Abstract

A general boundary mapping method is proposed to enable the designing of various transformation devices with arbitrary shapes by reducing the traditional space-to-space mapping to boundary-to-boundary mapping. The method also makes the designing of complex-shaped transformation devices more feasible and flexible. Using the boundary mapping method, an arbitrarily shaped perfect electric conductor (PEC) reshaping device, which is called a “PEC reshaper,” is demonstrated to visually reshape a PEC with an arbitrary shape to another arbitrary one. Unlike the previously reported simple PEC reshaping devices, the arbitrarily shaped PEC reshaper designed here does not need to share a common domain. Moreover, the flexibilities of the boundary mapping method are expected to inspire some novel PEC reshapers with attractive new functionalities.

© 2011 OSA

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2011 (1)

A. Diatta and S. Guenneau, “Non-singular cloaks allow mimesis,” J. Opt. 13(2), 024012–024022 (2011).
[CrossRef]

2010 (6)

2009 (7)

A. Veltri, “Designs for electromagnetic cloaking a three-dimensional arbitrary shaped star-domain,” Opt. Express 17(22), 20494–20501 (2009).
[CrossRef] [PubMed]

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” New J. Phys. 11(11), 113001 (2009).
[CrossRef]

G. Dupont, S. Guenneau, S. Enoch, G. Demesy, A. Nicolet, F. Zolla, and A. Diatta, “Revolution analysis of three-dimensional arbitrary cloaks,” Opt. Express 17(25), 22603–22608 (2009).
[CrossRef] [PubMed]

Q. Cheng, W. X. Jiang, and T. J. Cui, “Investigations of the electromagnetic properties of three-dimensional arbitrarily-shaped cloaks,” Prog. Electromagn. Res. 94, 105–117 (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]

X. Chen, Y. Q. Fu, and N. C. Yuan, “Invisible cloak design with controlled constitutive parameters and arbitrary shaped boundaries through Helmholtz’s equation,” Opt. Express 17(5), 3581–3586 (2009).
[CrossRef] [PubMed]

J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson's equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).
[CrossRef]

2008 (10)

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 ), 066607 (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]

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10(4), 043040 (2008).
[CrossRef]

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

R. V. Kohn, H. Shen, M. S. Vogelius, and M. I. Weinstein, “Cloaking via change of variables in electric impedance tomography,” Inverse Probl. 24(1), 015016 (2008).
[CrossRef]

J. J. Zhang, Y. Luo, H. S. Chen, and B. I. Wu, “Cloak of arbitrary shape,” J. Opt. Soc. Am. B 25(11), 1776–1779 (2008).
[CrossRef]

H. Ma, S. B. Qu, Z. Xu, and J. F. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 036608 (2008).
[CrossRef] [PubMed]

H. Y. Chen, X. Zhang, X. Luo, H. Ma, and C. T. Chan, “Reshaping the perfect electrical conductor cylinder arbitrarily,” New J. Phys. 10(11), 113016 (2008).
[CrossRef]

A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10(11), 115022 (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 transformations of Maxwell’s equations,” Photonics Nanostruct. Fund. Appl. 6, 89–95 (2008).

2007 (1)

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275(3), 749–789 (2007).
[CrossRef]

2006 (1)

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

1994 (1)

J. P. Dowling and C. M. Bowden, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41(2), 345–351 (1994).
[CrossRef]

1980 (1)

M. Machura and R. A. Sweet, “A survey of software for partial differential equations,” ACM Trans. Math. Softw. 6(4), 461–488 (1980).
[CrossRef]

Bowden, C. M.

J. P. Dowling and C. M. Bowden, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41(2), 345–351 (1994).
[CrossRef]

Cao, X. Y.

J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson's equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).
[CrossRef]

Chan, C. T.

H. Y. Chen, X. Zhang, X. Luo, H. Ma, and C. T. Chan, “Reshaping the perfect electrical conductor cylinder arbitrarily,” New J. Phys. 10(11), 113016 (2008).
[CrossRef]

Chen, H. S.

Chen, H. Y.

H. Y. Chen, X. Zhang, X. Luo, H. Ma, and C. T. Chan, “Reshaping the perfect electrical conductor cylinder arbitrarily,” New J. Phys. 10(11), 113016 (2008).
[CrossRef]

Chen, X.

