Abstract

In this paper we apply the methodology of transformation optics for design of a novel invisibility cloak which can possess an open tunnel. Such a cloak facilitates the insertion (retrieval) of matter into (from) the cloak’s interior without significantly affecting the cloak’s performance, overcoming the matter exchange bottleneck inherent to most previously proposed cloak designs. We achieve this by applying a transformation which expands a point at the origin in electromagnetic space to a finite area in physical space in a highly anisotropic manner. The invisibility performance of the proposed cloak is verified by using full-wave finite-element simulations.

© 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 (2006).
    [CrossRef] [PubMed]
  2. U. Leonhardt, "Optical conformal mapping," Science 312, 1777 (2006).
    [CrossRef] [PubMed]
  3. 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 the Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
    [CrossRef]
  4. M. Yan, W. Yan, and M. Qiu, "Cylindrical superlens by a coordinate transformation," Phys. Rev. B 78, 125113 (2008).
    [CrossRef]
  5. H. Chen, and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
    [CrossRef]
  6. W. Yan, M. Yan, Z. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," N. J. Phys. 10, 043040 (2008).
    [CrossRef]
  7. H. Chen, "Transformation optics in orthogonal coordinates," J. Opt. A, Pure Appl. Opt. 11, 075102 (2009).
    [CrossRef]
  8. D. Kwon, and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502 (2008).
    [CrossRef]
  9. D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-21-9794.
    [CrossRef] [PubMed]
  10. S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
    [CrossRef]
  11. H. Ma, S. Qu, Z. Xu, and J. Wang, "The open cloak," Appl. Phys. Lett. 94, 103501 (2009).
    [CrossRef]
  12. J. B. Pendry, A. J. Holden, and D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  13. D. Schurig, J. J. Mock, and D. R. Smith, "Electric field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109 (2006).
    [CrossRef]

2009 (2)

H. Chen, "Transformation optics in orthogonal coordinates," J. Opt. A, Pure Appl. Opt. 11, 075102 (2009).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, "The open cloak," Appl. Phys. Lett. 94, 103501 (2009).
[CrossRef]

2008 (4)

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

D. Kwon, and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502 (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 the Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

M. Yan, W. Yan, and M. Qiu, "Cylindrical superlens by a coordinate transformation," Phys. Rev. B 78, 125113 (2008).
[CrossRef]

2007 (1)

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

2006 (5)

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

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

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-21-9794.
[CrossRef] [PubMed]

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

D. Schurig, J. J. Mock, and D. R. Smith, "Electric field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

1999 (1)

J. B. Pendry, A. J. Holden, and D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Chan, C. T.

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

Chen, H.

H. Chen, "Transformation optics in orthogonal coordinates," J. Opt. A, Pure Appl. Opt. 11, 075102 (2009).
[CrossRef]

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

Cummer, S. A.

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

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

Holden, A. J.

J. B. Pendry, A. J. Holden, and D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Kwon, D.

D. Kwon, and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502 (2008).
[CrossRef]

Leonhardt, U.

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

Ma, H.

H. Ma, S. Qu, Z. Xu, and J. Wang, "The open cloak," Appl. Phys. Lett. 94, 103501 (2009).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, and D. R. Smith, "Electric field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

Pendry, J.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[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 the Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

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

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-21-9794.
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, and D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Popa, B. I.

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

Qiu, M.

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

M. Yan, W. Yan, and M. Qiu, "Cylindrical superlens by a coordinate transformation," Phys. Rev. B 78, 125113 (2008).
[CrossRef]

Qu, S.

H. Ma, S. Qu, Z. Xu, and J. Wang, "The open cloak," Appl. Phys. Lett. 94, 103501 (2009).
[CrossRef]

Rahm, M.

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

Robbins, D. J.

J. B. Pendry, A. J. Holden, and D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Roberts, D. A.

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

Ruan, Z.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," N. J. Phys. 10, 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 the Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

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

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-21-9794.
[CrossRef] [PubMed]

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

D. Schurig, J. J. Mock, and D. R. Smith, "Electric field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109 (2006).
[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 the Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

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

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

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-21-9794.
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, "Electric field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, and D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Wang, J.

