Abstract

Invisibility cloaks for ellipsoids, rounded cuboids and rounded cylinders have been studied on the basis of the coordinate transformation approach. The resultant material property tensors for irregular cloaks are more complicated in comparison with those for the spherical invisibility cloak. A generalized Discrete Dipole Approximation (DDA) formalism has been used to simulate the scattered field distribution in the vicinity of the aforementioned irregular cloaks illuminated by an incident plane wave. Simulated scattering efficiencies are on the order of 10-5, and the simulated electric-field distribution outside of a cloak is the same as that of the incident radiation.

© 2008 Optical Society of America

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    [CrossRef]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
    [CrossRef] [PubMed]
  3. U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys. 8, 247 (2006).
    [CrossRef]
  4. 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]
  5. U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  6. U. Leonhardt, "Notes on conformal invisibility devices," New J. Phys. 8, 118 (2006).
    [CrossRef]
  7. D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007).
    [CrossRef] [PubMed]
  8. S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
    [CrossRef]
  9. 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 (2006).
    [CrossRef] [PubMed]
  10. H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
    [CrossRef] [PubMed]
  11. B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
    [CrossRef]
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    [CrossRef]
  13. H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
    [CrossRef]
  14. D.-H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
  16. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shavlaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
    [CrossRef]
  17. B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary surface voltage effect in the invisibility cloak with an active device inside," Phys. Rev. Lett. 100, 063904 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2008

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, 87-95 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

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

Y. You, G. W. Kattawar, P.-W. Zhai, and P. Yang, "Zero-backscatter cloak for aspherical particles using a generalized DDA formalism," Opt. Express 16, 2068-2079 (2008).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary surface voltage effect in the invisibility cloak with an active device inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

2007

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shavlaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007).
[CrossRef] [PubMed]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

2006

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (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, 977 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef] [PubMed]

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

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

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Notes on conformal invisibility devices," New J. Phys. 8, 118 (2006).
[CrossRef]

2002

T. Wriedt, "Using the T-Matrix method for light scattering computations by non-axisymmetric particles: superellipsoids and realistically shapes particles," Part. Part. Syst. Charact. 19, 256-268 (2002).
[CrossRef]

1996

A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell??s equations," J. Mod. Opt. 43, 773-793 (1996).
[CrossRef]

1994

1988

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

1973

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shavlaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
[CrossRef]

Chen, B.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Chen, H.

B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary surface voltage effect in the invisibility cloak with an active device inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shavlaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
[CrossRef]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell??s equations," Photon. Nanostruct. Fundam. Appl. 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 (2006).
[CrossRef] [PubMed]

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

Draine, B. T.

B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

Flatau, P. J.

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 (2006).
[CrossRef] [PubMed]

Kattawar, G. W.

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shavlaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
[CrossRef]

Kong, J. A.

B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary surface voltage effect in the invisibility cloak with an active device inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Kwon, D.-H.

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

Leonhardt, U.

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Notes on conformal invisibility devices," New J. Phys. 8, 118 (2006).
[CrossRef]

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

Luo, Y.

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Ma, H.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[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 (2006).
[CrossRef] [PubMed]

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 transformations of Maxwell??s equations," Photon. Nanostruct. Fundam. Appl. 6, 87-95 (2008).
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007).
[CrossRef] [PubMed]

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

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef] [PubMed]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (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, 977 (2006).
[CrossRef] [PubMed]

A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell??s equations," J. Mod. Opt. 43, 773-793 (1996).
[CrossRef]

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Philbin, T. G.

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

Popa, B.-I.

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

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Qu, S.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Rahm, M.

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

Ran, L.

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Roberts, D. A.

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

Schurig, D.

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

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007).
[CrossRef] [PubMed]

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

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

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (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 (2006).
[CrossRef] [PubMed]

Shavlaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shavlaev, "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 transformations of Maxwell??s equations," Photon. Nanostruct. Fundam. Appl. 6, 87-95 (2008).
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007).
[CrossRef] [PubMed]

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

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (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]

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 (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 (2006).
[CrossRef] [PubMed]

Wang, J.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Ward, A. J.

