Abstract

This paper proposes a radial dependent dispersive finite-difference time-domain method for the modeling of electromagnetic cloaking structures. The permittivity and permeability of the cloak are mapped to the Drude dispersion model and taken into account in dispersive FDTD simulations. Numerical simulations demonstrate that under ideal conditions, objects placed inside the cloak are ‘invisible’ to external electromagnetic fields. However for the simplified cloak based on linear transformations, the back scattering has a similar level to the case of a PEC cylinder without any cloak, rendering the object still being ‘visible’. It is also demonstrated numerically that the simplified cloak based on high-order transformations can indeed improve the cloaking performance.

© 2008 Optical Society of America

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  6. U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  33. O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microw. Theory Tech. 41, 658-664 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  38. Y. Zhao, P. A. Belov, and Y. Hao, "Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries," J. Opt. A: Pure Appl. Opt. 9, 468-475 (2007).
    [CrossRef]
  39. Y. Zhao, and Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007).
    [CrossRef]

2008 (4)

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

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

G. Isic, R. Gajic, B. Novakovic, Z. V. Popovic, and K. Hingerl, "Radiation and scattering from imperfect cylindrical electromagnetic cloaks," Opt. Express 16, 1413-1422 (2008).
[CrossRef] [PubMed]

M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035122 (2008).
[CrossRef]

2007 (15)

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

M. G. Silveirinha, A. Alu, and N. Engheta, "Parallel-plate metamaterials for cloaking structures," Phys. Rev. E 75, 036603 (2007).
[CrossRef]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Y. Huang, Y. Feng, and T. Jiang, "Electromagnetic cloaking by layered structure of homogeneous isotropic materials," Opt. Express 15, 11133-11141 (2007).
[CrossRef] [PubMed]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Improvement of cylindrical cloaking with the SHS lining," Opt. Express 15, 12717-12734 (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]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99113903 (2007).
[CrossRef] [PubMed]

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

Q1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

H. Cory, Y. Lee, and Y. Hao, "On the use of conjugate dielectric and metamaterial slabs as radomes," IET Microw. Antenna Propag. 1, 137-143 (2007).
[CrossRef]

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

Y. Zhao, P. A. Belov, and Y. Hao, "Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries," J. Opt. A: Pure Appl. Opt. 9, 468-475 (2007).
[CrossRef]

Y. Zhao, and Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007).
[CrossRef]

2006 (7)

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

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

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

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

D. A. B. Miller, "On perfect cloaking," Opt. Express 14, 12457-12466 (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]

G. W. Milton, and N. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. A 462, 3027-3059 (2006).
[CrossRef]

2005 (1)

A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

1999 (1)

J.-Y. Lee and N.-H. Myung, "Locally tensor conformal FDTD method for modelling arbitrary dielectric surfaces," Microw. Opt. Tech. Lett. 23, 245-249 (1999).
[CrossRef]

1994 (1)

J. R. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
[CrossRef]

1993 (1)

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microw. Theory Tech. 41, 658-664 (1993).
[CrossRef]

1992 (1)

D. M. Sullivan, "Frequency-dependent FDTD methods using Z transforms," IEEE Trans. Antennas Propag. 40, 1223-1230 (1992).
[CrossRef]

1990 (1)

R. Luebbers, F. P. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromagn. Compat. 32, 222-227 (1990).
[CrossRef]

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative value of ?? and ??," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

1966 (1)

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell??s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Alu, A.

M. G. Silveirinha, A. Alu, and N. Engheta, "Parallel-plate metamaterials for cloaking structures," Phys. Rev. E 75, 036603 (2007).
[CrossRef]

A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Belov, P. A.

Y. Zhao, P. A. Belov, and Y. Hao, "Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries," J. Opt. A: Pure Appl. Opt. 9, 468-475 (2007).
[CrossRef]

Berenger, J. R.

J. R. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
[CrossRef]

Cai, W.

Q1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Chan, C. T.

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, H.

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]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

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

Chen, J.-Y.

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microw. Theory Tech. 41, 658-664 (1993).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Q1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (2007).
[CrossRef]

Cory, H.

H. Cory, Y. Lee, and Y. Hao, "On the use of conjugate dielectric and metamaterial slabs as radomes," IET Microw. Antenna Propag. 1, 137-143 (2007).
[CrossRef]

Cummer, S. A

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

Cummer, S. A.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

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

Engheta, N.

M. G. Silveirinha, A. Alu, and N. Engheta, "Parallel-plate metamaterials for cloaking structures," Phys. Rev. E 75, 036603 (2007).
[CrossRef]

A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Feng, Y.

Gajic, R.

Gandhi, O. P.

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microw. Theory Tech. 41, 658-664 (1993).
[CrossRef]

Gao, B.-Q.

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microw. Theory Tech. 41, 658-664 (1993).
[CrossRef]

Greenleaf, A.

Hao, Y.

