Abstract

We study an invisibility cloak with a twin cavity, simulated by a plane algebraic curve- hippopede. The cloaked region, which looks like eight for some sets of geometric parameters, is expanded from one single point. Using a geometric transformation approach, we demonstrate that the material parameters of cloaking layer can be exactly determined. Numerical simulations show that the incoming rays pass in and out the cloaking region twice, and return to their original trajectory outside the curved cloak. A notable feature is that the cloaking region has two hollow regions in which two objects can be hidden at one time and that they could not perceive each other.

© 2009 Optical Society of America

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    [CrossRef]

2009 (7)

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, "Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell," Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef] [PubMed]

G. X. Yu, W. X. Jiang, and T. J. Cui, "Invisible slab cloaks via embedded optical transformation," Appl. Phys. Lett. 94, 041904 (2009).
[CrossRef]

U. Leonhardt and T. Tyc, "Broadband invisibility by non-Euclidean cloaking," Science 323, 110 (2009).
[CrossRef]

Q. Wu, K. Zhang, F. Y. Meng and L. W. Li, "Material parameters characterization for arbitrary N-sided regular polygonal invisible cloak," J. Phys. D: Appl. Phys. 42, 035408 (2009).
[CrossRef]

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

X. Chen, Y. Fu, and N. Yuan, "Invisible cloak design with controlled constitutive parameters and arbitrary shaped boundaries through Helmholtz’s equation," Opt. Express 17, 3581-3586 (2009).
[CrossRef] [PubMed]

Y. You, G. W. Kattawar, and P. Yang, "Invisibility cloaks for toroids," Opt. Express 17, 6591-6599 (2009).
[CrossRef] [PubMed]

2008 (15)

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

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

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. Liu, and D. R. Smith, "Invisibility cloak without singularity," Appl. Phys. Lett. 93, 194102 (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]

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]

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

H. Chen, X. Luo, and H. Ma, "The anti-cloak," Opt. Express 16, 14603-14608 (2008).
[CrossRef] [PubMed]

H. Ma, S. Qu, Z. Xu, and J. Wang, "Approximation approach of designing practical cloaks with arbitrary shapes," Opt. Express 16, 15449-15454 (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]

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]

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

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

A. N. Norris, "Acoustic cloaking theory," Proc. R. Soc. London, Ser. A 464, 2411-2434 (2008).
[CrossRef]

J. Zhang, and J. Huangfu, Y. Luo, H. Chen, J. A. Kong, and B. I. Wu, "Cloak for multilayered and gradually changing media," Phys. Rev. B 77, 035116 (2008).
[CrossRef]

T. Chen, C. N. Weng and J. S. Chen, "Cloak for curvilinearly anisotropic media in conduction," Appl. Phys. Lett. 93, 114103 (2008).
[CrossRef]

2007 (5)

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

G. W. Milton and J. R. Willis, "On modifications of Newton’s second law and linear continuum elastodynamics," Proc. R. Soc. London, Ser. A 463, 855-880 (2007).
[CrossRef]

A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, "Electromagnetic wormholes and virtual magnetic monopoles from metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

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

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007).
[CrossRef]

2006 (4)

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

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]

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]

2004 (1)

A. Nicolet, S. Guenneau and F. Zolla, "Modelling of twisted optical waveguides with edge elements," Eur. Phys. J. Appl. Phys. 28153-157 (2004).
[CrossRef]

2003 (1)

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

1996 (1)

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

1994 (2)

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 75, 6036-6038 (1994).
[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]

Chan, C. T.

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, "Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell," Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef] [PubMed]

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007).
[CrossRef]

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

Chen, H.

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, "Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell," Phys. Rev. Lett. 102, 093901 (2009).
[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]

J. Zhang, and J. Huangfu, Y. Luo, H. Chen, J. A. Kong, and B. I. Wu, "Cloak for multilayered and gradually changing media," Phys. Rev. B 77, 035116 (2008).
[CrossRef]

H. Chen, X. Luo, and H. Ma, "The anti-cloak," Opt. Express 16, 14603-14608 (2008).
[CrossRef] [PubMed]

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

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007).
[CrossRef]

Chen, J. S.

T. Chen, C. N. Weng and J. S. Chen, "Cloak for curvilinearly anisotropic media in conduction," Appl. Phys. Lett. 93, 114103 (2008).
[CrossRef]

Chen, T.

T. Chen, C. N. Weng and J. S. Chen, "Cloak for curvilinearly anisotropic media in conduction," Appl. Phys. Lett. 93, 114103 (2008).
[CrossRef]

Chen, X.