Cheng, Q.

Q. Cheng, W. X. Jiang, and T. J. Cui, “Investigations of the electromagnetic properties of three-dimensional arbitrarily-shaped cloaks,” Prog. Electromagn. Res. 94, 105–117 (2009).
[CrossRef]

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 ), 066607 (2008).
[CrossRef] [PubMed]

Chin, J. Y.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 ), 066607 (2008).
[CrossRef] [PubMed]

Cui, T. J.

Q. Cheng, W. X. Jiang, and T. J. Cui, “Investigations of the electromagnetic properties of three-dimensional arbitrarily-shaped cloaks,” Prog. Electromagn. Res. 94, 105–117 (2009).
[CrossRef]

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 ), 066607 (2008).
[CrossRef] [PubMed]

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,” Photonics Nanostruct. Fund. Appl. 6, 89–95 (2008).

Demesy, G.

Deng, Q. L.

Diatta, A.

Dong, X. C.

Dowling, J. P.

J. P. Dowling and C. M. Bowden, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41(2), 345–351 (1994).
[CrossRef]

Du, C. L.

Dupont, G.

Enoch, S.

Fu, Y. Q.

Fu, Z. Y.

W. Li, J. G. Guan, W. Wang, Z. G. Sun, and Z. Y. Fu, “A general cloak to shift the scattering of different objects,” J. Phys. D Appl. Phys. 43(24), 245102 (2010).
[CrossRef]

Gao, H. T.

Gao, L.

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275(3), 749–789 (2007).
[CrossRef]

Guan, J. G.

W. Li, J. G. Guan, Z. G. Sun, and W. Wang, “Shifting cloaks constructed with homogeneous materials,” Comput. Mater. Sci. 50(2), 607–611 (2010).
[CrossRef]

W. Li, J. G. Guan, W. Wang, Z. G. Sun, and Z. Y. Fu, “A general cloak to shift the scattering of different objects,” J. Phys. D Appl. Phys. 43(24), 245102 (2010).
[CrossRef]

Guenneau, S.

Hu, G. K.

Hu, J.

Huang, M.

Jiang, W. X.

Q. Cheng, W. X. Jiang, and T. J. Cui, “Investigations of the electromagnetic properties of three-dimensional arbitrarily-shaped cloaks,” Prog. Electromagn. Res. 94, 105–117 (2009).
[CrossRef]

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 ), 066607 (2008).
[CrossRef] [PubMed]

Kohn, R. V.

R. V. Kohn, H. Shen, M. S. Vogelius, and M. I. Weinstein, “Cloaking via change of variables in electric impedance tomography,” Inverse Probl. 24(1), 015016 (2008).
[CrossRef]

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275(3), 749–789 (2007).
[CrossRef]

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275(3), 749–789 (2007).
[CrossRef]

Li, C.

Li, F.

Li, W.

W. Li, J. G. Guan, W. Wang, Z. G. Sun, and Z. Y. Fu, “A general cloak to shift the scattering of different objects,” J. Phys. D Appl. Phys. 43(24), 245102 (2010).
[CrossRef]

W. Li, J. G. Guan, Z. G. Sun, and W. Wang, “Shifting cloaks constructed with homogeneous materials,” Comput. Mater. Sci. 50(2), 607–611 (2010).
[CrossRef]

Li, Z.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 ), 066607 (2008).
[CrossRef] [PubMed]

Liu, C. H.

Liu, R. P.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 ), 066607 (2008).
[CrossRef] [PubMed]

Liu, T.

J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson's equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).
[CrossRef]

Lu, Y. G.

Luo, X.

H. Y. Chen, X. Zhang, X. Luo, H. Ma, and C. T. Chan, “Reshaping the perfect electrical conductor cylinder arbitrarily,” New J. Phys. 10(11), 113016 (2008).
[CrossRef]

Luo, Y.

Ma, H.

H. Ma, S. B. Qu, Z. Xu, and J. F. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 036608 (2008).
[CrossRef] [PubMed]

H. Y. Chen, X. Zhang, X. Luo, H. Ma, and C. T. Chan, “Reshaping the perfect electrical conductor cylinder arbitrarily,” New J. Phys. 10(11), 113016 (2008).
[CrossRef]

Ma, J. J.

J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson's equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).
[CrossRef]

Machura, M.

