Abstract

Transformation optics is extended to the design of two-dimensional (2D) cloaks with non-conformal inner and outer boundaries. General and explicit expressions of the transformed medium parameters are derived, which are of the utmost importance in a cloak design procedure. A 2D cloak with irregular and non-conformal boundaries is designed as an example. Full-wave simulations combined with Huygens’ Principle are applied to verify the invisibility of the cloak to external incident waves. All the theoretical and numerical results verify the effectiveness of the proposed method. The generalization in this Paper highly improves the flexibilities for cloak design.

© 2008 Optical Society of America

1. Introduction

Recently, transformation optics opens an exciting gateway to design optical and electromagnetic (EM) ‘invisibility cloak devices’ and becomes a topic of great interest in applied optics and electromagnetics society [1-23]. The basic principle is to squeeze a volume in a virtual space into a shell with complex medium parameters in the physical space, which excluding EM waves in the concealment volume [1-4]. Experimentally, an invisible cloak with simplified material parameters has been implemented at microwave regime [2] and a nonmagnetic cloak is designed at optical wavelengths [5]. The possibility of the ‘invisibility’ was lately studied intensively with analytical and numerical methods [6-14]. For example, the sensitivity of the field to the tiny perturbations of the cloak’s parameters was studied in Ref. 6 and 7, and the method to extend the bandwidth of the cloaks was studied in Ref. 8. Inspired by the idea of the invisible cloak, some interesting applications, such as the concentrators [15] and field rotators [16], have also been proposed. Up to now, most of the studies are focused on the spherical and cylindrical cloaks [1-14] with rotational symmetry. Latterly, cloaks possessing geometries with reduced symmetries, such as elliptic cylinders [17], eccentric elliptic cylinders [18] and square cloaks [15] were proposed. Most recently, design of cloaks with arbitrary shapes was investigated by the authors [19] and other research groups [20-22]. However, for all the structures mentioned above, the inner and outer boundaries of the cloaks are geometrically conformal. In practice, it is sometimes desirable to make the outer boundary of a cloak not conformal to its inner boundary. For example, Kwon and Werner have proposed a 2D elliptic cloak with a uniform thickness, which is more convenient to conceal objects with long and thin shapes [23]. However, their transformation procedure is only suitable for design of cloaks with their individual shape. Although the medium parameters of invisibility cloaks with arbitrary non-conformal boundaries can be obtained numerically as proposed by Hao et.al.[24], their method is still inconvenient for the analysis and design of cloaks since the medium parameters should be derived point by point with complex matrix operations.

Toward the practical and flexible realizations of EM cloaks, this Paper presents a general transformation method to design 2D cloaks with non-conformal inner and outer boundaries. The general and explicit expressions for the complex medium parameters are derived, which is the fundamental of a cloak design procedure. A 2D cloak device with irregular and non-conformal boundaries is designed. Full-wave simulation results are provided for verification. The invisibility of the cloak to external incident waves is also quantitatively evaluated based on the Huygens’ Principle, in which the scatter width is calculated from the simulated near field. The generalization in this Paper highly improves the flexibilities for cloak design.

2. Medium transformation for 2D EM cloaks with non-conformal boundaries

In the original space, a point can be described by (x, y, z) in Cartesian coordinate or (r, θ, z) in Cylindrical coordinate with relationship

x=rcosθ,y=rsinθ.

To compress the cylindrical volume defined by rR 2(θ) in the original space into an annular volume defined by R1(θ’)≤r’≤R 2(θ’) in the transformed space, the coordinate transformation can be defined as

r'=R1(θ)+R2(θ)R1(θ)R2(θ)r,θ'=θ,z'=z.

Outside this domain the identity transformation is adopted. Then,

x'=r'cosθ',y'=r'sinθ'

is applied to complete the whole transformation between the transformed Cartesian coordinate (x’, y’, z’) and the original Cartesian coordinate (x, y, z), which can finally be derived as

x'=xx2+y2R1(tan1yx)+xR2(tan1yx)R1(tan1yx)R2(tan1yx),
y'=yx2+y2R1(tan1yx)+yR2(tan1yx)R1(tan1yx)R2(tan1yx),
z'=z.