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]

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. Liu, and D. R. Smith, "Invisibility cloak without singularity," Appl. Phys. Lett. 93, 194102 (2008).
[CrossRef]

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

Chin, J. Y.

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

Cui, T. J.

G. X. Yu, W. X. Jiang, and T. J. Cui, "Invisible slab cloaks via embedded optical transformation," Appl. Phys. Lett. 94, 041904 (2009).
[CrossRef]

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. Liu, and D. R. Smith, "Invisibility cloak without singularity," Appl. Phys. Lett. 93, 194102 (2008).
[CrossRef]

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

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. Appl. 6, 87-95 (2008).
[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]

Fu, Y.

Genon, A.

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 75, 6036-6038 (1994).
[CrossRef]

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, "Electromagnetic wormholes and virtual magnetic monopoles from metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

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.

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]

A. Nicolet, S. Guenneau and F. Zolla, "Modelling of twisted optical waveguides with edge elements," Eur. Phys. J. Appl. Phys. 28153-157 (2004).
[CrossRef]

Hu, J.

Huangfu, J.

J. Zhang, and J. Huangfu, Y. Luo, H. Chen, J. A. Kong, and B. I. Wu, "Cloak for multilayered and gradually changing media," Phys. Rev. B 77, 035116 (2008).
[CrossRef]

Jiang, W. X.

G. X. Yu, W. X. Jiang, and T. J. Cui, "Invisible slab cloaks via embedded optical transformation," Appl. Phys. Lett. 94, 041904 (2009).
[CrossRef]

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. Liu, and D. R. Smith, "Invisibility cloak without singularity," Appl. Phys. Lett. 93, 194102 (2008).
[CrossRef]

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

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.

Kong, J. A.

J. Zhang, and J. Huangfu, Y. Luo, H. Chen, J. A. Kong, and B. I. Wu, "Cloak for multilayered and gradually changing media," Phys. Rev. B 77, 035116 (2008).
[CrossRef]

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, "Electromagnetic wormholes and virtual magnetic monopoles from metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Kwon, D. H.

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

Lai, Y.

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, "Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell," Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef] [PubMed]

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, "Electromagnetic wormholes and virtual magnetic monopoles from metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

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

Legros, W.

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 75, 6036-6038 (1994).
[CrossRef]

Leonhardt, U.

U. Leonhardt and T. Tyc, "Broadband invisibility by non-Euclidean cloaking," Science 323, 110 (2009).
[CrossRef]

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

Li, C.

Li, F.

Li, J.

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

Li, L. W.

Q. Wu, K. Zhang, F. Y. Meng and L. W. Li, "Material parameters characterization for arbitrary N-sided regular polygonal invisible cloak," J. Phys. D: Appl. Phys. 42, 035408 (2009).
[CrossRef]

Li, Z.

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

Liu, R.

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

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. Liu, and D. R. Smith, "Invisibility cloak without singularity," Appl. Phys. Lett. 93, 194102 (2008).
[CrossRef]

Luo, X.

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]

J. Zhang, and J. Huangfu, Y. Luo, H. Chen, J. A. Kong, and B. I. Wu, "Cloak for multilayered and gradually changing media," Phys. Rev. B 77, 035116 (2008).
[CrossRef]

Ma, H.

McPhedran, R. C.

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

Meng, F. Y.

Q. Wu, K. Zhang, F. Y. Meng and L. W. Li, "Material parameters characterization for arbitrary N-sided regular polygonal invisible cloak," J. Phys. D: Appl. Phys. 42, 035408 (2009).
[CrossRef]

Meys, B.

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 75, 6036-6038 (1994).
[CrossRef]

Milton, G. W.

G. W. Milton and J. R. Willis, "On modifications of Newton’s second law and linear continuum elastodynamics," Proc. R. Soc. London, Ser. A 463, 855-880 (2007).
[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]

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-8482 (1994).
[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]

Nicolet, A.

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]

A. Nicolet, S. Guenneau and F. Zolla, "Modelling of twisted optical waveguides with edge elements," Eur. Phys. J. Appl. Phys. 28153-157 (2004).
[CrossRef]

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 75, 6036-6038 (1994).
[CrossRef]

Nicorovici, N. A.

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

Norris, A. N.

A. N. Norris, "Acoustic cloaking theory," Proc. R. Soc. London, Ser. A 464, 2411-2434 (2008).
[CrossRef]

Pendry, J. B.

J. Li and J. B. Pendry, "Hiding under the carpet: A new strategy for cloaking," Phys. Rev. Lett. 101, 203901 (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. 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, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (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]

Qu, S.

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. Appl. 6, 87-95 (2008).
[CrossRef]

Remacle, J. F.

