6]); 2) the carpet cloak has a very large size (in the microwave experiment, the area ratio of the carpet cloak to the cloaked region is as high as 65.7 [5]). The above restrictions make the carpet cloak be difficult in real applications.

Here, we demonstrate experimentally the first broadband and low-loss directive free-space cloak and compact-sized carpet cloak in the free-space background. The experiments are based on a recent theoretical study [7], which proposed a simplified carpet cloak (or ground-plane cloak) made of only a few blocks of all-dielectric isotropic materials. In our experiments, the simplified carpet cloak is realized using non-resonant metamaterials in the microwave frequency, which has a much smaller size than the full carpet cloak reported in Ref. [5]. The area ratio of the cloak to the cloaked region is as small as 7.33, which is only 11.2% of the full cloak. However, the presented carpet cloak has equally good invisibility performance. Furthermore, a broadband and low-loss directive free-space cloak is realized, that cloaks the radiation originating from specified directions. Hence the presented work makes a major step towards the real applications of invisibility cloaks.

2. Simplified Carpet Cloak

For the design of the simplified carpet cloak, we consider a 2D problem in which all the fields are invariant in the z direction and the electric fields are z-polarized. The cloaked object is a car model, which is placed under a triangular conducting region. The reason to choose the triangular shape is for easy installation in real applications. We want to design a compact-sized carpet cloak which is covering on the triangular region to make the whole system appear as the original flat conducting plane as if the car does not exist. We choose the shape of cloak as a rectangle with the width 125 mm and hight 50 mm except that the bottom boundary is partially triangularly-shaped to place the car. Hence the car model is concealed between the carpet cloak and the conducting plane as shown in Fig. 1(c).

 figure: Fig. 1.

Fig. 1. The design for a compact-sized carpet cloak in free-space background. (a) Metamaterial refractive index distribution of the complete carpet cloaking region in which the mesh lines indicate the quasi-conformal mapping. The compact-sized cloaking region is shown within the box. (b) Expanded view of the compact-sized cloaking region in which the refractive indices below one are all designed as 1. (c) Photograph of the fabricated metamaterial carpet cloak and the concealed car model. (d) The design of non-resonant elements. The dimensions of the metamaterial unit cells are a=3 mm, w=0.2 mm, l=h+2w mm, and h varying from 0 to 2.2 mm.

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 figure: Fig. 2.

Fig. 2. The effective parameters of the unit cells for h (shown in Fig. 1(d)) varying from 0 to 2.2 mm.

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 figure: Fig. 3.

Fig. 3. The dimensions (h in Fig. 1(d)) of the non-resonant unit cells for the simplified carpet cloak (Fig. 1(c)).

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 figure: Fig. 4.

Fig. 4. Measured electric-field mapping of (a) the ground plane, (b) triangular metallic bump, and (c) ground-plane cloaked bump when collimated beam is incident at 10GHz. The rays display the wave propagation direction, and the dashed line indicates the normal of the ground in free space and that of the ground-plane cloak in the transformed space. (d) Collimated beam incident on the ground-plane cloaked bump at 11 GHz. (e) Collimated beam incident on the ground-plane cloaked bump at 12 GHz. (f) Collimated beam incident on the ground-plane cloaked bump at 13 GHz. Far-field patterns when collimated beam is incident at 10 GHz on (g) the ground plane, (h) the triangular metallic bump, (i) the carpet cloaked bump.

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To design a compact-sized carpet cloak, the process of parameter calculation contains two stages. First, we followed the technique presented in [4] to get the complete cloaking region, in which a quasi-conformal coordinate mapping is generated by minimizing the Modified-Liao functional [20, 21] upon slipping boundary condition. The refractive-index distribution of the cloak is computed numerically, as shown in Fig. 1(a), in which the maximum anisotropic factor is 1.07. Secondly, we use the grid optimization by recursive division of Cartesian cells to sample the original refractive-index distribution. In such a course, the small regions near the base corners of the triangular object where the refractive-index is smaller than 1 are treated as free space. Since the background of the designed cloak is free space, the transformation generates cells in region I (Fig. 1(a)) whose refractive indices are nearly 1. Hence such a region can be simplified as free space, and the cloak will reduce to the region II (Fig. 1(a)). The refractive index distribution of the final carpet cloak is illustrated in Fig. 1(b), in which the refractive indices are varied from 1 to 1.69.