According to the form-invariant transformation theorem of Maxwell’s Equations, the associated permittivity and permeability tensors of the transformation media become [3]

εi'j'=det(Λii')1Λii'Λjj'εij,μi'j'=det(Λii')1Λii'Λjj'μij,

where

Λii'=qi'qi

is the Jacobian matrix between the transformed and the initial coordinates. Substitute Eq.(4) into (5), the resultant permittivity and permeability tensors become

εx'x'={[r'R1(θ')]2+U2}cos2θ'2Ur'sinθ'cosθ'+r'2sin2θ'r'[r'R1(θ')],
εx'y'=εy'x'={U2R1(θ')[2r'R1(θ')]}sinθ'cosθ'+Ur'(cos2θ'sin2θ')r'[r'R1(θ')],
εy'y'={[r'R1(θ')]2+U2}sin2θ'+2Ur'sinθ'cosθ'+r'2cos2θ'r'[r'R1(θ')],
εz'z'=r'R1(θ')r'[R2(θ')R2(θ')R1(θ')]2.

where

U=[r'R1(θ')]R1(θ')dR2(θ')dθ'[r'R2(θ')]dR1(θ')dθ'R2(θ')R2(θ')[R2(θ')R1(θ')].

The permeability tensor µ⇉′ is equal to ε⇉′. Here

dR1(θ')dθ'anddR2(θ')dθ'

represent the first order derivative of R1(θ’) and R2(θ’) over θ’. Eqs. (6)-(7) gives the general and explicit expressions of the medium parameters for 2D cloaks with arbitrarily non-conformal boundaries. For the special case R1(θ’)=τR2(θ’), where τ<1 represents the linear compression ratio between the inner and outer boundaries, the tensors in Eq. (6) can be simplified as

εx'x'=[r'τR2(θ')]2cos2θ'+τ2[dR2(θ')dθ']2cos2θ'2τr'dR2(θ')dθ'sinθ'cosθ'+r'2sin2θ'r'[r'τR2(θ')]
εx'y'=εy'x''=τR2(θ')[2r'τR2(θ')]sinθ'cosθ'+τ2sinθ'cosθ'[dR2(θ')dθ']2+τr'dR2(θ')dθ'(cos2θ'sin2θ')r'[r'τR2(θ')]
εy'y'=[r'τR2(θ')]2sin2θ'+τ2[dR2(θ')dθ']2sin2θ'+2τr'dR2(θ')dθ'sinθ'cosθ'+r'2cos2θ'r'[r'τR2(θ')]
εz'z'=(11τ)2r'τR2(θ')r'

Equation (8) is the medium parameters of 2D cloaks with conformal boundaries, as developed in Ref.19. For a cloak with uniform thickness T, we can set R2(θ’)=R1(θ’)+T in Eq. (6) to obtain the medium parameters. In fact, R1(θ’) and R2(θ’) can be chosen as arbitrary continuous functions with period 2π to represent closed contours with arbitrary shapes. They can be generally expressed by a Fourier series as

n=0Ancos(nθ')+n=1Bnsin(nθ')

If

dR1(θ')dθ'

and

dR2(θ')dθ'

are both continuous, the medium parameters will be continuously varying in the cloak region. If

dR1(θ')dθ'

or

dR2(θ')dθ'

is discontinuous in certain θd, which means the cloaks have sharp corners, the medium parameters will be discontinuous at the corresponding positions. Fortunately, it has been verified by the square cloak in Ref.15 that, such discontinuity does not break any fundamental cloaking properties. The above discussion means the generalization in this Paper can be specialized to all of the formerly designed cloaks.

 

Fig. 1. Generalized coordinate transformation. (a) The original space. (b) The transformed space. The region with r≤R2(θ) (shaded) in (a) is transformed to the region with R1(θ’)≤r’≤R2(θ’) (shaded) in (b).