M. Machura and R. A. Sweet, “A survey of software for partial differential equations,” ACM Trans. Math. Softw. 6(4), 461–488 (1980).
[CrossRef]

Maci, S.

A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10(11), 115022 (2008).
[CrossRef]

Nicolet, A.

Niu, W. W.

Novitsky, A.

C.-W. Qiu, A. Novitsky, and L. Gao, “Inverse design mechanism of cylindrical cloaks without knowledge of the required coordinate transformation,” J. Opt. Soc. Am. A 27(5), 1079–1082 (2010).
[CrossRef] [PubMed]

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” New J. Phys. 11(11), 113001 (2009).
[CrossRef]

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,” Photonics Nanostruct. Fund. Appl. 6, 89–95 (2008).

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

Peng, J. H.

Qiu, C. W.

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” New J. Phys. 11(11), 113001 (2009).
[CrossRef]

Qiu, C.-W.

Qiu, M.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10(4), 043040 (2008).
[CrossRef]

Qu, S. B.

H. Ma, S. B. Qu, Z. Xu, and J. F. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 036608 (2008).
[CrossRef] [PubMed]

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,” Photonics Nanostruct. Fund. Appl. 6, 89–95 (2008).

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,” Photonics Nanostruct. Fund. Appl. 6, 89–95 (2008).

Ruan, Z.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10(4), 043040 (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,” Photonics Nanostruct. Fund. Appl. 6, 89–95 (2008).

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

Shen, H.

R. V. Kohn, H. Shen, M. S. Vogelius, and M. I. Weinstein, “Cloaking via change of variables in electric impedance tomography,” Inverse Probl. 24(1), 015016 (2008).
[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,” Photonics Nanostruct. Fund. Appl. 6, 89–95 (2008).

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

Sun, Z. G.

W. Li, J. G. Guan, Z. G. Sun, and W. Wang, “Shifting cloaks constructed with homogeneous materials,” Comput. Mater. Sci. 50(2), 607–611 (2010).
[CrossRef]

W. Li, J. G. Guan, W. Wang, Z. G. Sun, and Z. Y. Fu, “A general cloak to shift the scattering of different objects,” J. Phys. D Appl. Phys. 43(24), 245102 (2010).
[CrossRef]

Sweet, R. A.

M. Machura and R. A. Sweet, “A survey of software for partial differential equations,” ACM Trans. Math. Softw. 6(4), 461–488 (1980).
[CrossRef]

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275(3), 749–789 (2007).
[CrossRef]

Veltri, A.

Vogelius, M. S.

R. V. Kohn, H. Shen, M. S. Vogelius, and M. I. Weinstein, “Cloaking via change of variables in electric impedance tomography,” Inverse Probl. 24(1), 015016 (2008).
[CrossRef]

Wang, J. F.

H. Ma, S. B. Qu, Z. Xu, and J. F. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 036608 (2008).
[CrossRef] [PubMed]

Wang, W.

W. Li, J. G. Guan, Z. G. Sun, and W. Wang, “Shifting cloaks constructed with homogeneous materials,” Comput. Mater. Sci. 50(2), 607–611 (2010).
[CrossRef]

W. Li, J. G. Guan, W. Wang, Z. G. Sun, and Z. Y. Fu, “A general cloak to shift the scattering of different objects,” J. Phys. D Appl. Phys. 43(24), 245102 (2010).
[CrossRef]

Weinstein, M. I.

R. V. Kohn, H. Shen, M. S. Vogelius, and M. I. Weinstein, “Cloaking via change of variables in electric impedance tomography,” Inverse Probl. 24(1), 015016 (2008).
[CrossRef]

Wu, B. I.

Xu, Z.

H. Ma, S. B. Qu, Z. Xu, and J. F. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 036608 (2008).
[CrossRef] [PubMed]

Yaghjian, A. D.

A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10(11), 115022 (2008).
[CrossRef]

Yan, M.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10(4), 043040 (2008).
[CrossRef]

Yan, W.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10(4), 043040 (2008).
[CrossRef]

Yang, C. F.

Yang, J. J.

Yu, K. M.

J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson's equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).
[CrossRef]

Yuan, G. S.

Yuan, N. C.

Zhang, J. J.

Zhang, X.