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 75, 6036-6038 (1994).
[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. 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 transfromations of Maxwell’s equations," Photon. Nanostruct. Fundam. Appl. 6, 87-95 (2008).
[CrossRef]

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.

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. Liu, and D. R. Smith, "Invisibility cloak without singularity," Appl. Phys. Lett. 93, 194102 (2008).
[CrossRef]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transfromations 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, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 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, 977-980 (2006).
[CrossRef] [PubMed]

Tyc, T.

U. Leonhardt and T. Tyc, "Broadband invisibility by non-Euclidean cloaking," Science 323, 110 (2009).
[CrossRef]

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, "Electromagnetic wormholes and virtual magnetic monopoles from metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

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

Wang, J.

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]

Weng, C. N.

T. Chen, C. N. Weng and J. S. Chen, "Cloak for curvilinearly anisotropic media in conduction," Appl. Phys. Lett. 93, 114103 (2008).
[CrossRef]

Werner, D. H.

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

Willis, J. R.

G. W. Milton and J. R. Willis, "On modifications of Newton’s second law and linear continuum elastodynamics," Proc. R. Soc. London, Ser. A 463, 855-880 (2007).
[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]

Wu, B. I.

J. Zhang, and J. Huangfu, Y. Luo, H. Chen, J. A. Kong, and B. I. Wu, "Cloak for multilayered and gradually changing media," Phys. Rev. B 77, 035116 (2008).
[CrossRef]

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

Wu, Q.

Q. Wu, K. Zhang, F. Y. Meng and L. W. Li, "Material parameters characterization for arbitrary N-sided regular polygonal invisible cloak," J. Phys. D: Appl. Phys. 42, 035408 (2009).
[CrossRef]

Xu, Z.

Yang, P.

Yang, X. M.

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. Liu, and D. R. Smith, "Invisibility cloak without singularity," Appl. Phys. Lett. 93, 194102 (2008).
[CrossRef]

You, Y.

Yu, G. X.

G. X. Yu, W. X. Jiang, and T. J. Cui, "Invisible slab cloaks via embedded optical transformation," Appl. Phys. Lett. 94, 041904 (2009).
[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]

Yuan, N.

Zhai, P. W.

Zhang, J.

J. Zhang, and J. Huangfu, Y. Luo, H. Chen, J. A. Kong, and B. I. Wu, "Cloak for multilayered and gradually changing media," Phys. Rev. B 77, 035116 (2008).
[CrossRef]

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

Zhang, K.

Q. Wu, K. Zhang, F. Y. Meng and L. W. Li, "Material parameters characterization for arbitrary N-sided regular polygonal invisible cloak," J. Phys. D: Appl. Phys. 42, 035408 (2009).
[CrossRef]

Zhang, Z. Q.

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, "Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell," Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef] [PubMed]

Zolla, F.

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]

A. Nicolet, S. Guenneau and F. Zolla, "Modelling of twisted optical waveguides with edge elements," Eur. Phys. J. Appl. Phys. 28153-157 (2004).
[CrossRef]

Appl. Phys. Lett. (6)

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007).
[CrossRef]

T. Chen, C. N. Weng and J. S. Chen, "Cloak for curvilinearly anisotropic media in conduction," Appl. Phys. Lett. 93, 114103 (2008).
[CrossRef]

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

G. X. Yu, W. X. Jiang, and T. J. Cui, "Invisible slab cloaks via embedded optical transformation," Appl. Phys. Lett. 94, 041904 (2009).
[CrossRef]

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

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. Liu, and D. R. Smith, "Invisibility cloak without singularity," Appl. Phys. Lett. 93, 194102 (2008).
[CrossRef]

Eur. Phys. J. Appl. Phys. (1)

A. Nicolet, S. Guenneau and F. Zolla, "Modelling of twisted optical waveguides with edge elements," Eur. Phys. J. Appl. Phys. 28153-157 (2004).
[CrossRef]

J. Appl. Phys. (1)

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 75, 6036-6038 (1994).
[CrossRef]

J. Mod. Opt. (1)

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. B (1)

J. Phys. D: Appl. Phys. (2)

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]

Q. Wu, K. Zhang, F. Y. Meng and L. W. Li, "Material parameters characterization for arbitrary N-sided regular polygonal invisible cloak," J. Phys. D: Appl. Phys. 42, 035408 (2009).
[CrossRef]

New J. Phys. (2)

S. A. Cummer and D. Schurig, "One path to acoustic cloaking," New J. Phys. 9, 45 (2007).
[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 (7)

Opt. Lett. (1)