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3. Electromagntic properties of a 2D cloak with non-conformal boundaries

To show the flexibility of the approach to design 2D irregular cloaks with non-conformal inner and outer boundaries,

R1(θ')=[12+2cos(θ')+sin(2θ')2sin(3θ')]/30,
R2(θ')=[10+sin(θ')sin(2θ')+2cos(5θ')]/12,

are chosen as an example. In this section, the interactions of the electromagnetic waves with the irregular cloak are studied. The exciting TM plane wave has an electric filed polarized in z’ direction with unit amplitude Ein′=ẑ′exp(-jk0 x′), and incident upon the cloak along the +x’ direction. The frequency of the time harmonic incident wave is set to be 1 GHz. Theoretically, the inner region of the cloak is shielded from external fields and consequently an object of any shape and material placed in it has no impact on the external fields. And the field distribution in the transformed space can be analytically mapped from the field distribution in the original space based on the transformation theory.

Ei'=qiqi'Ei

Figure 2 shows the theoretical electric field distribution by field transformation. The inner and outer boundaries of the cloak are shown as the black contours. The green lines indicate the electromagnetic power-flow lines. It’s seen that the electromagnetic waves are naturally guided around the inner region by the cloak with non-conformal inner and outer boundaries.

 

Fig. 2. Electric field distribution in the vicinity of the cloak obtained based on analytical field transformation. The green lines show the flow of EM power.

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Fig. 3. Full-wave simulation results for electric field distribution in the vicinity of the PEC cylinder without cloak.

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To further verify the field transformation and the medium parameters, the cloak performance is also investigated numerically based on finite-element method (FEM). In simulation, we fill the inner region of the cloak with perfect electric conductor (PEC) and see whether it can be “seen” from outside. Perfect matched layers (PMLs) are applied to terminate the computational domain in ±x’ and ±y’ directions to avoid unwanted reflections. In Fig. 3, the irregular PEC cylinder is directly exposed to the incoming wave, where strong scattering can be observed. Figure 4 shows the electric field distribution near the cloaked structure. It’s seen that, the wave is smoothly bent around the cloaked area and the phase fronts are perfectly restored when the wave exits the cloak. The field distribution agrees well with the theoretical results in Fig. 2.

 

Fig. 4. Full-wave simulation results for electric field distribution in the vicinity of the cloaked PEC cylinder with non-conformal boundaries (excited by a TM plane wave).

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Fig. 5. Full-wave simulation results for electric field distribution in the vicinity of the cloaked PEC cylinder with irregular shape (excited by a TM cylindrical wave).

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Since the proposed cloak has no symmetry in any directions, it’s necessary to study its interaction with EM waves from different orientations. An effective way is to investigate its property under the illumination of a cylindrical wave, which can be decomposed to different planar wave components. In the simulation, a line source is set at the position x’=-0.8m, y’=- 0.8m to generate the cylindrical wave. The results are given in Fig. 5. It’s seen that the cylindrical wave is perfectly guided around the cloaked object, and the circular phase fronts are remained outside the cloak without any obvious scattering.

To quantitatively evaluate the cloaking performance, the scatter width σ (the 2D equivalent of a radar cross section) is calculated based on the Huygens’ Principle. To determine σ, the scattered electric field in far field region is calculated by the integration of the simulated near field [19],

σ=k0r̂0×C[(n̂×Ec)η0r̂0×(n̂×Hc)]exp(ikr'·r̂0)dl24Ei2

where Ec and Hc is the EM fields on the integration contour C, r̂0 is the unit vector of the scattering direction, r⃗′ is the position vector on the contour C, and η0 is the free space wave impedance. In Fig. 6, the scatter widths of the PEC cylinder with and without cloaks are both calculated for comparison. Considering the non-symmetry of the structure, the scatter widths for TM plane waves from four different incident directions are studied. Table1 lists some parameters to describe and compare the scattering properties, including the averaged scatter widths σavg, the maximum scatter widths σmax, and the ratios between the cases with and without cloaks. It’s seen that the cloak greatly reduces the scatter width in different scattering angles. The total scatter power (equivalent to the averaged scatter width) of the irregular PEC cylinder is reduced more than 30 times and the maximum scatter width is reduced more than 160 times. No doubt the ratios could be pushed even larger with finer meshes in simulation. A more interesting phenomenon is that the scattering power of the cloaked structure is almost isotropy over all the angles, which is very different from conventional scattering from objects with irregular shapes.

