Abstract

Recently, there are emerging demands for isotropic material parameters, arising from the broadband requirement of the functional devices. Since inverse Laplace’s equation with sliding boundary condition will determine a quasi-conformal mapping, and a quasi-conformal mapping will minimize the transformation material anisotropy, so in this work, the inverse Laplace’s equation with sliding boundary condition is proposed for quasi-isotropic transformation material design. Examples of quasi-isotropic arbitrary carpet cloak and waveguide with arbitrary cross sections are provided to validate the proposed method. The proposed method is very simple compared with other quasi-conformal methods based on grid generation tools.

© 2010 OSA

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2009 (11)

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

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

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

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79(6), 063825 (2009).
[CrossRef]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

J. Hu, X. M. Zhou, and G. K. Hu, “A numerical method for designing acoustic cloak with arbitrary shapes,” Comput. Mater. Sci. 46(3), 708–712 (2009).
[CrossRef]

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

N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express 17(17), 14872–14879 (2009).
[CrossRef] [PubMed]

2008 (9)

Y. You, G. W. Kattawar, P. W. Zhai, and P. Yang, “Invisibility cloaks for irregular particles using coordinate transformations,” Opt. Express 16(9), 6134–6145 (2008).
[CrossRef] [PubMed]

A. Nicolet, F. Zolla, and S. Guenneau, “Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section,” Opt. Lett. 33(14), 1584–1586 (2008).
[CrossRef] [PubMed]

C. Li and F. Li, “Two-dimensional electromagnetic cloaks with arbitrary geometries,” Opt. Express 16(17), 13414–13420 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. Pendry, “Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell’s Equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

H. Ma, S. B. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77(1), 013825 (2008).
[CrossRef]

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

D. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92(1), 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(8), 085504 (2008).
[CrossRef]

P. Zhang, Y. Jin, and S. He, “Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak,” Appl. Phys. Lett. 93(24), 243502 (2008).
[CrossRef]

2006 (3)

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

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

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

Argyropoulos, C.

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79(6), 063825 (2009).
[CrossRef]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Chan, C. T.

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

Chen, B. W.

H. Ma, S. B. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77(1), 013825 (2008).
[CrossRef]

Chen, H.

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

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(8), 085504 (2008).
[CrossRef]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

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(8), 085504 (2008).
[CrossRef]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

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(8), 085504 (2008).
[CrossRef]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. Pendry, “Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell’s Equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

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

Gabrielli, L. H.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Genov, D. A.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

Guenneau, S.

Han, D.

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

Hao, Y.

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79(6), 063825 (2009).
[CrossRef]

He, S.

P. Zhang, Y. Jin, and S. He, “Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak,” Appl. Phys. Lett. 93(24), 243502 (2008).
[CrossRef]

Hu, G. K.

J. Hu, X. M. Zhou, and G. K. Hu, “A numerical method for designing acoustic cloak with arbitrary shapes,” Comput. Mater. Sci. 46(3), 708–712 (2009).
[CrossRef]

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

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

Hu, J.

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

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

J. Hu, X. M. Zhou, and G. K. Hu, “A numerical method for designing acoustic cloak with arbitrary shapes,” Comput. Mater. Sci. 46(3), 708–712 (2009).
[CrossRef]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

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(8), 085504 (2008).
[CrossRef]

Jin, Y.

P. Zhang, Y. Jin, and S. He, “Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak,” Appl. Phys. Lett. 93(24), 243502 (2008).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kallos, E.

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79(6), 063825 (2009).
[CrossRef]

Kattawar, G. W.

Kwon, D.

D. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92(1), 013505 (2008).
[CrossRef]

Lai, Y.

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

Landy, N. I.

Leonhardt, U.

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

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

Li, C.

Li, F.

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

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

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(8), 085504 (2008).
[CrossRef]

Lipson, M.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Ma, H.

H. Ma, S. B. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77(1), 013825 (2008).
[CrossRef]

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

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

Ng, J.

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

Nicolet, A.

Padilla, W. J.

Pendry, J.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. Pendry, “Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell’s Equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Pendry, J. B.

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

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

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

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Qu, S. B.

H. Ma, S. B. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77(1), 013825 (2008).
[CrossRef]

Rahm, M.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. Pendry, “Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell’s Equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. Pendry, “Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell’s Equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. Pendry, “Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell’s Equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

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

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

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. Pendry, “Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell’s Equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

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

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

Starr, A. F.

