Abstract

In this paper, based on transformation electromagnetics, the design procedure of a lens antenna, which steers the radiated beam of a patch array, is presented. Laplace’s equation is adopted to construct the mapping between the virtual space and the physical space. The two dimensional (2D) design method can be extended to a potential three-dimensional (3D) realization, and with a proper parameter simplification, the lens can be further realized by common metamaterials or isotropic graded refractive index (GRIN) materials. Full wave simulations are performed to validate the proposed concept. It is observed that by placing the lens on a feeding source, we are able to steer the radiation emitted by the latter source.

© 2015 Optical Society of America

1. Introduction

The use of Transformation Electromagnetics (TE) [1,2] to produce material with specific specifications that control electromagnetic fields in interesting and useful ways [3,4] has been discussed. Such unprecedented flexibility in controlling EM waves by various optical elements via coordinate transformation method has inspired considerable research interests in the design of new class of optical and electromagnetic devices. The best known design by this approach is the invisibility cloak [4]. Following this success, TE technique along with metamaterial technology has resulted in the development of interesting devices, including concentrators [5], waveguide bends and transitions [69], illusion systems [1015], lenses [1620] and antennas [2130]. However, both permittivity and permeability values tailored by traditional transformation are generally inhomogeneous and anisotropic, thus entailing a huge challenge for practical implementations. Besides that, transformation medium often needs the resonant artificial electromagnetic materials, which largely limits the frequency bandwidth and performance of devices.

In order to use the full potential of TE for practical design of optical devices, it is important to relax the exact required material parameters. Obviously this would deteriorate the performance of the device. Therefore, the mathematics of the transformation should be improved to find a trade-off between the exact required material parameters and the desired performance of the device. In order to design arbitrary shaped cloaks, Hu et al. [31] proposed an equivalence between coordinate transformation and spatial deformation by using Laplace’s equation to determine the deformation of coordinate grids during the transformation. In addition, the singularity of arbitrary 2D cloaks [32] can be easily avoided by such method. In this study, it is interesting to examine Laplace’s equation with sliding boundary for quasi-isotropic material design for transformation electromagnetics, since the mapping based on Laplace’s equation together with Dirichlet-Neumann (sliding) boundary is quasi-conformal [33]. It has also been shown that quasi-conformal mapping minimizes material anisotropy.

Quasi-Conformal Transformation Optics (QCTO) was proposed and have been widely applied to design quasi-isotropic devices, such as carpet cloaks [34] and bend waveguides [35,36]. Thus, some optical devices were realized simply with dielectric materials or gradient-index metamaterials [37,38]. Therefore, QCTO opens up new horizons for antenna designs where operation bandwidth is always a key design consideration. The method has been employed to conceive high-gain and multi-beam lens antennas [39,40], to achieve high directivity through a flattened lens [41], and to design conformal devices [42]. Though confined to two-dimensional (2D) geometries with TE polarized waves, this technique can be extended to three-dimensional (3D) models via the use of suitable mathematical method.

In this paper, we use Laplace’s equation to determine the transformation matrix in a unified manner. It is shown that the function of the transformation media corresponds in fact to specific boundary conditions. By applying two different boundary conditions, two different designs of a bean steering lens antenna with different properties, which support the same functionality, are proposed. Two-dimensional full wave simulations based on finite element method are used to validate the design method. Through the two lens designs, we show the effect of ignoring anisotropy in the material parameters on the beam steering performances of the lenses.

2. Theoretical design of the lens

The scalar two-dimensional Helmholtz equation is form invariant with respect to coordinate transformations which are equivalent to a conformal mapping. Thus QCTO is an approximate solution of minimizing the anisotropy for general boundary conditions. Here, we use QCTO to propose the design of a lens capable of deflecting electromagnetic waves. To transform the angle between the wave vector k and y-axis from 0° to 45°, we propose two designs based on Laplace’s equation, as illustrated by the schematics in in Fig. 1. For the first design, the virtual space which is free space filled with air and the physical space which is the transformed medium lens are respectively presented in Figs. 1(a) and 1(b). The points B’, C’ and D’ in the physical space share the same location as B, C and D in the virtual space. We consider the length of the segment CD to equal to W and that of BC to be L. Therefore the segment AB has a length W/cos(π/4) and DA has a length W + L. The second design is illustrated by the virtual and physical spaces shown in Figs. 1(c) and 1(d). The rectangle EFGH’ is mapped from the quadrilateral EFGH, where EF’ = W, FG’ = L. In the quadrilateral EFGH, the different dimensions are: EF=W/cos(π/4), FG=25L, GH = W and EH=W+25L. The determination of the mapping is introduced by solving Laplace’s equations subject to predefined boundary conditions by Comsol Multiphysics Partial Differential Equation (PDE) solver [43].

 figure: Fig. 1

Fig. 1 Illustration of conformal mapping from the virtual space to the physical space for the two different designs of the beam steering lens.