The compact-sized carpet cloak is divided to 3-by-3-mm squares with non-resonant elements shown in Figs. 1(c) and 1(d). The compact-sized carpet cloak is fabricated on copperclad printed circuit board (PCB) with F4B substrate (the substrate thickness is 0.25 mm, with a dielectric constant of 2.65 and loss tangent of 0.001), as shown in Fig. 1(d). After a well-established retrieval process [22], the effective permittivity, permeability, characteristic impedance and relative refractive index for a given element can be achieved by numerical simulations. By changing the dimension h (see Fig. 1(d)) from 0 to 2.2 mm, we are able to span the required permittivity range from ε=1.17 to 3.07, the permeability range from µ=1.07 to 0.96, the characteristic impedance range from Z=0.93 to 0.6, and the refractive index range from n=1.07 to 1.87 at 10 GHz, as shown in Fig. 2. Since the effective permeability approaches to 1, the permittivity map of the simplified cloak will be square of that demonstrated in Fig. 1(b) with the formula ε=n 2. The corresponding dimensions of the unit cells shown in Fig. 1(c) can be obtained according to the relationship between the distribution of refractive indices (Fig. 1(b)) and the responses of unit cells (Fig. 2), as illustrated in Fig. 3. Because the cell-to-cell change in dimension is minor, the impedance is matched gradually in the whole cloak over the entire measurement frequency range. The carpet has a size of 125×50 mm2 with a height of 12 mm. The cloaking transformation is specifically designed to compensate the triangular concealed region with the height 13 mm and the bottom 125 mm.

To validate the invisible effect of the simplified carpet cloak, we make use of a near-field scanning system [23] to map the electric-field distribution within a planar waveguide. In the planar waveguide, the wave polarization is restricted to transverse electric. The electric-field maps of the scattering region, including the collimated incident and scattered beams, are shown in Fig. 4. The incident waves are launched into the chamber from a standard X-band coax-to-waveguide coupler to produce a nearly collimated microwave plane beam. The beam is arbitrarily chosen to be incident on the ground plane at an angle of 45° with respect to the normal.

Figure 4 shows the measured near-field distributions and the far-field patterns of the carpet cloak. From Figs. 4(a) and (b), there is considerable difference between the reflections from the flat and curved surfaces. The beam reflected from the uncloaked triangular bump shows the strong scattering of the bump. The flat surface illustrates the expected collimation beam profile, similar to that of the incident wave. To hide the bump on the surface, the designed carpet cloak was placed around the bump and the measured result is shown in Fig. 4(c). Subsequently, similar to the flat reflecting surface, a single reflected beam is observed. This demonstrates that the cloak has successfully transformed the curved surface into a flat surface, giving the observer the impression that the beam was reflected from a flat surface. Owing to the fact that there is no penetration of light into the bump, the car model could be placed behind it and effectively hidden, making the car invisible. The far-field patterns are plotted in Figs. 4(g)–(i). For the ground plane and the cloaked triangular concealed region, the beam profiles show a very similar single peak; that is, the good cloaking performance is observed. Unlike the above cases, the bump alone exhibits a multi-peak far-field pattern (Fig. 4h), indicating the strong perturbation of the beam.

 figure: Fig. 5.

Fig. 5. The simulated near-electric-field distributions of (a) ground plane, (b) full-parameter carpet cloak, and (c) simplified carpet cloak. (d) The far-field patterns of above three cases.

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To verify the broadband properties of the carpet cloak, measurements were carried out over a wide range of frequencies. The cloaking behavior was confirmed in our measurements from 10 GHz to 13 GHz, as shown in Figs. 4(d), (e) and (f). The cloak is excepted to work very well within a more wide frequency band although it cannot be verified experimentally due to limitations of the measurement apparatus. Figs.4(d)–3(f) show similar cloaking behavior to the map taken at 10 GHz in Fig. 4(c).