A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell??s equations," J. Mod. Opt. 43, 773-793 (1996).
[CrossRef]

Werner, D. H.

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

Wriedt, T.

T. Wriedt, "Using the T-Matrix method for light scattering computations by non-axisymmetric particles: superellipsoids and realistically shapes particles," Part. Part. Syst. Charact. 19, 256-268 (2002).
[CrossRef]

Wu, B.-I.

B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary surface voltage effect in the invisibility cloak with an active device inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Xu, Z.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Yang, P.

You, Y.

Zhai, P.-W.

Zhang, B.

B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary surface voltage effect in the invisibility cloak with an active device inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Zhang, J.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Appl. Phys. Lett.

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

Astrophys. J.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

J. Mod. Opt.

A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell??s equations," J. Mod. Opt. 43, 773-793 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photon.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shavlaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
[CrossRef]

New J. Phys.

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

U. Leonhardt, "Notes on conformal invisibility devices," New J. Phys. 8, 118 (2006).
[CrossRef]

Opt. Express

Part. Part. Syst. Charact.

T. Wriedt, "Using the T-Matrix method for light scattering computations by non-axisymmetric particles: superellipsoids and realistically shapes particles," Part. Part. Syst. Charact. 19, 256-268 (2002).
[CrossRef]

Photon. Nanostruct. Fundam. Appl.

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, 87-95 (2008).
[CrossRef]

Phys. Rev. A

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Phys. Rev. B

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Phys. Rev. E

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

Phys. Rev. Lett.

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary surface voltage effect in the invisibility cloak with an active device inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

Science

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 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef] [PubMed]

Other

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, 1975).

I. D. Faux and M. J. Pratt, Computational geometry for design and manufacture (Wiley, Chichester 1979).

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Figures (9)

Fig. 1.
Fig. 1.

Illustration of the coordinate transformation used to determine the material properties of a cloak.

Fig. 2.
Fig. 2.

Application of the coordinate transformation to a spheroidal region subject to a plane-wave radiation propagating in the z-direction. Shown in the figures is the situation in the x-z plane, with the x- and z-axes as depicted in Fig. (a). The scales are in unit of λ. Figure (a) shows the closed region (green region) in Cartesian coordinates, with vacuum both inside and outside. The light rays (dark red lines) and wave fronts (dark blue lines) of the incident radiation are also shown. Figure (b) shows the transformed region according to the transformation Eq.(5) with a=0.5b, with the material properties in the cloaking region determined by Eq.(3a) and Eq.(3b). The light rays and wave fronts transform accordingly.

Fig. 3.
Fig. 3.

Same as Fig. 2, but for an incident radiation in the x-z plane making an angle of θ=30° to the z-axis.

Fig. 4.
Fig. 4.

(a) Approximations of a cube by order-n-cuboids with various n values, and α 1=α 1=α 3. (b) Comparison of phase functions pertaining to an order-10-cuboidal scattering particle with α 1=α 2=1, α 3=2 and pertaining to a cubical scattering particle with the same aspect ratio. Both particles are homogeneous and have the same size parameter x=4 and the same permittivity ε=1.44.

Fig. 5.
Fig. 5.

Same as Fig. 2(b), but for a rounded cuboidal cloak approximated by an order- 10-cuboid with x=8, a=0.5b, α 1=α 2=1, and α 3=2, subject to incident radiation propagating in various directions. (a) The incident radiation is along the z-axis; (b) The incident radiation is in the x-z plane, making an angle of θ=30° to the z-axis.

Fig. 6.
Fig. 6.

(a) Approximations of a cylinder by order-n-cylinders with various n values, and α 1=α 1=α 3. (b) Same as Fig. 4(b), but for an order-10-cylindrical scattering particle of the same size parameter and aspect ratio, and a cylindrical scattering particle.