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In Fig. 1, a color plot of the contour of the two designs is shown. For simplicity, the transformation deals with a 2D model with incident Transverse Electric (TE) polarized wave. In this case, the electric field only has the z-directed component. Suppose that the coordinate transformation between the physical space (x, y) and the virtual space (x’, y’) is x’ = f(x, y), y’ = g(x, y). The mathematical equivalence of this mapping can be expressed by a Jacobian matrix J whose elements are defined by J=(x',y')/(x,y). By solving Laplace’s equations in the virtual space with respect to specific boundary conditions, the Jacobian matrix J of the mapping can be obtained:

2x'x2+2x'y2=0,2y'x2+2y'y2=0

The physical space performs an inverse function of the virtual space. Thus the Jacobian matrix of this inverse transformation from (x, y) to (x’, y’) can be represented by J−1. Here we assume that the conformal module of the virtual space is 1 while the conformal module of the physical space is M. Once J−1 is known, the properties of the intermediate medium can be calculated. In terms of fields’ equivalence with the virtual space upon the outer boundaries, Neumann and Dirichlet boundary conditions are set at the edges of the lens. For the lens design 1, the boundary conditions are:

x'|B'C',C'D',D'A'=x,n^x'|A'B'=0y'|B'C',C'D'=y,y'|A'B'=tan(π4)*(xW2),n^y'|D'A'=0
For the lens design 2, the boundary conditions are:
x'|F'G',G'H',H'E'=x,n^x'|E'F'=0y'|G'H'=25y,y'|E'F'=tan(π4)*(xW2),n^y'|F'G',H'E'=0
where n^ is the outward normal to the surface boundaries. The designed lenses can be fully parameterized with W = 1 m and L = 0.5 m.

The properties of both lens designs shown in Fig. 2, share similar parameter variation but different range of values. It can be observed that the effective property tensors obtained from Laplace’s equation are not isotropic in the x-y plane anymore. But if the conformal module M of the physical space is not quite different with the conformal module of the virtual space, which is 1 in this case, Li and Pendry suggested that the small anisotropy can be ignored in this case [34]. Considering the polarization of the excitation, the properties of the intermediate medium can be further simplified as:

 figure: Fig. 2

Fig. 2 Material parameter values for the two different designs of the beam steering lens.

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ε=εrdet(J1),μ=1

It is clear that for the design 2 the conformal module difference between the virtual space and physical space is smaller than in design 1. In summary, the anisotropy in design 2 is smaller than in design 1.

3. Numerical validation

In this section, finite element method based numerical simulations are used to design and characterize the proposed transformed beam steering lens. In the models using Comsol Multiphysics, scattering boundary conditions are set around the computational domain. In the 2D models, a current line of length Ls = 0.1 m is used as source in the numerical simulations. The electric field of the source is polarized along the z-direction. The operation frequency is set to 10 GHz. As shown in Fig. 3, we consider that the radiation emitted by the source propagates into the lens from boundary AB’ or EF’ and exits at boundary CD’ or GH’. Both the electric field distribution and the norm of the electric field are presented in Fig. 3.

 figure: Fig. 3

Fig. 3 (a)-(b) Electric field distribution at 10 GHz illustrating the propagation of the radiated beam of a linear source through and out of the lens. (c)-(d) Norm of the electric field. A 45° beam deflection is observed in both designs.

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By applying the material properties obtained from calculations for the two different designs based on Laplace’s equation, the radiated beam is deflected by 45° after propagating through the lens, as it can be clearly observed in Fig. 3. The beam steering performances are also clearly shown by the antenna radiation patterns in Fig. 4.

 figure: Fig. 4

Fig. 4 Normalized antenna radiation patterns showing the beam steering performances of the two proposed lenses.

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In the x-y plane, the wavefronts in design 2 are less distorted compared to design 1. Out of plane, along z-direction, the distribution of ψzz also contributes in the beam steering mechanism. The anisotropy of the physical domain can be ignored since it is small enough [34]. Besides, if the in-plane anisotropy can be ignored, the proposed lenses can be further physically realized by isotropic graded refractive index (GRIN) materials. Such isotropic materials suggest a broadband frequency operation. So considering the polarization of the electric field, we neglect the permeability tensor, therefore assuming it to be the same as the virtual space (vacuum).