To further investigate the performance of the simplified carpet cloak, we make a comparison between the full-parameter cloak and the simplified cloak at 10 GHz, as shown in Fig. 5, in which Figs. 5(a), (b) and (c) are the near-field distributions of the ground plane, the full-parameter carpet cloak, and the simplified carpet cloak, respectively, and Fig. 5(d) shows the far-field patterns of the above three cases. Clearly, both the near-field distributions and far-field patterns have very good agreements, which demonstrate that the simplified carpet cloak has nearly the same good performance as the full-parameter cloak, and conceals the hidden object very well.

3. Directive Free-Space Cloak

The compact-sized carpet cloaks discussed above only work in the presence of ground-plane. Next, we consider a compact-sized and broadband free-space cloak based on the electromagnetic mirror principle although the free-space cloak works only for a specified direction, as suggested in [4, 7]. Such a kind of directive free-space cloaks can also find a lot of specific applications like air flight, space exploration, etc. For practical reason, here we choose the outer boundary of the free-space cloak as a prolate cylinder, whose long axis is 125 mm and short axis is 60 mm (see Fig. 6). Starting from the compact-sized carpet cloak design shown in Fig. 6(a), which is similar to Fig. 1(a), the ground plane is removed and the cloaked region in company with the object is mirrored on y=0. As a result, a metallic diamond-shaped object is surrounded with a free-space compact-sized cloaking material, as shown in Fig 6(b). Figs. 6(c) and 6(d) illustrate the photos of the free-space cloak and the diamond-shaped conducting object in free-space background. In the experiment, a foam, whose electromagnetic properties are similar to free space, was used to fix the metamaterials. Since the refractive indices on two sides of the cloak along the x axis are almost one as marked by the red dashed lines in Fig. 6(b), such areas can be designed as free space. The sample is fabricated by using non-resonant metamaterial unit elements similar to the compact-sized carpet cloak presented earlier. The permittivity profile is also the square of the refractive index shown in Fig. 6(b), and the corresponding dimensions of the unit cells shown in Fig. 6(c) are illustrated in Fig. 7, which are obtained from the relationship between the refractive indices (Fig. 6(b)) and the responses of unit cells (Fig. 2).

 figure: Fig. 6.

Fig. 6. The transformation optical design for the directive free-space cloak. The metamaterial cloak region is embedded in free-space background. (a) Refractive index distribution of half free-space cloak in which the mesh lines indicate the quasi-conformal mapping. (b) Expanded view of the free-space cloaking region in which the refractive indices below one are all designed as 1. (c) The photo of the fabricated metamaterial sample. (d) The side elevation of the fabricated metamaterial sample.

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 figure: Fig. 7.

Fig. 7. The dimensions (h in Fig. 1(d)) of the non-resonant unit cells for the free-space cloak shown in Fig. 6(c).

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To visualize the performance of the compact-sized and broadband free-space cloak, we make full-wave simulations based on the finite-element method. In principle, an incident electromagnetic wave would perceive a perfectly cloaked object as a metallic surface in the y=0 plane with infinitesimal thickness. Such a device will scatter the impinging wave significantly for most incident angles, except when the wave is propagating along the x direction. The simulation results are illustrated in Figs. 8(a) and 8(b) when a plane wave is impinging upon a conducting diamond-shaped object without and with the free-space cloak. A very strong shadow is observed behind the bare object, along with a weak backward scattering pattern due to the sharp edge of the diamond object (Fig. 8(a)). Subsequently, the designed cloak is placed around the diamond object. We observe that there is no shadow left as the wavefronts are bending and recomposing on the back of the object, with only a slight distortion, as shown in Fig. 8(b). Hence, the object would be effectively cloaked.

 figure: Fig. 8.

Fig. 8. Simulated electric-field distribution of the directive free-space cloak when a plane wave is incident horizontally at 10 GHz on (a) the bare metallic diamond-shaped object, (b) on the cloaked diamond-shaped object at 10 GHz. The rays display the wave propagation direction. Measured electric-field mapping of the directive free-space cloak when a plane wave is incident horizontally on (c) the bare metallic diamond-shaped object at 10 GHz, (d) the cloaked diamond-shaped object at 10 GHz, (e) the cloaked diamond-shaped object at 8 GHz, (f) the cloaked diamond-shaped object at 9 GHz, (g) the cloaked diamond-shaped object at 11 GHz, (h) the cloaked diamond-shaped object at 12 GHz.