H. Y. Chen, X. Zhang, X. Luo, H. Ma, and C. T. Chan, “Reshaping the perfect electrical conductor cylinder arbitrarily,” New J. Phys. 10(11), 113016 (2008).
[CrossRef]

Zhou, X. M.

Zolla, F.

Zouhdi, S.

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” New J. Phys. 11(11), 113001 (2009).
[CrossRef]

ACM Trans. Math. Softw. (1)

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[CrossRef]

Commun. Math. Phys. (1)

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275(3), 749–789 (2007).
[CrossRef]

Comput. Mater. Sci. (1)

W. Li, J. G. Guan, Z. G. Sun, and W. Wang, “Shifting cloaks constructed with homogeneous materials,” Comput. Mater. Sci. 50(2), 607–611 (2010).
[CrossRef]

Inverse Probl. (1)

R. V. Kohn, H. Shen, M. S. Vogelius, and M. I. Weinstein, “Cloaking via change of variables in electric impedance tomography,” Inverse Probl. 24(1), 015016 (2008).
[CrossRef]

J. Mod. Opt. (1)

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[CrossRef]

J. Opt. (1)

A. Diatta and S. Guenneau, “Non-singular cloaks allow mimesis,” J. Opt. 13(2), 024012–024022 (2011).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (1)

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

W. Li, J. G. Guan, W. Wang, Z. G. Sun, and Z. Y. Fu, “A general cloak to shift the scattering of different objects,” J. Phys. D Appl. Phys. 43(24), 245102 (2010).
[CrossRef]

New J. Phys. (4)

H. Y. Chen, X. Zhang, X. Luo, H. Ma, and C. T. Chan, “Reshaping the perfect electrical conductor cylinder arbitrarily,” New J. Phys. 10(11), 113016 (2008).
[CrossRef]

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10(4), 043040 (2008).
[CrossRef]

A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10(11), 115022 (2008).
[CrossRef]

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” New J. Phys. 11(11), 113001 (2009).
[CrossRef]

Opt. Express (7)

Opt. Lett. (1)

Photonics Nanostruct. Fund. 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 transformations of Maxwell’s equations,” Photonics Nanostruct. Fund. Appl. 6, 89–95 (2008).

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

H. Ma, S. B. Qu, Z. Xu, and J. F. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 036608 (2008).
[CrossRef] [PubMed]

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 ), 066607 (2008).
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Prog. Electromagn. Res. (1)

Q. Cheng, W. X. Jiang, and T. J. Cui, “Investigations of the electromagnetic properties of three-dimensional arbitrarily-shaped cloaks,” Prog. Electromagn. Res. 94, 105–117 (2009).
[CrossRef]

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J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson's equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).
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Science (1)

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Figures (12)

Fig. 1
Fig. 1

Scheme of the transformation for the cylindrical PEC reshaper which reshapes a cylinder of diameter of a to another cylinder of diameter of a'. (a) shows the original space and (b) shows the physical space. The outer radius of the reshaper is b.

Fig. 2
Fig. 2

Electric field distribution of (a) the effective PEC cylinder, (b) the PEC cylindrical reshaper when a TE plane wave is incident from left to right, and (c) scattering width curves correspond to (a) and (b). The dashed line in (b) outlines the effective PEC.

Fig. 3
Fig. 3

Scheme illustration of the transformation of the arbitrarily shaped PEC reshaper. (a) The original domain in virtual space, and (b) the transformed domain in physical space. Starting from the reference points (A and A'), the points on Γ'i are mapped onto Γ i one-to-one. For an arbitrary pair of points (B and B'), we have A'B'/l 1 = AB/l 2 (where l 1 and l 2 are total length of Γ'i and Γ i , respectively).

Fig. 4
Fig. 4

Scheme illustration of the transformation of the rectangular PEC reshaper. (a) The original domain in virtual space, and (b) the transformed domain in physical space. Coordinates of the vertexes are A' (−0.006, −0.057), B' (0, 0), C' (−0.118, 0.046), D' (0.015, 0.136), E' (0.132, −0.004) in original space, and A (−0.1, −0.1), B (−0.1, 0), C (−0.1, 0.1), D (0.1, 0.1), E (0.1, −0.1) in physical space. The outer boundaries in (a) and (b) are both squares with side lengths of 0.2 m and center at origin.