As shown in Fig. 5, the lenses are now assigned only a permittivity parameter along z-direction, while the permeability is isotropic. It is clear that, since the physical space of lens design 2 is less distorted and the conformal module is close to 1, the lens still steers the beam by 45° when we ignore the in-plane property tensors. On the other hand, when we assume the permeability to be isotropic in the lens design 1, the beam is steered by an angle of 28°, smaller than the expected 45°. This is due to the fact that the conformal module is much larger than 1. So the anisotropy cannot be ignored if a deflection of 45° is still desired. Therefore, the beam steering functionality is weakened when the anisotropy is ignored. If we consider the εzz distribution for both lens designs in Fig. 2, it can be noted that for design 1, εzz value ranges from 1 to 6.4. Such values can be achieved using nano- and micro-sized titanates dispersed in a polymeric host material [44] or by drilling holes in a high constant dielectric [19,20]. However for lens design 2, where 45° beam deflection is retained, εzz value ranges from 0.4 to 5.8. Though values higher than unity can be easily obtained from dielectrics, it is not the case for values less than 1. Such design 2 solution then implies the use of resonant metamaterials such as electric-LC (ELC) resonators [45] or cut wires [46,47] that present an electric resonance where the permittivity ranges from positive to negative values. However, such solution implies a limitation on the operating frequency bandwidth.

 figure: Fig. 5

Fig. 5 Permeability is assumed to be isotropic. (a)-(b) Electric field distribution at 10 GHz illustrating the propagation of the radiated beam of a linear source through and out of the lens. (c)-(d) Norm of the electric field. In the lens design 1, the beam is steered by only 28° since the conformal module is much larger than 1 and hence, beam steering capability is weakened when anisotropy is ignored. However, in lens design 2, 45° beam deflection is maintained even when ignoring material anisotropy since the conformal module is close to 1.

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Furthermore, we have designed a beam splitter by using four adjacent lenses based on the design 1. The line source is enlarged to Ls = 0.2 m and is placed in the middle of the four lenses as illustrated in Fig. 6. The electric field distribution and the norm of the electric field show clearly the transmission of four splitted beams through the lenses. The angle of deflection of the beams with respect to the normal is 28° as for the lens design 1.

 figure: Fig. 6

Fig. 6 Beam splitting device. (a) Electric field distribution at 10 GHz illustrating the transmission of four splitted beams. (b) Norm of the electric field.

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4. Conclusion

In conclusion, using transformation electromagnetics, we have proposed a concept to manipulate electromagnetic waves and design a beam steering lens. The latter manipulation is enabled by using quasi-conformal transformation and Laplace’s equation is utilized to construct the mapping between the virtual space and the physical space. Numerical verifications have been performed on two different designs; one where the conformal module of the mapping is close to 1 and another one were the conformal module is far from 1. The radiation of a current line source has been steered off the normal in both designs. It has also been observed that when ignoring material anisotropy in the design where the conformal module is far from 1, the beam steering functionality is weakened and hence, beam steering angle is less compared to the case where anisotropic parameters are used. However, when the conformal module is close to 1, material anisotropy can be ignored without deterioration of the steering performances. Such concept shows the potentials of transformation electromagnetics in both microwave and optical applications.

Acknowledgments

J. Yi acknowledges his PhD scholarship from the French Ministry of Higher Education and Research.

References and links

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4. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef]   [PubMed]  

5. 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 Maxwell’s equations,” Photon. Nanostruct.: Fundam. Appl. 6(1), 87–95 (2008). [CrossRef]  

6. M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008). [CrossRef]   [PubMed]  

7. M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008). [PubMed]  

8. D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008). [CrossRef]  

9. P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010). [CrossRef]   [PubMed]  

10. Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009). [CrossRef]   [PubMed]  

11. W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010). [CrossRef]  

12. W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(2), 026601 (2011). [CrossRef]   [PubMed]  

13. W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011). [CrossRef]  

14. W. Jiang, C.-W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013). [CrossRef]  

15. J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015). [CrossRef]  

16. D.-H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008). [CrossRef]  

17. M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008). [CrossRef]  

18. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010). [CrossRef]   [PubMed]  

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20. S. Li, Z. Zhang, J. Wang, and X. He, “Design of conformal lens by drilling holes materials using quasi-conformal transformation optics,” Opt. Express 22(21), 25455–25465 (2014). [PubMed]  

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22. J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett. 94(19), 194101 (2009). [CrossRef]  

23. B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett. 94(24), 244102 (2009). [CrossRef]  

24. Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95(19), 193506 (2009). [CrossRef]  

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26. Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84(16), 165111 (2011). [CrossRef]  

27. P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express 19(21), 20551–20556 (2011). [CrossRef]   [PubMed]  

28. C. García-Meca, A. Martínez, and U. Leonhardt, “Engineering antenna radiation patterns via quasi-conformal mappings,” Opt. Express 19(24), 23743–23750 (2011). [CrossRef]   [PubMed]  

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36. D. Liu, L. H. Gabrielli, M. Lipson, and S. G. Johnson, “Transformation inverse design,” Opt. Express 21(12), 14223–14243 (2013). [CrossRef]   [PubMed]  

37. D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036609 (2005). [CrossRef]   [PubMed]  

38. Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “A half maxwell fish-eye lens antenna based on gradient-index metamaterials,” IEEE Trans. Antenn. Propag. 60(1), 398–401 (2012). [CrossRef]  

39. I. Aghanejad, H. Abiri, and A. Yahaghi, “Design of high-gain lens antenna by gradient-index metamaterials using transformation optics,” IEEE Trans. Antenn. Propag. 60(9), 4074–4081 (2012). [CrossRef]  