 

Fig. 6. The scatter width of the cloaked and uncloaked PEC cylinder for different incident directions. The dotted lines are for PEC cylinder without cloak. The solid lines are for PEC cylinder with cloak. The blue, red, black, and green lines are for the incident direction (angle)+x(θ i=0°), -x(θ i=180°), +y(θ i=90°), -y(θ i=270°), respectively.

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Tables Icon

Table 1. Some parameters to describe and compare the scatter properties

4. Conclusion

A general transformation procedure for designing 2D cloaks with non-conformal inner and outer boundaries is demonstrated. The explicit expressions for the complex medium parameters are developed, which can be readily specialized to all of the previously designed 2D cloaks. A peculiar cloak device with irregular and non-conformal boundaries is designed as an example. Full-wave simulations combined with Huygens’ Principle are applied to verify the invisibility of the cloak to external incident waves. All the theoretical and numerical results verify the effectiveness of the proposed method. Although we confine ourselves to 2D cases in this paper, the method can be readily extended to design three dimensional (3D) cloaks with non-conformal boundaries. The generalization in this Paper highly improves the flexibilities for cloak design.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (60501018), the National Basic Research Program of China under Grant (2004CB719800), and the Knowledge Innovation Program of Chinese Academy of Sciences.

References and links

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

2. 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, 977–980 (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, 9794–9804 (2006). [CrossRef]   [PubMed]  

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

5. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007). [CrossRef]  

6. Z. Ruan, M. Yan., C. W. Neff, and M. Qiu, “Ideal Cylindrical Cloak:Perfect but Sensitive to Tiny Perturbations,” Phys. Rev. Lett. 99, 113903 (2007). [CrossRef]   [PubMed]  

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

8. H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007). [CrossRef]  

9. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Improvement of cylindrical cloaking with the SHS lining,” Opt. Express 15, 12717–12734 (2007). [CrossRef]   [PubMed]  

10. Y. Huang, Y. J. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15, 11133–11141 (2007). [CrossRef]   [PubMed]  

11. M. Yan, Z. C. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007). [CrossRef]   [PubMed]  

12. G. Isic, R. Gajic, B. Novakovic, Z. V. Popovic, and K. Hingerl, “Radiation and scattering from imperfect cylindrical electromagnetic cloaks,” Opt. Express 16, 1413–1422 (2008). [CrossRef]   [PubMed]  

13. Y. Zhao, C. Argyropoulos, and Y. Hao, “Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures,” Opt. Express 16, 6717–6730 (2008). [CrossRef]   [PubMed]  

14. F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).

15. 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 Transfromations of Maxwell’s Equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008). [CrossRef]  

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

17. H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2007). [CrossRef]  

18. D. H. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008). [CrossRef]  

19. C. Li and F. Li, “Two-dimensional electromagnetic cloaks with arbitrary geometries,” Opt. Express 16, 13414–13420 (2008). [CrossRef]   [PubMed]  

20. W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008). [CrossRef]  

21. Y. You, G. W. Kattawar, P-W Zhai, and P. Yang, “Invisibility cloaks for irregular particles using coordinate transformations,” Opt. Express 16, 6134–6145 (2008). [CrossRef]   [PubMed]  

22. W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E 77, 066607 (2008). [CrossRef]  

23. D. H. Kwon and D. H. Werner, “Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions,” Appl. Phys. Lett. 92, 013505 (2008). [CrossRef]  