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 figure: Fig. 9.

Fig. 9. Simulated electric-field distribution of the directive free-space cloak when a plane wave is incident with a 8-degree angle at 10 GHz on (a) the bare metallic diamond-shaped object, (b) on the cloaked diamond-shaped object at 10 GHz. The rays display the wave propagation direction. Measured electric-field mapping of the directive free-space cloak when a plane wave is incident with a 8-degree angle on (c) the bare metallic diamond-shaped object at 10 GHz, (d) the cloaked diamond-shaped object at 10 GHz, (e) the cloaked diamond-shaped object at 8 GHz, (f) the cloaked diamond-shaped object at 9 GHz, (g) the cloaked diamond-shaped object at 11 GHz, (h) the cloaked diamond-shaped object at 12 GHz.

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The measurement results of the diamond-shaped metallic object without and with the free-space directive cloak are shown in Figs. 8(c) and 8(d) when the collimated beam is incident horizontally at 10 GHz. Obviously, the measured field patterns have excellent agreements to the simulation results. From Fig. 8(d), we observe that when the wave reaches the left corner of the diamond-shaped metallic object, the index gradient is increasing away from the boundary of the object, and hence the wave bends away from the object. Then, near the tip of the object, the wave bends back towards the object because the index gradient is reversed. Finally, due to the increasing index gradient away from the object near the right corner, the wave is bent away from the object, and then return back to their original propagation direction.

To verify the broadband properties of the free-space cloak, measurements were implemented over a wide range of frequencies. The cloaking behavior has been confirmed in these measurements from 8 to 12 GHz. We illustrate the broad bandwidth of the cloak with the field maps taken at 8 GHz in Fig. 8(e), 9 GHz in Fig. 8(f), 11 GHz in Fig. 8(g) and 12 GHz in Fig. 8(h), which show similar cloaking behavior to the map taken at 10 GHz in Fig. 8(d). This method would be increasingly favorable for compact-sized cloaking objects in free-space background when considering its design simplicity, since only a few blocks of all-dielectric materials are required in order to achieve broadband and low-loss performance.

To further investigate the performance of the free-space cloak, the case that there is a 8-degree angle between incident waves and cloaked objected has been considered, as shown in Fig. 9. Similar to Fig. 8, the simulation results show that a strong shadow exists behind the object without the cloak (Fig. 9(a)), and the shadow will disappear when the object is covered with the free-space cloak (Fig. 9(b)). The corresponding measurement results are shown in Figs. 9(c) and 9(d), which demonstrate good agreements to the simulation results. The measurements were also implemented over a wide range of frequencies from 8 GHz to 12 GHz to confirm the broadband properties of the free-space cloak. The measurement results were taken at 8 GHz in Fig. 9(e), 9 GHz in Fig. 9(f), 11 GHz in Fig. 9(g), and 12 GHz in Fig. 9(h). These results also show the similar cloak behaviors to the map taken at 10 GHz. The results illustrate that such a free-space cloak also can work very well with broadband and low-loss performance, even though there exists a small angle between the incident waves and the cloaked object.

4. Conclusions

Both compact-sized carpet cloak and directive free-space cloak are designed based on the isotropic and non-resonant unit elements, hence the presented cloaks are broadband and low-loss. The agreement between the measured field patterns and the theory [7] provides convincing evidence that metamaterials can indeed be widely applied in practice. The experimental demonstration of compact-sized invisibility cloaks represents a major step towards real applications of invisibility devices.

Acknowledgments

This work was supported in part by a Major Project of the National Science Foundation of China under Grant Nos. 60990320 and 60990324, in part by the National Science Foundation of China under Grant Nos. 60871016, 60671015, 60601002, and 60621002, in part by the Natural Science Foundation of Jiangsu Province under Grant No. BK2008031, in part by the the National Basic Research Program (973) of China under Grant No. 2004CB719802, and in part by the 111 Project under Grant No. 111-2-05.