40. Q. Wu, Z. H. Jiang, O. Quevedo-Teruel, J. P. Turpin, W. X. Tang, Y. Hao, and D. H. Werner, “Transformation optics inspired multibeam lens antennas for broadband directive radiation,” IEEE Trans. Antenn. Propag. 61(12), 5910–5922 (2013). [CrossRef]  

41. R. Yang, Z. Y. Lei, L. Chen, Z. X. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014). [CrossRef]  

42. R. Schmied, J. C. Halimeh, and M. Wegener, “Conformal carpet and grating cloaks,” Opt. Express 18(23), 24361–24367 (2010). [CrossRef]   [PubMed]  

43. Comsol MULTIPHYSICS Modeling, (http://www.comsol.com).

44. O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013). [CrossRef]   [PubMed]  

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47. A. Sellier, S. N. Burokur, B. Kanté, and A. de Lustrac, “Negative refractive index metamaterials using only metallic cut wires,” Opt. Express 17(8), 6301–6310 (2009). [CrossRef]   [PubMed]  

References

  • View by:

  1. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [Crossref] [PubMed]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref] [PubMed]
  3. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
    [Crossref] [PubMed]
  4. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
    [Crossref] [PubMed]
  5. 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 Maxwell’s equations,” Photon. Nanostruct.: Fundam. Appl. 6(1), 87–95 (2008).
    [Crossref]
  6. M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
    [Crossref] [PubMed]
  7. M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
    [PubMed]
  8. D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
    [Crossref]
  9. P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).
    [Crossref] [PubMed]
  10. Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
    [Crossref] [PubMed]
  11. W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
    [Crossref]
  12. W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(2), 026601 (2011).
    [Crossref] [PubMed]
  13. W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
    [Crossref]
  14. W. Jiang, C.-W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
    [Crossref]
  15. J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
    [Crossref]
  16. D.-H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
    [Crossref]
  17. M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
    [Crossref]
  18. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
    [Crossref] [PubMed]
  19. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
    [Crossref] [PubMed]
  20. S. Li, Z. Zhang, J. Wang, and X. He, “Design of conformal lens by drilling holes materials using quasi-conformal transformation optics,” Opt. Express 22(21), 25455–25465 (2014).
    [PubMed]
  21. Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online 4(7), 795–800 (2008).
    [Crossref]
  22. J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett. 94(19), 194101 (2009).
    [Crossref]
  23. B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett. 94(24), 244102 (2009).
    [Crossref]
  24. Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
    [Crossref]
  25. P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B 83(15), 155108 (2011).
    [Crossref]
  26. Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84(16), 165111 (2011).
    [Crossref]
  27. P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express 19(21), 20551–20556 (2011).
    [Crossref] [PubMed]
  28. C. García-Meca, A. Martínez, and U. Leonhardt, “Engineering antenna radiation patterns via quasi-conformal mappings,” Opt. Express 19(24), 23743–23750 (2011).
    [Crossref] [PubMed]
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  30. P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
    [Crossref] [PubMed]
  31. J. Hu, X. Zhou, and G. Hu, “Design method for electromagnetic cloak with arbitrary shapes based on Laplace’s equation,” Opt. Express 17(3), 1308–1320 (2009).
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  32. J. Hu, X. Zhou, and G. Hu, “Nonsingular two dimensional cloak of arbitrary shape,” Appl. Phys. Lett. 95(1), 011107 (2009).
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  34. J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
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  35. Z. Chang, X. Zhou, J. Hu, and G. Hu, “Design method for quasi-isotropic transformation materials based on inverse Laplace’s equation with sliding boundaries,” Opt. Express 18(6), 6089–6096 (2010).
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  36. D. Liu, L. H. Gabrielli, M. Lipson, and S. G. Johnson, “Transformation inverse design,” Opt. Express 21(12), 14223–14243 (2013).
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  38. Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “A half maxwell fish-eye lens antenna based on gradient-index metamaterials,” IEEE Trans. Antenn. Propag. 60(1), 398–401 (2012).
    [Crossref]
  39. I. Aghanejad, H. Abiri, and A. Yahaghi, “Design of high-gain lens antenna by gradient-index metamaterials using transformation optics,” IEEE Trans. Antenn. Propag. 60(9), 4074–4081 (2012).
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  40. Q. Wu, Z. H. Jiang, O. Quevedo-Teruel, J. P. Turpin, W. X. Tang, Y. Hao, and D. H. Werner, “Transformation optics inspired multibeam lens antennas for broadband directive radiation,” IEEE Trans. Antenn. Propag. 61(12), 5910–5922 (2013).
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  41. R. Yang, Z. Y. Lei, L. Chen, Z. X. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
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    [Crossref] [PubMed]
  45. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
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  46. S. N. Burokur, A. Sellier, B. Kanté, and A. de Lustrac, “Symmetry breaking in metallic cut wire pairs metamaterials for negative refractive index,” Appl. Phys. Lett. 94(20), 201111 (2009).
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  47. A. Sellier, S. N. Burokur, B. Kanté, and A. de Lustrac, “Negative refractive index metamaterials using only metallic cut wires,” Opt. Express 17(8), 6301–6310 (2009).
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2015 (1)

