Abstract

An inverse way to define the parameters of cylindrical cloaks is developed, in which the cloaking parameters can be independently obtained without any knowledge of the corresponding coordinate transformation. The required parameters are derived in terms of the integral form of cloaking generators, which are very general and allow us to examine the significance of the parametric profiles. The validity of such inverse way and the invisibility characteristics are presented in full-wave numerical simulation of plane wave scattering by cloaked cylinders.

© 2010 Optical Society of America

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [CrossRef] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef] [PubMed]
  3. A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas 24, 413–419 (2003).
    [CrossRef] [PubMed]
  4. U. Leonhardt, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
    [CrossRef]
  5. S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New J. Phys. 9, 45 (2007).
    [CrossRef]
  6. D. Torrent and J. Sanchez-Dehesa, “Acoustic cloaking in two dimensions: a feasible approach,” New J. Phys. 10, 063015 (2008).
    [CrossRef]
  7. M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134501 (2008).
    [CrossRef] [PubMed]
  8. G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
    [CrossRef]
  9. D. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008).
    [CrossRef]
  10. W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, “Arbitrarily elliptical–cylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
    [CrossRef]
  11. A. Nicolet, F. Zolla, and S. Guenneau, “Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section,” Opt. Lett. 33, 1584–1586 (2008).
    [CrossRef] [PubMed]
  12. J. Zhang, Y. Luo, H. Chen, and B.-I. Wu, “Cloak of arbitrary shape,” J. Opt. Soc. Am. B 25, 1776–1779 (2008).
    [CrossRef]
  13. 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]
  14. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nature Mater. 8, 568–571 (2009).
    [CrossRef]
  15. H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
    [CrossRef] [PubMed]
  16. C.-W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
    [CrossRef]
  17. R. Weder, “The boundary conditions for point transformed electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 065207 (2008).
    [CrossRef]
  18. C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E 79, 047602 (2009).
    [CrossRef]
  19. C. W. Qiu, L. Hu, B. Zhang, B. Wu, S. Johnson, and J. Joannopoulos, “Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coating,” Opt. Express 17, 13467–13478 (2009).
    [CrossRef] [PubMed]
  20. L. S. Dolin, “On the possibility of comparing three-dimensional electromagnetic systems with non-uniform anisotropic fillings,” Izv. Vyssh. Uchebn. Zaved. Fiz. 4, 964–967 (1961).
  21. U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
    [CrossRef]
  22. M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
    [CrossRef]
  23. B. Zhang, H. Chen, and B.-I. Wu, “Limitations of high-order transformation and incident angle on simplified invisibility cloaks,” Opt. Express 16, 14655–14660 (2008).
    [CrossRef] [PubMed]
  24. 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]
  25. B. I. Popa and S. A. Cummer, “Cloaking with optimized homogeneous anisotropic layers,” Phys. Rev. A 79, 023806 (2009).
    [CrossRef]

2009

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

C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E 79, 047602 (2009).
[CrossRef]

C. W. Qiu, L. Hu, B. Zhang, B. Wu, S. Johnson, and J. Joannopoulos, “Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coating,” Opt. Express 17, 13467–13478 (2009).
[CrossRef] [PubMed]

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
[CrossRef]

B. I. Popa and S. A. Cummer, “Cloaking with optimized homogeneous anisotropic layers,” Phys. Rev. A 79, 023806 (2009).
[CrossRef]

2008

R. Weder, “The boundary conditions for point transformed electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 065207 (2008).
[CrossRef]

B. Zhang, H. Chen, and B.-I. Wu, “Limitations of high-order transformation and incident angle on simplified invisibility cloaks,” Opt. Express 16, 14655–14660 (2008).
[CrossRef] [PubMed]

D. Torrent and J. Sanchez-Dehesa, “Acoustic cloaking in two dimensions: a feasible approach,” New J. Phys. 10, 063015 (2008).
[CrossRef]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134501 (2008).
[CrossRef] [PubMed]

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

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, “Arbitrarily elliptical–cylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

A. Nicolet, F. Zolla, and S. Guenneau, “Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section,” Opt. Lett. 33, 1584–1586 (2008).
[CrossRef] [PubMed]

J. Zhang, Y. Luo, H. Chen, and B.-I. Wu, “Cloak of arbitrary shape,” J. Opt. Soc. Am. B 25, 1776–1779 (2008).
[CrossRef]

2007

S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New J. Phys. 9, 45 (2007).
[CrossRef]

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

C.-W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

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

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

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

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

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

D. Schurig, 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]

2003

A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas 24, 413–419 (2003).
[CrossRef] [PubMed]

1961

L. S. Dolin, “On the possibility of comparing three-dimensional electromagnetic systems with non-uniform anisotropic fillings,” Izv. Vyssh. Uchebn. Zaved. Fiz. 4, 964–967 (1961).