References and links

1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006). [CrossRef]   [PubMed]  

2. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006). [CrossRef]   [PubMed]  

3. D. Schurig, et al. “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006). [CrossRef]   [PubMed]  

4. J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008). [CrossRef]   [PubMed]  

5. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009). [CrossRef]   [PubMed]  

6. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009). [CrossRef]   [PubMed]  

7. E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79, 063825 (2009). [CrossRef]  

8. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwells equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008). [CrossRef]  

9. W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008). [CrossRef]  

10. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007). [CrossRef]  

11. W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E 78, 066607 (2008). [CrossRef]  

12. W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008). [CrossRef]  

13. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006). [CrossRef]   [PubMed]  

14. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006). [CrossRef]  

15. S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006). [CrossRef]  

16. H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic Wave Interactions with a Metamaterial Cloak,” Phys. Rev. Lett. 99, 063903 (2007). [CrossRef]   [PubMed]  

17. J. B. Pendry, A. J. Holden, D. J. Roberts, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999). [CrossRef]  

18. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon., in press (2009). Preprintat <http://arxiv.org/abs/0904.3508>. [CrossRef]  

19. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007). [CrossRef]   [PubMed]  

20. P. Knupp and S. Steinberg, “Fundamentals of Grid Generation,” (CRC Press, Boca Raton, 1994).

21. J. F. Thompson, B. K. Soni, and N. P. Weatherill, “Handbook of Grid Generation,” (CRC Press, Boca Raton, 1999).

22. L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys. 103, 064904 (2008). [CrossRef]  

23. B. J. Justice, J. J. Mock, L. H. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 16, 8694–8705, (2006). [CrossRef]  

References

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  • |

  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [Crossref] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [Crossref] [PubMed]
  3. D. Schurig, et al. “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
    [Crossref] [PubMed]
  4. J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
    [Crossref] [PubMed]
  5. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
    [Crossref] [PubMed]
  6. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
    [Crossref] [PubMed]
  7. E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79, 063825 (2009).
    [Crossref]
  8. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwells equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
    [Crossref]
  9. W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
    [Crossref]
  10. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
    [Crossref]
  11. W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E 78, 066607 (2008).
    [Crossref]
  12. W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
    [Crossref]
  13. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
    [Crossref] [PubMed]
  14. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
    [Crossref]
  15. S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
    [Crossref]
  16. H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic Wave Interactions with a Metamaterial Cloak,” Phys. Rev. Lett. 99, 063903 (2007).
    [Crossref] [PubMed]
  17. J. B. Pendry, A. J. Holden, D. J. Roberts, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
    [Crossref]
  18. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon., in press (2009). Preprintat <http://arxiv.org/abs/0904.3508>.
    [Crossref]
  19. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
    [Crossref] [PubMed]
  20. P. Knupp and S. Steinberg, “Fundamentals of Grid Generation,” (CRC Press, Boca Raton, 1994).
  21. J. F. Thompson, B. K. Soni, and N. P. Weatherill, “Handbook of Grid Generation,” (CRC Press, Boca Raton, 1999).
  22. L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys. 103, 064904 (2008).
    [Crossref]
  23. B. J. Justice, J. J. Mock, L. H. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 16, 8694–8705, (2006).
    [Crossref]

2009 (3)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref] [PubMed]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79, 063825 (2009).
[Crossref]

2008 (6)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwells equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E 78, 066607 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[Crossref] [PubMed]

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys. 103, 064904 (2008).
[Crossref]

2007 (3)

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
[Crossref] [PubMed]

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic Wave Interactions with a Metamaterial Cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
[Crossref]

2006 (7)

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
[Crossref] [PubMed]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[Crossref]

S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[Crossref] [PubMed]

D. Schurig, et al. “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

B. J. Justice, J. J. Mock, L. H. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 16, 8694–8705, (2006).
[Crossref]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Roberts, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Argyropoulos, C.

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79, 063825 (2009).
[Crossref]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon., in press (2009). Preprintat <http://arxiv.org/abs/0904.3508>.
[Crossref]

Chan, C. T.

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
[Crossref]

Chen, H.

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
[Crossref]

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic Wave Interactions with a Metamaterial Cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

Cheng, Q.