J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
[Crossref]

2014 (2)

S. Li, Z. Zhang, J. Wang, and X. He, “Design of conformal lens by drilling holes materials using quasi-conformal transformation optics,” Opt. Express 22(21), 25455–25465 (2014).
[PubMed]

R. Yang, Z. Y. Lei, L. Chen, Z. X. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

2013 (5)

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).
[Crossref] [PubMed]

D. Liu, L. H. Gabrielli, M. Lipson, and S. G. Johnson, “Transformation inverse design,” Opt. Express 21(12), 14223–14243 (2013).
[Crossref] [PubMed]

Q. Wu, Z. H. Jiang, O. Quevedo-Teruel, J. P. Turpin, W. X. Tang, Y. Hao, and D. H. Werner, “Transformation optics inspired multibeam lens antennas for broadband directive radiation,” IEEE Trans. Antenn. Propag. 61(12), 5910–5922 (2013).
[Crossref]

P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
[Crossref] [PubMed]

W. Jiang, C.-W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

2012 (3)

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Broadband high directivity multibeam emission through transformation optics-enabled metamaterial lenses,” IEEE Trans. Antenn. Propag. 60(11), 5063–5074 (2012).
[Crossref]

Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “A half maxwell fish-eye lens antenna based on gradient-index metamaterials,” IEEE Trans. Antenn. Propag. 60(1), 398–401 (2012).
[Crossref]

I. Aghanejad, H. Abiri, and A. Yahaghi, “Design of high-gain lens antenna by gradient-index metamaterials using transformation optics,” IEEE Trans. Antenn. Propag. 60(9), 4074–4081 (2012).
[Crossref]

2011 (6)

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B 83(15), 155108 (2011).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84(16), 165111 (2011).
[Crossref]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express 19(21), 20551–20556 (2011).
[Crossref] [PubMed]

C. García-Meca, A. Martínez, and U. Leonhardt, “Engineering antenna radiation patterns via quasi-conformal mappings,” Opt. Express 19(24), 23743–23750 (2011).
[Crossref] [PubMed]

W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(2), 026601 (2011).
[Crossref] [PubMed]

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

2010 (6)

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).
[Crossref] [PubMed]

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
[Crossref]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

Z. Chang, X. Zhou, J. Hu, and G. Hu, “Design method for quasi-isotropic transformation materials based on inverse Laplace’s equation with sliding boundaries,” Opt. Express 18(6), 6089–6096 (2010).
[PubMed]

R. Schmied, J. C. Halimeh, and M. Wegener, “Conformal carpet and grating cloaks,” Opt. Express 18(23), 24361–24367 (2010).
[Crossref] [PubMed]

2009 (8)

S. N. Burokur, A. Sellier, B. Kanté, and A. de Lustrac, “Symmetry breaking in metallic cut wire pairs metamaterials for negative refractive index,” Appl. Phys. Lett. 94(20), 201111 (2009).
[Crossref]

A. Sellier, S. N. Burokur, B. Kanté, and A. de Lustrac, “Negative refractive index metamaterials using only metallic cut wires,” Opt. Express 17(8), 6301–6310 (2009).
[Crossref] [PubMed]

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett. 94(19), 194101 (2009).
[Crossref]

B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett. 94(24), 244102 (2009).
[Crossref]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[Crossref]

J. Hu, X. Zhou, and G. Hu, “Design method for electromagnetic cloak with arbitrary shapes based on Laplace’s equation,” Opt. Express 17(3), 1308–1320 (2009).
[Crossref] [PubMed]

J. Hu, X. Zhou, and G. Hu, “Nonsingular two dimensional cloak of arbitrary shape,” Appl. Phys. Lett. 95(1), 011107 (2009).
[Crossref]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

2008 (8)

D.-H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
[Crossref]

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[Crossref]

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 Maxwell’s equations,” Photon. Nanostruct.: Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online 4(7), 795–800 (2008).
[Crossref]

2006 (5)

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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(21), 9794–9804 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[Crossref]

2005 (1)

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036609 (2005).
[Crossref] [PubMed]

Abiri, H.

I. Aghanejad, H. Abiri, and A. Yahaghi, “Design of high-gain lens antenna by gradient-index metamaterials using transformation optics,” IEEE Trans. Antenn. Propag. 60(9), 4074–4081 (2012).
[Crossref]

Aghanejad, I.

I. Aghanejad, H. Abiri, and A. Yahaghi, “Design of high-gain lens antenna by gradient-index metamaterials using transformation optics,” IEEE Trans. Antenn. Propag. 60(9), 4074–4081 (2012).
[Crossref]

Allen, J.

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett. 94(19), 194101 (2009).
[Crossref]

B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett. 94(24), 244102 (2009).
[Crossref]

Bai, J.

Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “A half maxwell fish-eye lens antenna based on gradient-index metamaterials,” IEEE Trans. Antenn. Propag. 60(1), 398–401 (2012).
[Crossref]

Burokur, S. N.

J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
[Crossref]

P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B 83(15), 155108 (2011).
[Crossref]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express 19(21), 20551–20556 (2011).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).
[Crossref] [PubMed]

S. N. Burokur, A. Sellier, B. Kanté, and A. de Lustrac, “Symmetry breaking in metallic cut wire pairs metamaterials for negative refractive index,” Appl. Phys. Lett. 94(20), 201111 (2009).
[Crossref]

A. Sellier, S. N. Burokur, B. Kanté, and A. de Lustrac, “Negative refractive index metamaterials using only metallic cut wires,” Opt. Express 17(8), 6301–6310 (2009).
[Crossref] [PubMed]

Chan, C. T.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Chang, Z.

Chen, H.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[Crossref]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online 4(7), 795–800 (2008).
[Crossref]

Chen, L.

R. Yang, Z. Y. Lei, L. Chen, Z. X. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

Cheng, Q.

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
[Crossref]

Cui, T. J.

W. Jiang, C.-W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “A half maxwell fish-eye lens antenna based on gradient-index metamaterials,” IEEE Trans. Antenn. Propag. 60(1), 398–401 (2012).
[Crossref]

W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(2), 026601 (2011).
[Crossref] [PubMed]

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

Cummer, S. A.

B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett. 94(24), 244102 (2009).
[Crossref]

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett. 94(19), 194101 (2009).
[Crossref]

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 Maxwell’s equations,” Photon. Nanostruct.: Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

de Lustrac, A.

J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
[Crossref]

P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express 19(21), 20551–20556 (2011).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B 83(15), 155108 (2011).
[Crossref]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).
[Crossref] [PubMed]

A. Sellier, S. N. Burokur, B. Kanté, and A. de Lustrac, “Negative refractive index metamaterials using only metallic cut wires,” Opt. Express 17(8), 6301–6310 (2009).
[Crossref] [PubMed]

S. N. Burokur, A. Sellier, B. Kanté, and A. de Lustrac, “Symmetry breaking in metallic cut wire pairs metamaterials for negative refractive index,” Appl. Phys. Lett. 94(20), 201111 (2009).
[Crossref]

Dyke, A.

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).
[Crossref] [PubMed]

Dyke, H.

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).
[Crossref] [PubMed]

Gabrielli, L. H.

García-Meca, C.

Germain, D.

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B 83(15), 155108 (2011).
[Crossref]

Gregory, M. D.

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Broadband high directivity multibeam emission through transformation optics-enabled metamaterial lenses,” IEEE Trans. Antenn. Propag. 60(11), 5063–5074 (2012).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84(16), 165111 (2011).
[Crossref]

Halimeh, J. C.

Han, D.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Han, T. C.

W. Jiang, C.-W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Hao, Y.

R. Yang, Z. Y. Lei, L. Chen, Z. X. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

Q. Wu, Z. H. Jiang, O. Quevedo-Teruel, J. P. Turpin, W. X. Tang, Y. Hao, and D. H. Werner, “Transformation optics inspired multibeam lens antennas for broadband directive radiation,” IEEE Trans. Antenn. Propag. 61(12), 5910–5922 (2013).
[Crossref]

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).
[Crossref] [PubMed]

Haq, S.

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).
[Crossref] [PubMed]

He, X.

Hu, G.

Hu, J.

Huangfu, J.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[Crossref]

Jiang, W.

W. Jiang, C.-W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Jiang, W. X.

W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(2), 026601 (2011).
[Crossref] [PubMed]

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
[Crossref]

Jiang, Z. H.

Q. Wu, Z. H. Jiang, O. Quevedo-Teruel, J. P. Turpin, W. X. Tang, Y. Hao, and D. H. Werner, “Transformation optics inspired multibeam lens antennas for broadband directive radiation,” IEEE Trans. Antenn. Propag. 61(12), 5910–5922 (2013).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Broadband high directivity multibeam emission through transformation optics-enabled metamaterial lenses,” IEEE Trans. Antenn. Propag. 60(11), 5063–5074 (2012).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84(16), 165111 (2011).
[Crossref]

Johnson, S. G.

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Kanté, B.

S. N. Burokur, A. Sellier, B. Kanté, and A. de Lustrac, “Symmetry breaking in metallic cut wire pairs metamaterials for negative refractive index,” Appl. Phys. Lett. 94(20), 201111 (2009).
[Crossref]

A. Sellier, S. N. Burokur, B. Kanté, and A. de Lustrac, “Negative refractive index metamaterials using only metallic cut wires,” Opt. Express 17(8), 6301–6310 (2009).
[Crossref] [PubMed]

Kong, J. A.