24. X. Hou, Q. Xu, P. Niu, and F. L. Teixeira, “Numerical design of arbitrarily shaped electromagnetic cloaks,” International Conference on Microwave and Millimeter Wave Technology, 2008, ICMMT 2008 3, 1565–1568 (2008) [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. 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, 977–980 (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, 9794–9804 (2006).
    [Crossref] [PubMed]
  4. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys 8, 247 (2006).
    [Crossref]
  5. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
    [Crossref]
  6. Z. Ruan, M. Yan., C. W. Neff, and M. Qiu, “Ideal Cylindrical Cloak:Perfect but Sensitive to Tiny Perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
    [Crossref] [PubMed]
  7. H. S. Chen, B.-I. Wu, B. L. Zhang, and J. A. Kong, “Electromagnetic wave Interactions with a Metamaterial Cloak,” Phys. Rev. Lett. 99, 063903 (2007).
    [Crossref] [PubMed]
  8. H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
    [Crossref]
  9. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Improvement of cylindrical cloaking with the SHS lining,” Opt. Express 15, 12717–12734 (2007).
    [Crossref] [PubMed]
  10. Y. Huang, Y. J. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15, 11133–11141 (2007).
    [Crossref] [PubMed]
  11. M. Yan, Z. C. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
    [Crossref] [PubMed]
  12. G. Isic, R. Gajic, B. Novakovic, Z. V. Popovic, and K. Hingerl, “Radiation and scattering from imperfect cylindrical electromagnetic cloaks,” Opt. Express 16, 1413–1422 (2008).
    [Crossref] [PubMed]
  13. Y. Zhao, C. Argyropoulos, and Y. Hao, “Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures,” Opt. Express 16, 6717–6730 (2008).
    [Crossref] [PubMed]
  14. F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
  15. 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 Transfromations of Maxwell’s Equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
    [Crossref]
  16. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
    [Crossref]
  17. H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2007).
    [Crossref]
  18. D. H. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008).
    [Crossref]
  19. C. Li and F. Li, “Two-dimensional electromagnetic cloaks with arbitrary geometries,” Opt. Express 16, 13414–13420 (2008).
    [Crossref] [PubMed]
  20. W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
    [Crossref]
  21. Y. You, G. W. Kattawar, P-W Zhai, and P. Yang, “Invisibility cloaks for irregular particles using coordinate transformations,” Opt. Express 16, 6134–6145 (2008).
    [Crossref] [PubMed]
  22. W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E 77, 066607 (2008).
    [Crossref]
  23. D. H. Kwon and D. H. Werner, “Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions,” Appl. Phys. Lett. 92, 013505 (2008).
    [Crossref]
  24. X. Hou, Q. Xu, P. Niu, and F. L. Teixeira, “Numerical design of arbitrarily shaped electromagnetic cloaks,” International Conference on Microwave and Millimeter Wave Technology, 2008, ICMMT 2008 3, 1565–1568 (2008)
    [Crossref]

2008 (10)

G. Isic, R. Gajic, B. Novakovic, Z. V. Popovic, and K. Hingerl, “Radiation and scattering from imperfect cylindrical electromagnetic cloaks,” Opt. Express 16, 1413–1422 (2008).
[Crossref] [PubMed]

Y. Zhao, C. Argyropoulos, and Y. Hao, “Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures,” Opt. Express 16, 6717–6730 (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 Transfromations of Maxwell’s Equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[Crossref]

D. H. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008).
[Crossref]

C. Li and F. Li, “Two-dimensional electromagnetic cloaks with arbitrary geometries,” Opt. Express 16, 13414–13420 (2008).
[Crossref] [PubMed]

W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
[Crossref]

Y. You, G. W. Kattawar, P-W Zhai, and P. Yang, “Invisibility cloaks for irregular particles using coordinate transformations,” Opt. Express 16, 6134–6145 (2008).
[Crossref] [PubMed]

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

D. H. Kwon and D. H. Werner, “Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions,” Appl. Phys. Lett. 92, 013505 (2008).
[Crossref]

X. Hou, Q. Xu, P. Niu, and F. L. Teixeira, “Numerical design of arbitrarily shaped electromagnetic cloaks,” International Conference on Microwave and Millimeter Wave Technology, 2008, ICMMT 2008 3, 1565–1568 (2008)
[Crossref]

2007 (10)

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

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2007).
[Crossref]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
[Crossref]

Z. Ruan, M. Yan., C. W. Neff, and M. Qiu, “Ideal Cylindrical Cloak:Perfect but Sensitive to Tiny Perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[Crossref] [PubMed]

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

H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[Crossref]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Improvement of cylindrical cloaking with the SHS lining,” Opt. Express 15, 12717–12734 (2007).
[Crossref] [PubMed]

Y. Huang, Y. J. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15, 11133–11141 (2007).
[Crossref] [PubMed]

M. Yan, Z. C. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
[Crossref] [PubMed]

2006 (4)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (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, 977–980 (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]

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

Argyropoulos, C.