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

Tyc, T.

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Wang, J. F.

H. Ma, S. B. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77(1), 013825 (2008).
[CrossRef]

Werner, D. H.

D. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92(1), 013505 (2008).
[CrossRef]

Xiao, J.

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

Xu, Z.

H. Ma, S. B. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77(1), 013825 (2008).
[CrossRef]

Yang, P.

You, Y.

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(8), 085504 (2008).
[CrossRef]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Zhai, P. W.

Zhang, J. Q.

H. Ma, S. B. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77(1), 013825 (2008).
[CrossRef]

Zhang, P.

P. Zhang, Y. Jin, and S. He, “Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak,” Appl. Phys. Lett. 93(24), 243502 (2008).
[CrossRef]

Zhang, S.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

Zhang, X.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Zhang, Z. Q.

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

Zhou, X. M.

J. Hu, X. M. Zhou, and G. K. Hu, “A numerical method for designing acoustic cloak with arbitrary shapes,” Comput. Mater. Sci. 46(3), 708–712 (2009).
[CrossRef]

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

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

Zolla, F.

Appl. Phys. Lett. (3)

D. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92(1), 013505 (2008).
[CrossRef]

P. Zhang, Y. Jin, and S. He, “Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak,” Appl. Phys. Lett. 93(24), 243502 (2008).
[CrossRef]

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

Comput. Mater. Sci. (1)

J. Hu, X. M. Zhou, and G. K. Hu, “A numerical method for designing acoustic cloak with arbitrary shapes,” Comput. Mater. Sci. 46(3), 708–712 (2009).
[CrossRef]

J. Phys. D Appl. Phys. (1)

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(8), 085504 (2008).
[CrossRef]

Nat. Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Nat. Photonics (1)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Nat. Phys. (1)

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Photon. Nanostruct. Fundam. Appl. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. Pendry, “Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell’s Equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Phys. Rev. A (2)

H. Ma, S. B. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77(1), 013825 (2008).
[CrossRef]

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79(6), 063825 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

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

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

Science (5)

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

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
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U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
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Other (2)

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Figures (4)

Fig. 1
Fig. 1

(a) The out-of-plane permittivity of dielectric carpet cloak for TE waves with transformation grids in black, (b) the electric field pattern for a Gaussian beam of frequency 0.8GHz impinging the cloak, (c) the electric field pattern of a PEC object without cloak and (d) the electric field pattern of a conducting ground plane.

Fig. 2
Fig. 2

(a) The out-of-plane permittivity of an arbitrary carpet cloak for TE waves with transformation grids in black, (b) the electric field pattern for a Gaussian beam of frequency 0.8GHz impinging the cloak, (c) the electric field pattern of a PEC object without cloak and (d) the electric field pattern of a conducting ground plane.

Fig. 3
Fig. 3

The scheme of the boundary settings for an arbitrary waveguide. A ( a ' ) = a and A ( b ' ) = b indicate the correspondences between the boundaries a and b before and after the transformation.

Fig. 4
Fig. 4

(a) The out-of-plane permittivity of a dielectric waveguide of arbitrary cross sections with transformation grids in black, and (b) the electric field pattern for a Gaussian beam of frequency 0.5GHz propagating in the waveguide.

Equations (12)

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ε = A ε 0 A T det A ,
μ = A μ 0 A T det A ,
ε = ε 0 diag [ λ 1 λ 2 λ 3 , λ 2 λ 1 λ 3 , λ 3 λ 1 λ 2 ] ,
μ = μ 0 diag [ λ 1 λ 2 λ 3 , λ 2 λ 1 λ 3 , λ 3 λ 1 λ 2 ] .
x 2 x = 0.
x 2 x = 0.
F L ( x ) = 1 2 Ω ( g 11 + g 22 ) d x ,
F W ( x ) = 1 2 Ω ( g 11 + g 22 ) d x .
F W ( x ) = 1 2 Ω g 11 + g 22 g d x ,
F W ( x ) = 1 2 Ω ( λ 1 λ 2 + λ 2 λ 1 ) d x .
F M L ( x ) = 1 2 Ω ( g 11 + g 22 ) 2 g d x .
F M L ( x ) = 1 2 Ω ( λ 1 λ 2 + λ 2 λ 1 ) 2 d x .

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