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online 4(7), 795–800 (2008).
[Crossref]

Kundtz, N.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett. 94(19), 194101 (2009).
[Crossref]

Kwon, D.-H.

D.-H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
[Crossref]

Lai, Y.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Lei, Z. Y.

R. Yang, Z. Y. Lei, L. Chen, Z. X. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

Leonhardt, U.

Li, J.

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

Li, S.

Lipson, M.

Liu, D.

Luo, Y.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[Crossref]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online 4(7), 795–800 (2008).
[Crossref]

Ma, H. F.

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

Martínez, A.

Mei, Z. L.

Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “A half maxwell fish-eye lens antenna based on gradient-index metamaterials,” IEEE Trans. Antenn. Propag. 60(1), 398–401 (2012).
[Crossref]

Mitchell-Thomas, R. C.

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).
[Crossref] [PubMed]

Mock, J. J.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036609 (2005).
[Crossref] [PubMed]

Ng, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Niu, T. M.

Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “A half maxwell fish-eye lens antenna based on gradient-index metamaterials,” IEEE Trans. Antenn. Propag. 60(1), 398–401 (2012).
[Crossref]

Pendry, J. B.

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (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 Maxwell’s equations,” Photon. Nanostruct.: Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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(21), 9794–9804 (2006).
[Crossref] [PubMed]

Popa, B. I.

B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett. 94(24), 244102 (2009).
[Crossref]

Psaltis, D.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[Crossref]

Qiu, C.-W.

W. Jiang, C.-W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
[Crossref] [PubMed]

Quevedo-Teruel, O.

Q. Wu, Z. H. Jiang, O. Quevedo-Teruel, J. P. Turpin, W. X. Tang, Y. Hao, and D. H. Werner, “Transformation optics inspired multibeam lens antennas for broadband directive radiation,” IEEE Trans. Antenn. Propag. 61(12), 5910–5922 (2013).
[Crossref]

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).
[Crossref] [PubMed]

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 Maxwell’s equations,” Photon. Nanostruct.: Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]

Ran, L.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[Crossref]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online 4(7), 795–800 (2008).
[Crossref]

Roberts, D. A.

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett. 94(19), 194101 (2009).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

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 Maxwell’s equations,” Photon. Nanostruct.: Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Schmied, R.

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 Maxwell’s equations,” Photon. Nanostruct.: Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[Crossref]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036609 (2005).
[Crossref] [PubMed]

Sellier, A.

A. Sellier, S. N. Burokur, B. Kanté, and A. de Lustrac, “Negative refractive index metamaterials using only metallic cut wires,” Opt. Express 17(8), 6301–6310 (2009).
[Crossref] [PubMed]

S. N. Burokur, A. Sellier, B. Kanté, and A. de Lustrac, “Symmetry breaking in metallic cut wire pairs metamaterials for negative refractive index,” Appl. Phys. Lett. 94(20), 201111 (2009).
[Crossref]

Smith, D. R.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett. 94(19), 194101 (2009).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (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 Maxwell’s equations,” Photon. Nanostruct.: Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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(21), 9794–9804 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[Crossref]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036609 (2005).
[Crossref] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036609 (2005).
[Crossref] [PubMed]

Tang, W.

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).
[Crossref] [PubMed]

Tang, W. X.

Q. Wu, Z. H. Jiang, O. Quevedo-Teruel, J. P. Turpin, W. X. Tang, Y. Hao, and D. H. Werner, “Transformation optics inspired multibeam lens antennas for broadband directive radiation,” IEEE Trans. Antenn. Propag. 61(12), 5910–5922 (2013).
[Crossref]

Tichit, P.-H.

J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
[Crossref]

P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express 19(21), 20551–20556 (2011).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B 83(15), 155108 (2011).
[Crossref]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).
[Crossref] [PubMed]

Tsang, M.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[Crossref]

Turpin, J. P.

Q. Wu, Z. H. Jiang, O. Quevedo-Teruel, J. P. Turpin, W. X. Tang, Y. Hao, and D. H. Werner, “Transformation optics inspired multibeam lens antennas for broadband directive radiation,” IEEE Trans. Antenn. Propag. 61(12), 5910–5922 (2013).
[Crossref]

Wang, J.

Wang, Z. X.

R. Yang, Z. Y. Lei, L. Chen, Z. X. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

Wegener, M.

Werner, D. H.

Q. Wu, Z. H. Jiang, O. Quevedo-Teruel, J. P. Turpin, W. X. Tang, Y. Hao, and D. H. Werner, “Transformation optics inspired multibeam lens antennas for broadband directive radiation,” IEEE Trans. Antenn. Propag. 61(12), 5910–5922 (2013).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Broadband high directivity multibeam emission through transformation optics-enabled metamaterial lenses,” IEEE Trans. Antenn. Propag. 60(11), 5063–5074 (2012).
[Crossref]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84(16), 165111 (2011).
[Crossref]

D.-H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
[Crossref]

Wu, Q.