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
[Crossref]

Chan, C. T.

H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[Crossref]

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

Chen, B. W.

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2007).
[Crossref]

Chen, H.

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

Chen, H. S.

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

Chen, H. Y.

H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[Crossref]

Cheng, Q.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
[Crossref]

Chin, J. Y.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

Cui, T. J.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E 77, 066607 (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 Transfromations of Maxwell’s Equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (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, 977–980 (2006).
[Crossref] [PubMed]

Feng, Y. J.

Gajic, R.

Greenleaf, A.

Guenneau, S.

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).

Hao, Y.

Hingerl, K.

Hou, X.

X. Hou, Q. Xu, P. Niu, and F. L. Teixeira, “Numerical design of arbitrarily shaped electromagnetic cloaks,” International Conference on Microwave and Millimeter Wave Technology, 2008, ICMMT 2008 3, 1565–1568 (2008)
[Crossref]

Huang, Y.

Isic, G.

Jiang, T.

Jiang, W. X.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

Jiang, X. Y.

H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[Crossref]

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, 977–980 (2006).
[Crossref] [PubMed]

Kattawar, G. W.

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
[Crossref]

Kong, J. A.

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

Kurylev, Y.

Kwon, D. H.

D. H. Kwon and D. H. Werner, “Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions,” Appl. Phys. Lett. 92, 013505 (2008).
[Crossref]

D. H. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008).
[Crossref]

Lassas, M.

Leonhardt, U.

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

Li, C.

Li, F.

Li, Z.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

Liang, Z. X.

H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[Crossref]

Liu, R. P.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

Ma, H.

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2007).
[Crossref]

H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[Crossref]

Mock, J. 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, 977–980 (2006).
[Crossref] [PubMed]

Neff, C. W.

Z. Ruan, M. Yan., C. W. Neff, and M. Qiu, “Ideal Cylindrical Cloak:Perfect but Sensitive to Tiny Perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[Crossref] [PubMed]

Nicolet, A.

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).

Niu, P.

X. Hou, Q. Xu, P. Niu, and F. L. Teixeira, “Numerical design of arbitrarily shaped electromagnetic cloaks,” International Conference on Microwave and Millimeter Wave Technology, 2008, ICMMT 2008 3, 1565–1568 (2008)
[Crossref]

Novakovic, B.

Pendry, J. B.

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 Transfromations of Maxwell’s Equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[Crossref]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).

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, 977–980 (2006).
[Crossref] [PubMed]

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]

Philbin, T. G.

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

Popovic, Z. V.

Qiu, M.

W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
[Crossref]

Z. Ruan, M. Yan., C. W. Neff, and M. Qiu, “Ideal Cylindrical Cloak:Perfect but Sensitive to Tiny Perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[Crossref] [PubMed]

M. Yan, Z. C. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
[Crossref] [PubMed]

Qu, S.

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2007).
[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 Transfromations of Maxwell’s Equations,” Photon. Nanostruct.: Fundam. Applic. 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 Transfromations of Maxwell’s Equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[Crossref]

Ruan, Z.

Z. Ruan, M. Yan., C. W. Neff, and M. Qiu, “Ideal Cylindrical Cloak:Perfect but Sensitive to Tiny Perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[Crossref] [PubMed]

Ruan, Z. C.

W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
[Crossref]

M. Yan, Z. C. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
[Crossref] [PubMed]

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 Transfromations of Maxwell’s Equations,” Photon. Nanostruct.: Fundam. Applic. 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. 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, 977–980 (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]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
[Crossref]

Smith, D. R.

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 Transfromations of Maxwell’s Equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[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]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (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, 977–980 (2006).
[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, 977–980 (2006).
[Crossref] [PubMed]

Teixeira, F. L.

X. Hou, Q. Xu, P. Niu, and F. L. Teixeira, “Numerical design of arbitrarily shaped electromagnetic cloaks,” International Conference on Microwave and Millimeter Wave Technology, 2008, ICMMT 2008 3, 1565–1568 (2008)
[Crossref]

Uhlmann, G.

Wang, J. F.