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E 78, 066607 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref] [PubMed]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys. 103, 064904 (2008).
[Crossref]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref] [PubMed]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E 78, 066607 (2008).
[Crossref]

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys. 103, 064904 (2008).
[Crossref]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwells equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[Crossref]

Degiron, A.

B. J. Justice, J. J. Mock, L. H. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 16, 8694–8705, (2006).
[Crossref]

Gabrielli, L. H.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon., in press (2009). Preprintat <http://arxiv.org/abs/0904.3508>.
[Crossref]

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
[Crossref] [PubMed]

Guo, L. H.

B. J. Justice, J. J. Mock, L. H. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 16, 8694–8705, (2006).
[Crossref]

Hao, Y.

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79, 063825 (2009).
[Crossref]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Roberts, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Hou, L. L.

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys. 103, 064904 (2008).
[Crossref]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref] [PubMed]

Jiang, W. X.

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E 78, 066607 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

Justice, B. J.

B. J. Justice, J. J. Mock, L. H. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 16, 8694–8705, (2006).
[Crossref]

Kallos, E.

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79, 063825 (2009).
[Crossref]

Knupp, P.

P. Knupp and S. Steinberg, “Fundamentals of Grid Generation,” (CRC Press, Boca Raton, 1994).

Kong, J. A.

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic Wave Interactions with a Metamaterial Cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
[Crossref] [PubMed]

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
[Crossref] [PubMed]

Leonhardt, U.

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[Crossref]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[Crossref] [PubMed]

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[Crossref] [PubMed]

Lipson, M.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon., in press (2009). Preprintat <http://arxiv.org/abs/0904.3508>.
[Crossref]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref] [PubMed]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

Liu, R. P.

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys. 103, 064904 (2008).
[Crossref]

Ma, H. F.

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref] [PubMed]

B. J. Justice, J. J. Mock, L. H. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 16, 8694–8705, (2006).
[Crossref]

Pendry, J. B.

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[Crossref] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwells equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
[Crossref] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Roberts, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[Crossref]

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon., in press (2009). Preprintat <http://arxiv.org/abs/0904.3508>.
[Crossref]

Popa, B. I.

S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[Crossref]

Qi, L. X.

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys. 103, 064904 (2008).
[Crossref]

Rahm, M.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwells equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwells equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

Roberts, D. J.

J. B. Pendry, A. J. Holden, D. J. Roberts, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwells equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

D. Schurig, et al. “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[Crossref]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
[Crossref] [PubMed]

B. J. Justice, J. J. Mock, L. H. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 16, 8694–8705, (2006).
[Crossref]

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[Crossref] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwells equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
[Crossref] [PubMed]

S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[Crossref]

B. J. Justice, J. J. Mock, L. H. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 16, 8694–8705, (2006).
[Crossref]

Soni, B. K.

J. F. Thompson, B. K. Soni, and N. P. Weatherill, “Handbook of Grid Generation,” (CRC Press, Boca Raton, 1999).

Steinberg, S.

P. Knupp and S. Steinberg, “Fundamentals of Grid Generation,” (CRC Press, Boca Raton, 1994).

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Roberts, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Thompson, J. F.

J. F. Thompson, B. K. Soni, and N. P. Weatherill, “Handbook of Grid Generation,” (CRC Press, Boca Raton, 1999).

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
[Crossref] [PubMed]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Weatherill, N. P.

J. F. Thompson, B. K. Soni, and N. P. Weatherill, “Handbook of Grid Generation,” (CRC Press, Boca Raton, 1999).

Wu, B. I.

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic Wave Interactions with a Metamaterial Cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

Xu, F. Y.

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys. 103, 064904 (2008).
[Crossref]

Yang, X. M.

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys. 103, 064904 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E 78, 066607 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Zhang, B.

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic Wave Interactions with a Metamaterial Cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Zhou, X. Y.