Fig. 5
Fig. 5

Numerical solutions of the Laplace equations of (16) (left panel) and (17) (right panel).

Fig. 6
Fig. 6

Material parameter distribution of the square PEC reshaper. (a) η xx , (b) η xy yx ), (c) η yy , (d) η zz . η represents μ or ε. Other components of the material tensor all equal to zero everywhere.

Fig. 7
Fig. 7

Electric field distribution of (a) the effective polygon PEC, (b) the square PEC reshaper when a TE plane wave is incident from left to right, and (c) scattering width curves for the effective PEC in (a), and the PEC reshaper in (b). The dashed line in (b) outlines the effective polygon PEC.

Fig. 8
Fig. 8

The plots of path lengths versus coordinates for the (a) effective PEC boundary in original space (x', y') and (b) inner boundary in physical space (x, y) of the PEC reshaper.

Fig. 9
Fig. 9

Numerical solutions of the Laplace equations for (a) u and (b) v in the domain of the arbitrarily shaped PEC reshaper.

Fig. 10
Fig. 10

Material parameter distribution of the PEC reshaper. (a) η xx , (b) η xy yx ), (c) η yy , (d) η zz . η represents μ or ε. The reshaper can be simplified by replacing the abnormal parameters (values exceeding the range of the color scale bars or with absolute value less than 0.2) with their nearest appropriate values. Other components of the material tensor all equal to zero everywhere.

Fig. 11
Fig. 11

Electric field distribution of (a) the effective PEC, (b) the PEC reshaper when a TE plane wave is incident from left to right, and (c) scattering width curves for the effective PEC in (a), the PEC reshaper in (b) and the simplified PEC reshaper. The dashed line in (b) outlines the effective PEC.

Fig. 12
Fig. 12

Electric field distribution of (a) the effective PEC, (b) the PEC reshaper with one physical PEC, (c) the PEC reshaper with two physical PEC, under the illumination of a TE plane wave from right to left, and (d) scattering width curves corresponding to (a), (b) and (c). The dashed line in (b, c) outlines the effective PEC. The physical PECs of the reshapers do not share a domain with their effective PEC.

Equations (24)

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x ' = f 1 ( x , y ) , y ' = f 2 ( x , y ) , z ' = z
x = f 1 1 ( x ' , y ' ) , y = f 2 1 ( x ' , y ' ) , z = z '
ε = μ = J J T / det ( J )
Δ f 1 = 0 , Δ f 2 = 0
f 1 | Γ i = x 0 , f 1 | Γ o = x , f 2 | Γ i = y 0 , f 2 | Γ o = y
r ' = b a ' b a r + a ' a b a b , θ ' = θ , z ' = z
r ' = u ( r , θ ) , θ ' = θ , z ' = z
u ( b , θ ) = b
u ( a , θ ) = a '
{ 2 u r 2 + 1 r u r + 1 r 2 2 u θ 2 = 0 u ( a , θ ) = a ' , u ( b , θ ) = b
u ( r , θ ) = c 1 + c 2 ln r
c 1 = b ( b a ' ) ln b ln ( b / a ) ,   and   c 2 = b a ' ln ( b / a )
μ = ε = d i a g ( r ' c 2 , c 2 r ' , c 2 r ' r 2 )
x ' = u ( x , y ) , y ' = v ( x , y ) , z ' = z
u | Γ o = x , v | Γ o = y
u | Γ i = h 1 , v | Γ i = h 2
2 u x 2 + 2 u y 2 = 0
2 v x 2 + 2 v y 2 = 0
x ' ( 0.006 ) 0 ( 0.006 ) = y ' ( 0.057 ) 0 ( 0.057 ) = y ( 0.1 ) 0 ( 0.1 )
x ' = 0.06 ( y + 0.1 ) 0.006 , y ' = 0.57 ( y + 0.1 ) 0.057
x ' = 1.18 y , y ' = 0.46 y
x ' = 0.0266 ( x + 0.1 ) 0.118 , y ' = 0.018 ( x + 0.1 ) + 0.046
x ' = 0.0234 ( y 0.1 ) + 0.015 , y ' = 0.028 ( y 0.1 ) 0.136
x ' = 0.0276 ( x + 0.1 ) 0.006 , y ' = 0.0106 ( y + 0.1 ) 0.057

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