Bartal, G.

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

Briane, M.

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

Chen, H.

J. Zhang, Y. Luo, H. Chen, and B.-I. Wu, “Cloak of arbitrary shape,” J. Opt. Soc. Am. B 25, 1776–1779 (2008).
[CrossRef]

B. Zhang, H. Chen, and B.-I. Wu, “Limitations of high-order transformation and incident angle on simplified invisibility cloaks,” Opt. Express 16, 14655–14660 (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 interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Cheng, Q.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, “Arbitrarily elliptical–cylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Chin, J. Y.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, “Arbitrarily elliptical–cylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Cui, T. J.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, “Arbitrarily elliptical–cylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Cummer, S. A.

B. I. Popa and S. A. Cummer, “Cloaking with optimized homogeneous anisotropic layers,” Phys. Rev. A 79, 023806 (2009).
[CrossRef]

S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New J. Phys. 9, 45 (2007).
[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]

Dolin, L. S.

L. S. Dolin, “On the possibility of comparing three-dimensional electromagnetic systems with non-uniform anisotropic fillings,” Izv. Vyssh. Uchebn. Zaved. Fiz. 4, 964–967 (1961).

Enoch, S.

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134501 (2008).
[CrossRef] [PubMed]

Farhat, M.

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134501 (2008).
[CrossRef] [PubMed]

Feng, Y.

C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E 79, 047602 (2009).
[CrossRef]

Greenleaf, A.

A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas 24, 413–419 (2003).
[CrossRef] [PubMed]

Guenneau, S.

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134501 (2008).
[CrossRef] [PubMed]

A. Nicolet, F. Zolla, and S. Guenneau, “Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section,” Opt. Lett. 33, 1584–1586 (2008).
[CrossRef] [PubMed]

Hu, L.

Jiang, W. X.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, “Arbitrarily elliptical–cylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Joannopoulos, J.

Johnson, S.

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]

Kong, J. A.

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

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.

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

Lassas, M.

A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas 24, 413–419 (2003).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
[CrossRef]

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

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

Li, J.

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

Li, L. W.

C.-W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

Lin, X. Q.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, “Arbitrarily elliptical–cylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Luo, Y.

J. Zhang, Y. Luo, H. Chen, and B.-I. Wu, “Cloak of arbitrary shape,” J. Opt. Soc. Am. B 25, 1776–1779 (2008).
[CrossRef]

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]

Milton, G. W.

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[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]

Movchan, A. B.

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134501 (2008).
[CrossRef] [PubMed]

Nicolet, A.

Pendry, J. B.

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]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
[CrossRef]

Popa, B. I.

B. I. Popa and S. A. Cummer, “Cloaking with optimized homogeneous anisotropic layers,” Phys. Rev. A 79, 023806 (2009).
[CrossRef]

Qiu, C. W.

Qiu, C.-W.

C.-W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

Qiu, M.

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[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]

Ruan, Z.

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

Sanchez-Dehesa, J.

D. Torrent and J. Sanchez-Dehesa, “Acoustic cloaking in two dimensions: a feasible approach,” New J. Phys. 10, 063015 (2008).
[CrossRef]

Schurig, D.

S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New J. Phys. 9, 45 (2007).
[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]

Smith, D. R.

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]

Torrent, D.

D. Torrent and J. Sanchez-Dehesa, “Acoustic cloaking in two dimensions: a feasible approach,” New J. Phys. 10, 063015 (2008).
[CrossRef]

Uhlmann, G.

A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas 24, 413–419 (2003).
[CrossRef] [PubMed]

Valentine, J.

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

Weder, R.

R. Weder, “The boundary conditions for point transformed electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 065207 (2008).
[CrossRef]

Werner, D. H.

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

Willis, J. R.

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

Wu, B.

Wu, B. I.

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

Wu, B.-I.

Xu, X.