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E 78, 066607 (2008).
[Crossref]

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

Appl. Phys. Lett. (3)

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
[Crossref]

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
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IEEE Trans. Microwave Theory Tech. (1)

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J. Appl. Phys. (1)

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Nat. Mater. (1)

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Photon. Nanostruct. Fundam. Appl. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwells equations,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
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Phys. Rev. A (1)

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79, 063825 (2009).
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Phys. Rev. E (2)

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E 78, 066607 (2008).
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[Crossref]

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Figures (9)

Fig. 1.
Fig. 1. The design for a compact-sized carpet cloak in free-space background. (a) Metamaterial refractive index distribution of the complete carpet cloaking region in which the mesh lines indicate the quasi-conformal mapping. The compact-sized cloaking region is shown within the box. (b) Expanded view of the compact-sized cloaking region in which the refractive indices below one are all designed as 1. (c) Photograph of the fabricated metamaterial carpet cloak and the concealed car model. (d) The design of non-resonant elements. The dimensions of the metamaterial unit cells are a=3 mm, w=0.2 mm, l=h+2w mm, and h varying from 0 to 2.2 mm.
Fig. 2.
Fig. 2. The effective parameters of the unit cells for h (shown in Fig. 1(d)) varying from 0 to 2.2 mm.
Fig. 3.
Fig. 3. The dimensions (h in Fig. 1(d)) of the non-resonant unit cells for the simplified carpet cloak (Fig. 1(c)).
Fig. 4.
Fig. 4. Measured electric-field mapping of (a) the ground plane, (b) triangular metallic bump, and (c) ground-plane cloaked bump when collimated beam is incident at 10GHz. The rays display the wave propagation direction, and the dashed line indicates the normal of the ground in free space and that of the ground-plane cloak in the transformed space. (d) Collimated beam incident on the ground-plane cloaked bump at 11 GHz. (e) Collimated beam incident on the ground-plane cloaked bump at 12 GHz. (f) Collimated beam incident on the ground-plane cloaked bump at 13 GHz. Far-field patterns when collimated beam is incident at 10 GHz on (g) the ground plane, (h) the triangular metallic bump, (i) the carpet cloaked bump.
Fig. 5.
Fig. 5. The simulated near-electric-field distributions of (a) ground plane, (b) full-parameter carpet cloak, and (c) simplified carpet cloak. (d) The far-field patterns of above three cases.
Fig. 6.
Fig. 6. The transformation optical design for the directive free-space cloak. The metamaterial cloak region is embedded in free-space background. (a) Refractive index distribution of half free-space cloak in which the mesh lines indicate the quasi-conformal mapping. (b) Expanded view of the free-space cloaking region in which the refractive indices below one are all designed as 1. (c) The photo of the fabricated metamaterial sample. (d) The side elevation of the fabricated metamaterial sample.
Fig. 7.
Fig. 7. The dimensions (h in Fig. 1(d)) of the non-resonant unit cells for the free-space cloak shown in Fig. 6(c).
Fig. 8.
Fig. 8. Simulated electric-field distribution of the directive free-space cloak when a plane wave is incident horizontally at 10 GHz on (a) the bare metallic diamond-shaped object, (b) on the cloaked diamond-shaped object at 10 GHz. The rays display the wave propagation direction. Measured electric-field mapping of the directive free-space cloak when a plane wave is incident horizontally on (c) the bare metallic diamond-shaped object at 10 GHz, (d) the cloaked diamond-shaped object at 10 GHz, (e) the cloaked diamond-shaped object at 8 GHz, (f) the cloaked diamond-shaped object at 9 GHz, (g) the cloaked diamond-shaped object at 11 GHz, (h) the cloaked diamond-shaped object at 12 GHz.
Fig. 9.
Fig. 9. Simulated electric-field distribution of the directive free-space cloak when a plane wave is incident with a 8-degree angle at 10 GHz on (a) the bare metallic diamond-shaped object, (b) on the cloaked diamond-shaped object at 10 GHz. The rays display the wave propagation direction. Measured electric-field mapping of the directive free-space cloak when a plane wave is incident with a 8-degree angle on (c) the bare metallic diamond-shaped object at 10 GHz, (d) the cloaked diamond-shaped object at 10 GHz, (e) the cloaked diamond-shaped object at 8 GHz, (f) the cloaked diamond-shaped object at 9 GHz, (g) the cloaked diamond-shaped object at 11 GHz, (h) the cloaked diamond-shaped object at 12 GHz.

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