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2007).
[Crossref]

Werner, D. H.

D. H. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008).
[Crossref]

D. H. Kwon and D. H. Werner, “Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions,” Appl. Phys. Lett. 92, 013505 (2008).
[Crossref]

Wu, B.-I.

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

Xu, Q.

X. Hou, Q. Xu, P. Niu, and F. L. Teixeira, “Numerical design of arbitrarily shaped electromagnetic cloaks,” International Conference on Microwave and Millimeter Wave Technology, 2008, ICMMT 2008 3, 1565–1568 (2008)
[Crossref]

Xu, Z.

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2007).
[Crossref]

Yan, M.

W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
[Crossref]

M. Yan, Z. C. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
[Crossref] [PubMed]

Yan, W.

W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
[Crossref]

Yan., M.

Z. Ruan, M. Yan., C. W. Neff, and M. Qiu, “Ideal Cylindrical Cloak:Perfect but Sensitive to Tiny Perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[Crossref] [PubMed]

Yang, P.

Yao, P. J.

H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[Crossref]

You, Y.

Zhai, P-W

Zhang, B. L.

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

Zhang, J. Q.

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2007).
[Crossref]

Zhao, Y.

Zolla, F.

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).

Appl. Phys. Lett. (3)

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

D. H. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008).
[Crossref]

D. H. Kwon and D. H. Werner, “Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions,” Appl. Phys. Lett. 92, 013505 (2008).
[Crossref]

International Conference on Microwave and Millimeter Wave Technology, 2008, ICMMT 2008 (1)

X. Hou, Q. Xu, P. Niu, and F. L. Teixeira, “Numerical design of arbitrarily shaped electromagnetic cloaks,” International Conference on Microwave and Millimeter Wave Technology, 2008, ICMMT 2008 3, 1565–1568 (2008)
[Crossref]

Nat. Photon. (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
[Crossref]

New J. Phys (1)

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

New J. Phys. (1)

W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
[Crossref]

Opt. Express (8)

Opt. Lett. (1)

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).

Photon. Nanostruct.: Fundam. Applic. (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 Transfromations of Maxwell’s Equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[Crossref]

Phys. Rev. A (1)

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2007).
[Crossref]

Phys. Rev. B (1)

H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[Crossref]

Phys. Rev. E (1)

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

Phys. Rev. Lett. (2)

Z. Ruan, M. Yan., C. W. Neff, and M. Qiu, “Ideal Cylindrical Cloak:Perfect but Sensitive to Tiny Perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[Crossref] [PubMed]

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

Science (2)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (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, 977–980 (2006).
[Crossref] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

Generalized coordinate transformation. (a) The original space. (b) The transformed space. The region with r≤R2(θ) (shaded) in (a) is transformed to the region with R1(θ’)≤r’≤R2(θ’) (shaded) in (b).

Fig. 2.
Fig. 2.

Electric field distribution in the vicinity of the cloak obtained based on analytical field transformation. The green lines show the flow of EM power.

Fig. 3.
Fig. 3.

Full-wave simulation results for electric field distribution in the vicinity of the PEC cylinder without cloak.

Fig. 4.
Fig. 4.

Full-wave simulation results for electric field distribution in the vicinity of the cloaked PEC cylinder with non-conformal boundaries (excited by a TM plane wave).

Fig. 5.
Fig. 5.

Full-wave simulation results for electric field distribution in the vicinity of the cloaked PEC cylinder with irregular shape (excited by a TM cylindrical wave).

Fig. 6.
Fig. 6.

The scatter width of the cloaked and uncloaked PEC cylinder for different incident directions. The dotted lines are for PEC cylinder without cloak. The solid lines are for PEC cylinder with cloak. The blue, red, black, and green lines are for the incident direction (angle)+x(θ i=0°), -x(θ i=180°), +y(θ i=90°), -y(θ i=270°), respectively.