C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E 79, 047602 (2009).
[CrossRef]

Yan, M.

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

Yeo, T. S.

C.-W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

Yu, G. X.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, “Arbitrarily elliptical–cylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Zentgraf, T.

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

Zhang, B.

C. W. Qiu, L. Hu, B. Zhang, B. Wu, S. Johnson, and J. Joannopoulos, “Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coating,” Opt. Express 17, 13467–13478 (2009).
[CrossRef] [PubMed]

B. Zhang, H. Chen, and B.-I. Wu, “Limitations of high-order transformation and incident angle on simplified invisibility cloaks,” Opt. Express 16, 14655–14660 (2008).
[CrossRef] [PubMed]

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

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]

Zhang, J.

Zhang, X.

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

Zolla, F.

Zouhdi, S.

C.-W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

Appl. Phys. Lett.

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

Izv. Vyssh. Uchebn. Zaved. Fiz.

L. S. Dolin, “On the possibility of comparing three-dimensional electromagnetic systems with non-uniform anisotropic fillings,” Izv. Vyssh. Uchebn. Zaved. Fiz. 4, 964–967 (1961).

J. Opt. Soc. Am. B

J. Phys. A: Math. Theor.

R. Weder, “The boundary conditions for point transformed electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 065207 (2008).
[CrossRef]

J. Phys. D: Appl. Phys.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, “Arbitrarily elliptical–cylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Nature Mater.

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

New J. Phys.

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

S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New J. Phys. 9, 45 (2007).
[CrossRef]

D. Torrent and J. Sanchez-Dehesa, “Acoustic cloaking in two dimensions: a feasible approach,” New J. Phys. 10, 063015 (2008).
[CrossRef]

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

B. I. Popa and S. A. Cummer, “Cloaking with optimized homogeneous anisotropic layers,” Phys. Rev. A 79, 023806 (2009).
[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

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Figures (2)

Fig. 1
Fig. 1

Scheme of the proposed inverse design mechanism for cylindrical cloaks. The virtual space denoted by Ω ( r ) ( r < b ) is compressed into the physical space Ω ( r ) denoted by the shell on the right (blue online) ( a < r < b ) , in which the required coordinate transformation is not specified. Based on the cloaking generator and the properties of the inverse mechanism, all the cloaking parameters in Eq. (1) can be determined uniquely. More importantly, the initially “indefinite” transformation can be revealed in turn.

Fig. 2
Fig. 2

Total electric field Re [ E z ] on the x - y plane when n = 1 (upper row) and n = 20 (lower row) for the power cloak generators. The plane wave is propagating along the x-axis and its electric field is polarized along the z-axis. The working frequency is 3 GHz . The inner rod is a perfect electrical conductor of radius a = λ , and the outer radius is b = 2 λ .

Tables (1)

Tables Icon

Table 1 Cloaking Parameters under Different Power Cloak Generators for ζ z ( r ) Profile a

Equations (14)

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ζ ¯ ( r ) = [ ζ r ( r ) 0 0 0 ζ φ ( r ) 0 0 0 ζ z ( r ) ] = [ λ r ( λ φ λ z ) 0 0 0 λ φ ( λ r λ z ) 0 0 0 λ z ( λ r λ φ ) ] ,
λ r = d r d r ,
λ φ = r r ,
λ z = 1 ,
ζ r ( r ) ζ φ ( r ) = 1 ,
ζ r ( r ) ζ z ( r ) = r 2 r 2 ,
ζ φ ( r ) ζ z ( r ) = d r d r .
r ζ r ( r ) ζ z ( r ) d [ r ζ r ( r ) ζ z ( r ) ] d r = r ζ z ( r ) .
r 2 ζ z ( r ) ζ r ( r ) = C + a r 2 r 1 ζ z ( r 1 ) d r 1 ,
b 2 = a b 2 r 1 ζ z ( r 1 ) d r 1 ,
ζ z ( r ) = b 2 g ( r ) 2 a b r 1 g ( r 1 ) d r 1 .
ζ r ( r ) = 2 a r r 1 g ( r 1 ) d r 1 r 2 g ( r ) ,
ζ φ ( r ) = r 2 g ( r ) 2 a r r 1 g ( r 1 ) d r 1 .
r = b a r r 1 g ( r 1 ) d r 1 a b r 1 g ( r 1 ) d r 1 .

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