Photon. Nanostruct. Fundam. Appl. (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. Appl. 6, 87-95 (2008).
[CrossRef]

Phys. Rev. B (2)

J. Zhang, and J. Huangfu, Y. Luo, H. Chen, J. A. Kong, and B. I. Wu, "Cloak for multilayered and gradually changing media," Phys. Rev. B 77, 035116 (2008).
[CrossRef]

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

Phys. Rev. E (1)

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. 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. (3)

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

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, "Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell," Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef] [PubMed]

A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, "Electromagnetic wormholes and virtual magnetic monopoles from metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Physiol. Meas. (1)

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

Proc. R. Soc. London, Ser. A (2)

A. N. Norris, "Acoustic cloaking theory," Proc. R. Soc. London, Ser. A 464, 2411-2434 (2008).
[CrossRef]

G. W. Milton and J. R. Willis, "On modifications of Newton’s second law and linear continuum elastodynamics," Proc. R. Soc. London, Ser. A 463, 855-880 (2007).
[CrossRef]

Science (4)

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

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]

U. Leonhardt and T. Tyc, "Broadband invisibility by non-Euclidean cloaking," Science 323, 110 (2009).
[CrossRef]

Other (6)

J. D. Lawrence, A Catalog of Special Plane Curves (New York: Dover, 1972).

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (New York: McGraw-Hill, 1961).

J. F. Remacle, A. Nicolet, A. Genon, and W. Legros, "Comparison of boundary elements and transformed finite elements for open magnetic problems," in Boundary Element Method XVI, C. A. Brebbia, ed., (Computational Mechanics Publications, Southhampton, 1994), pp. 109-116.

E. J. Post, Formal Structure of Electromagnetics: General Covariance and Electromagnetics (North-Holland, Amsterdam, 1962).

U. Leonhardt and T.G. Philbin, "Transformation optics and the geometry of Light," arXiv: 0805.4778; Prog. Optics (to appear).

R. V. Kohn and M. Vogelius, "Identification of an unknown conductivity by means of measurements at the boundary," in Inverse problems, D.W. McLaughlin, ed., (American Mathematical Society, Providence, RI, 1984), pp. 113-123.

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Figures (5)

Fig. 1.
Fig. 1.

The hippopedal curves, described by Eq. (1), with different sets of parameters (a) a > b (dashed lines), (b) a = b (solid line), (c) a < b (dotted lines).

Fig. 2.
Fig. 2.

The magnitudes of material properties εxx ′, εyy ′, εzz ′, and εxy ′ inside the hippopedal cloaking layer (a = 1, b = 1) .

Fig. 3.
Fig. 3.

Snapshot of the electric field distribution. The plane waves are incident in the horizontal direction. (a) a = 0.12, b = 0.1, (b) a = 0.15, b = 0.15, (c) a = 0.11, b = 0.16.

Fig. 4.
Fig. 4.

Snapshot of the electric field distribution (a), and stream lines (b). The plane waves are incident at an oblique angle of 30° with a = 0.15, b = 0.15.

Fig. 5.
Fig. 5.

A schematic illustration of a few plane curves. (a) double folium, r = 4acosθsin2 θ (dashed line), (b) sinusoidal spirals, r = (acos3θ)1/3 (dotted line).

Equations (14)

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

r2=4b(absin2θ),
r(θ)=r(θ)=r(πθ)=r(π+θ).
(x2+y2)2+4b(bc)(x2+y2)4b2x2=0.
((xb)2+y2b2)((x+b)2+y2b2)=0.
Ωi:ri=2abb2sin2θ ,
Ωo:ro=2mabb2sin2θ ,
x'=rrx=(α+rir)x,y=rry=(α+rir)y,z=z,
ε'=ATdetA , μ=ATdetA,
A=(x',y',z')(x,y,z)=(α+4by2((a+b)r22by2)r5ri4bxy((a+b)r22by2)r5ri04bxy(ar22by2)r5riα+4bx2(ar22by2)r5ri0001).
εxx=μxx=rαr [(α+4by2((a+b)r22by2)r5ri)2+(4bxy((a+b)r22by2)r5ri)2] ,
εyy=μyy=rαr [α+(4bx2(ar22by2)r5ri)2+(4bxy(ar22by2)r5ri)2] ,
εzz=μzz=rαr ,
εzz=μxy=rαr [(4bxy(4br2(ar22by2)(ar2+b(x2y2))αr5ri((2a+b)r24by2))r10ri2)].
ε'=μ'=(r'rir'+4b2sin22θri2r'(r'ri)2b2sin2θri(r'ri)0r'r'ri0sym1α2r'rir').

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