Q. Wu, Z. H. Jiang, O. Quevedo-Teruel, J. P. Turpin, W. X. Tang, Y. Hao, and D. H. Werner, “Transformation optics inspired multibeam lens antennas for broadband directive radiation,” IEEE Trans. Antenn. Propag. 61(12), 5910–5922 (2013).
[Crossref]

Xiao, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Yahaghi, A.

I. Aghanejad, H. Abiri, and A. Yahaghi, “Design of high-gain lens antenna by gradient-index metamaterials using transformation optics,” IEEE Trans. Antenn. Propag. 60(9), 4074–4081 (2012).
[Crossref]

Yang, R.

R. Yang, Z. Y. Lei, L. Chen, Z. X. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

Yang, X. M.

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

Yi, J.

J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
[Crossref]

Zhang, J.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[Crossref]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online 4(7), 795–800 (2008).
[Crossref]

Zhang, L.

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).
[Crossref] [PubMed]

Zhang, S.

W. Jiang, C.-W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Zhang, Z.

Zhang, Z.-Q.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Zhou, X.

Adv. Funct. Mater. (1)

W. Jiang, C.-W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Appl. Phys. Lett. (9)

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96(12), 121910 (2010).
[Crossref]

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett. 94(19), 194101 (2009).
[Crossref]

B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett. 94(24), 244102 (2009).
[Crossref]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[Crossref]

J. Hu, X. Zhou, and G. Hu, “Nonsingular two dimensional cloak of arbitrary shape,” Appl. Phys. Lett. 95(1), 011107 (2009).
[Crossref]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[Crossref]

S. N. Burokur, A. Sellier, B. Kanté, and A. de Lustrac, “Symmetry breaking in metallic cut wire pairs metamaterials for negative refractive index,” Appl. Phys. Lett. 94(20), 201111 (2009).
[Crossref]

IEEE Trans. Antenn. Propag. (5)

Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “A half maxwell fish-eye lens antenna based on gradient-index metamaterials,” IEEE Trans. Antenn. Propag. 60(1), 398–401 (2012).
[Crossref]

I. Aghanejad, H. Abiri, and A. Yahaghi, “Design of high-gain lens antenna by gradient-index metamaterials using transformation optics,” IEEE Trans. Antenn. Propag. 60(9), 4074–4081 (2012).
[Crossref]

Q. Wu, Z. H. Jiang, O. Quevedo-Teruel, J. P. Turpin, W. X. Tang, Y. Hao, and D. H. Werner, “Transformation optics inspired multibeam lens antennas for broadband directive radiation,” IEEE Trans. Antenn. Propag. 61(12), 5910–5922 (2013).
[Crossref]

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Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Broadband high directivity multibeam emission through transformation optics-enabled metamaterial lenses,” IEEE Trans. Antenn. Propag. 60(11), 5063–5074 (2012).
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J. Appl. Phys. (1)

J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
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Nat. Commun. (1)

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Opt. Express (11)

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J. Hu, X. Zhou, and G. Hu, “Design method for electromagnetic cloak with arbitrary shapes based on Laplace’s equation,” Opt. Express 17(3), 1308–1320 (2009).
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Figures (6)

Fig. 1
Fig. 1 Illustration of conformal mapping from the virtual space to the physical space for the two different designs of the beam steering lens.
Fig. 2
Fig. 2 Material parameter values for the two different designs of the beam steering lens.
Fig. 3
Fig. 3 (a)-(b) Electric field distribution at 10 GHz illustrating the propagation of the radiated beam of a linear source through and out of the lens. (c)-(d) Norm of the electric field. A 45° beam deflection is observed in both designs.
Fig. 4
Fig. 4 Normalized antenna radiation patterns showing the beam steering performances of the two proposed lenses.
Fig. 5
Fig. 5 Permeability is assumed to be isotropic. (a)-(b) Electric field distribution at 10 GHz illustrating the propagation of the radiated beam of a linear source through and out of the lens. (c)-(d) Norm of the electric field. In the lens design 1, the beam is steered by only 28° since the conformal module is much larger than 1 and hence, beam steering capability is weakened when anisotropy is ignored. However, in lens design 2, 45° beam deflection is maintained even when ignoring material anisotropy since the conformal module is close to 1.
Fig. 6
Fig. 6 Beam splitting device. (a) Electric field distribution at 10 GHz illustrating the transmission of four splitted beams. (b) Norm of the electric field.

Equations (4)

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2 x' x 2 + 2 x' y 2 =0, 2 y' x 2 + 2 y' y 2 =0
x'| B'C',C'D',D'A' =x , n ^ x'| A'B' =0 y'| B'C',C'D' =y ,y'| A'B' =tan( π 4 ) *( x W 2 ), n ^ y'| D'A' =0
x'| F'G',G'H',H'E' =x , n ^ x'| E'F' =0 y'| G'H' = 2 5 y ,y'| E'F' =tan( π 4 ) *( x W 2 ), n ^ y'| F'G',H'E' =0
ε= ε r det( J 1 ) ,μ=1

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