Fig. 7.
Fig. 7.

3-D views of light rays and wave fronts associated with the three irregular invisibility cloaks: (a) ellipsoid, (b) rounded-cuboid, and (c) rounded cylinder.

Fig. 8.
Fig. 8.

The DDA simulations of the electric-field distribution in the vicinity of an ellipsoidal cloak in the x-z plane.

Fig. 9.
Fig. 9.

The DDA simulations of the electric-field distribution in the vicinity of an order-10- cuboidal cloak in the x-z plane.

Equations (27)

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T i j = det ( Λ i i ) 1 Λ i i Λ j j T i j ,
Λ i i = x i x i
ε i j = det ( Λ i i ) 1 Λ i i Λ j j ε i j ,
μ i j = det ( Λ i i ) 1 Λ i i Λ j j μ i j .
( x 1 α 1 b ) 2 + ( x 2 α 2 b ) 2 + ( x 3 α 3 b ) 2 = 1 ,
x i = b a b x i δ i i + a x i r δ i i , ( a < b )
r = [ i = 1 3 ( x i α i ) 2 ] 1 2 .
( x 1 α 1 b ) 2 + ( x 2 α 2 b ) 2 + ( x 3 α 3 b ) 2 = ε 2 ,
( x 1 α 1 a ) 2 + ( x 2 α 2 a ) 2 + ( x 3 α 3 a ) 2 = 1 ,
Λ j i = r r δ j i a x i x k δ i i δ kj α j 2 r 3
ε ij = μ ij = b b a [ δ ij x i x j ( a r 3 ( α i 2 + α j 2 ) a 2 r ~ 2 r 4 k = 1 3 ( x ~ k ) 2 α k 4 ) ] .
x ~ i = x i b a b + a r = and r ~ = r a b a · b .
[ ( x α 1 b ) 2 e + ( y α 2 b ) 2 e ] e m + ( z α 3 b ) 2 m = 1 ,
( x 1 α 1 b ) n + ( x 2 α 2 b ) n + ( x 3 α 3 b ) n = 1 .
r = [ i = 1 3 ( x i α i ) n ] 1 n .
Λ j i = r r δ j i a x i ( x k ) n 1 δ i i δ kj α j n r n + 1 ,
ε ij = μ ij
= b b a [ δ ij x i x j ×
( a r 3 r ~ n 2 ( ( x ~ i ) n 2 α i n + ( x ~ j ) n 2 α j n ) a 2 r ~ 2 ( n 1 ) r 4 k = 1 3 ( x ~ k ) 2 n 2 α k 2 n ) ] ,
[ ( x 1 α 1 b ) 2 + ( x 2 α 2 b ) 2 ] n 2 + ( x 3 α 3 b ) n = 1 ,
r = ( [ ( x 1 α 1 ) 2 + ( x 2 α 2 ) 2 ] n 2 + ( x 3 α 3 ) n ) 1 n .
Λ j i = r r δ j i a r n + 1 x i δ i i [ x k δ kj ρ n 2 α j 2 ( δ 1 j + δ 2 j ) + ( x k ) n 1 δ kj α j 2 δ 3 j ] ,
ε ij = μ ij
= b b a [ δ ij x i x j ×
( a r 3 r ~ n 2 [ ρ n 2 ( 1 α i 2 ( δ 1 i + δ 2 i ) + 1 α j 2 ( δ 1 j + δ 2 j ) ) +
( x ~ i ) n 2 α i n δ 3 i + ( x ~ j ) n 2 α j n δ 3 j ]
a 2 r ~ 2 ( n 1 ) r 4 [ ρ 2 n 4 ( ( x ~ 1 ) 2 α 1 4 + ( x ~ 2 ) 2 α 2 4 ) + ( x ~ 3 ) 2 n 2 α 3 2 n ] ) ] ,

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