H. Ma, S. Qu, Z. Xu, and J. Wang, "The open cloak," Appl. Phys. Lett. 94, 103501 (2009).
[CrossRef]

Werner, D. H.

D. Kwon, and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502 (2008).
[CrossRef]

Xu, Z.

H. Ma, S. Qu, Z. Xu, and J. Wang, "The open cloak," Appl. Phys. Lett. 94, 103501 (2009).
[CrossRef]

Yan, M.

M. Yan, W. Yan, and M. Qiu, "Cylindrical superlens by a coordinate transformation," Phys. Rev. B 78, 125113 (2008).
[CrossRef]

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

Yan, W.

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

M. Yan, W. Yan, and M. Qiu, "Cylindrical superlens by a coordinate transformation," Phys. Rev. B 78, 125113 (2008).
[CrossRef]

Appl. Phys. Lett. (4)

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

D. Kwon, and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, "The open cloak," Appl. Phys. Lett. 94, 103501 (2009).
[CrossRef]

D. Schurig, J. J. Mock, and D. R. Smith, "Electric field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

J. B. Pendry, A. J. Holden, and D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

H. Chen, "Transformation optics in orthogonal coordinates," J. Opt. A, Pure Appl. Opt. 11, 075102 (2009).
[CrossRef]

N. J. Phys. (1)

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

Opt. Express (1)

Photonics 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 transformations of the Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Phys. Rev. B (1)

M. Yan, W. Yan, and M. Qiu, "Cylindrical superlens by a coordinate transformation," Phys. Rev. B 78, 125113 (2008).
[CrossRef]

Phys. Rev. E (1)

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

Science (2)

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

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

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Figures (5)

Fig. 1
Fig. 1

Material parameters for the cardioid cloak; a = 1m and b = 2.5m. It should be noticed that the xy- and yx-components of the tensors are equal. In the plot, we have only shown the material parameter values up to 20. Higher values are denoted with a saturated dark-red color.

Fig. 2
Fig. 2

Ez field distribution for a plane wave interacting with a cardioid cloak. (a) left-to-right propagation; (b) bottom-to-top propagation.

Fig. 3
Fig. 3

Ez field distribution for a plane wave interacting with an open cardioid cloak. (a) left-to-right propagation; (b) bottom-to-top propagation.

Fig. 4
Fig. 4

Far field scattering patterns of a bare PEC cardioid, a PEC cardioid coated with a cloak, and a PEC cardioid (with an openning) coated with an open cloak, for plane waves incident from (a) left-to- right and (b) bottom-to-top. The maximum far field caused by the bare cardioid PEC is taken as reference, i.e. 0 dB.

Fig. 5
Fig. 5

Far-field scattering patterns of a bare PEC cardioid, an ideal open cardioid cloak, and reduced open cardioid cloaks designed with various μmax values, for plane waves incident from left-to-right. The maximum far field caused by the bare PEC cardioid is taken as reference i.e. 0 dB.

Equations (10)

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

r = r a ( 1 + cos θ ) b a ( 1 + cos θ ) b ,
r = b a ( 1 + cos θ ) b r + a ( 1 + cos θ ) .
Λ = [ r r r r θ 0 0 r r θ θ 0 0 0 1 ] .
r r = b a ( 1 + cos θ ) b , r θ = a ( r b ) b sin θ .
ɛ = μ = Λ Λ T / det ( Λ ) ,
ɛ r r = μ r r = ( r r ) 2 + ( r r θ ) 2 r r r r ,
ɛ θ r = ɛ r θ = μ θ r = μ r θ = r r θ r r ,
ɛ θ θ = μ θ θ = r r r r ,
ɛ z z = μ z z = 1 r r r r .
ɛ cart = μ cart = R ɛ R T / det ( R ) = R μ R T / det ( R ) .

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