Tables (1)

Tables Icon

Table 1. Some parameters to describe and compare the scatter properties

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

x = r cos θ , y = r sin θ .
r ' = R 1 ( θ ) + R 2 ( θ ) R 1 ( θ ) R 2 ( θ ) r , θ ' = θ , z ' = z .
x ' = r ' cos θ ' , y ' = r ' sin θ '
x ' = x x 2 + y 2 R 1 ( tan 1 y x ) + x R 2 ( tan 1 y x ) R 1 ( tan 1 y x ) R 2 ( tan 1 y x ) ,
y ' = y x 2 + y 2 R 1 ( tan 1 y x ) + y R 2 ( tan 1 y x ) R 1 ( tan 1 y x ) R 2 ( tan 1 y x ) ,
z ' = z .
ε i ' j ' = det ( Λ i i ' ) 1 Λ i i ' Λ j j ' ε ij , μ i ' j ' = det ( Λ i i ' ) 1 Λ i i ' Λ j j ' μ ij ,
ε x ' x ' = { [ r ' R 1 ( θ ' ) ] 2 + U 2 } cos 2 θ ' 2 U r ' sin θ ' cos θ ' + r ' 2 sin 2 θ ' r ' [ r ' R 1 ( θ ' ) ] ,
ε x ' y ' = ε y ' x ' = { U 2 R 1 ( θ ' ) [ 2 r ' R 1 ( θ ' ) ] } sin θ ' cos θ ' + U r ' ( cos 2 θ ' sin 2 θ ' ) r ' [ r ' R 1 ( θ ' ) ] ,
ε y ' y ' = { [ r ' R 1 ( θ ' ) ] 2 + U 2 } sin 2 θ ' + 2 U r ' sin θ ' cos θ ' + r ' 2 cos 2 θ ' r ' [ r ' R 1 ( θ ' ) ] ,
ε z ' z ' = r ' R 1 ( θ ' ) r ' [ R 2 ( θ ' ) R 2 ( θ ' ) R 1 ( θ ' ) ] 2 .
U = [ r ' R 1 ( θ ' ) ] R 1 ( θ ' ) d R 2 ( θ ' ) d θ ' [ r ' R 2 ( θ ' ) ] d R 1 ( θ ' ) d θ ' R 2 ( θ ' ) R 2 ( θ ' ) [ R 2 ( θ ' ) R 1 ( θ ' ) ] .
ε x ' x ' = [ r ' τ R 2 ( θ ' ) ] 2 cos 2 θ ' + τ 2 [ d R 2 ( θ ' ) d θ ' ] 2 cos 2 θ ' 2 τ r ' d R 2 ( θ ' ) d θ ' sin θ ' cos θ ' + r ' 2 sin 2 θ ' r ' [ r ' τ R 2 ( θ ' ) ]
ε x ' y ' = ε y ' x ' ' = τ R 2 ( θ ' ) [ 2 r ' τ R 2 ( θ ' ) ] sin θ ' cos θ ' + τ 2 sin θ ' cos θ ' [ d R 2 ( θ ' ) d θ ' ] 2 + τ r ' d R 2 ( θ ' ) d θ ' ( cos 2 θ ' sin 2 θ ' ) r ' [ r ' τ R 2 ( θ ' ) ]
ε y ' y ' = [ r ' τ R 2 ( θ ' ) ] 2 sin 2 θ ' + τ 2 [ d R 2 ( θ ' ) d θ ' ] 2 sin 2 θ ' + 2 τ r ' d R 2 ( θ ' ) d θ ' sin θ ' cos θ ' + r ' 2 cos 2 θ ' r ' [ r ' τ R 2 ( θ ' ) ]
ε z ' z ' = ( 1 1 τ ) 2 r ' τ R 2 ( θ ' ) r '
n = 0 A n cos ( n θ ' ) + n = 1 B n sin ( n θ ' )
R 1 ( θ ' ) = [ 12 + 2 cos ( θ ' ) + sin ( 2 θ ' ) 2 sin ( 3 θ ' ) ] / 30 ,
R 2 ( θ ' ) = [ 10 + sin ( θ ' ) sin ( 2 θ ' ) + 2 cos ( 5 θ ' ) ] / 12 ,
E i ' = q i q i ' E i
σ = k 0 r ̂ 0 × C [ ( n ̂ × E c ) η 0 r ̂ 0 × ( n ̂ × H c ) ] exp ( i k r ' · r ̂ 0 ) d l 2 4 E i 2

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