Y. Zhao, P. A. Belov, and Y. Hao, "Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries," J. Opt. A: Pure Appl. Opt. 9, 468-475 (2007).
[CrossRef]

Y. Zhao, and Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007).
[CrossRef]

H. Cory, Y. Lee, and Y. Hao, "On the use of conjugate dielectric and metamaterial slabs as radomes," IET Microw. Antenna Propag. 1, 137-143 (2007).
[CrossRef]

Hingerl, K.

Huang, Y.

Hunsberger, F. P.

R. Luebbers, F. P. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromagn. Compat. 32, 222-227 (1990).
[CrossRef]

Isic, G.

Jiang, T.

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]

Kildishev, A. V.

Q1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Kong, J. A.

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

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

Kunz, K.

R. Luebbers, F. P. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromagn. Compat. 32, 222-227 (1990).
[CrossRef]

Kurylev, Y.

Kwon, D.-H.

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

Lassas, M.

Lee, J.-Y.

J.-Y. Lee and N.-H. Myung, "Locally tensor conformal FDTD method for modelling arbitrary dielectric surfaces," Microw. Opt. Tech. Lett. 23, 245-249 (1999).
[CrossRef]

Lee, Y.

H. Cory, Y. Lee, and Y. Hao, "On the use of conjugate dielectric and metamaterial slabs as radomes," IET Microw. Antenna Propag. 1, 137-143 (2007).
[CrossRef]

Leonhardt, U.

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

Luebbers, R.

R. Luebbers, F. P. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromagn. Compat. 32, 222-227 (1990).
[CrossRef]

Luo, Y.

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Miller, D. A. B.

Milton, G. W.

G. W. Milton, and N. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. A 462, 3027-3059 (2006).
[CrossRef]

Mock, J. J.

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

Myung, N.-H.

J.-Y. Lee and N.-H. Myung, "Locally tensor conformal FDTD method for modelling arbitrary dielectric surfaces," Microw. Opt. Tech. Lett. 23, 245-249 (1999).
[CrossRef]

Neff, C. W.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99113903 (2007).
[CrossRef] [PubMed]

Nicorovici, N. P.

G. W. Milton, and N. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. A 462, 3027-3059 (2006).
[CrossRef]

Novakovic, B.

Pendry, J. B.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

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]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

Popa, B.-I.

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

Popovic, Z. V.

Psaltis, D.

M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035122 (2008).
[CrossRef]

Qiu, M.

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

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99113903 (2007).
[CrossRef] [PubMed]

Rahm, M.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

Ran, L.

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Ruan, Z.

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

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99113903 (2007).
[CrossRef] [PubMed]

Schneider, M.

R. Luebbers, F. P. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromagn. Compat. 32, 222-227 (1990).
[CrossRef]

Schurig, D.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

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

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

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Q1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (2007).
[CrossRef]

Silveirinha, M. G.

M. G. Silveirinha, A. Alu, and N. Engheta, "Parallel-plate metamaterials for cloaking structures," Phys. Rev. E 75, 036603 (2007).
[CrossRef]

Smith, D. R.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

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

S. A. Cummer, B.-I. Popa, D. Schurig, and D. R. Smith, "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, 9794-9804 (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]

Standler, R.

R. Luebbers, F. P. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromagn. Compat. 32, 222-227 (1990).
[CrossRef]

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]

Sullivan, D. M.

D. M. Sullivan, "Frequency-dependent FDTD methods using Z transforms," IEEE Trans. Antennas Propag. 40, 1223-1230 (1992).
[CrossRef]

Tsang, M.

M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035122 (2008).
[CrossRef]

Uhlmann, G.

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative value of ?? and ??," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Werner, D. H.

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

Wu, B.-I.

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

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

Yan, M.

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

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99113903 (2007).
[CrossRef] [PubMed]

Yee, K. S.

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell??s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Zhang, B.

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

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Zhao, Y.

Y. Zhao, P. A. Belov, and Y. Hao, "Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries," J. Opt. A: Pure Appl. Opt. 9, 468-475 (2007).
[CrossRef]

Y. Zhao, and Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007).
[CrossRef]

Appl. Phys. Lett. (4)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

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

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

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

IEEE Trans. Antennas Propag. (3)

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell??s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

D. M. Sullivan, "Frequency-dependent FDTD methods using Z transforms," IEEE Trans. Antennas Propag. 40, 1223-1230 (1992).
[CrossRef]

Y. Zhao, and Y. Hao, "Finite-difference time-domain study of guided modes in nano-plasmonic waveguides," IEEE Trans. Antennas Propag. 55, 3070-3077 (2007).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

R. Luebbers, F. P. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromagn. Compat. 32, 222-227 (1990).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

O. P. Gandhi, B.-Q. Gao, and J.-Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microw. Theory Tech. 41, 658-664 (1993).
[CrossRef]

IET Microw. Antenna Propag. (1)

H. Cory, Y. Lee, and Y. Hao, "On the use of conjugate dielectric and metamaterial slabs as radomes," IET Microw. Antenna Propag. 1, 137-143 (2007).
[CrossRef]

J. Comput. Phys. (1)

J. R. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
[CrossRef]

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

Y. Zhao, P. A. Belov, and Y. Hao, "Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries," J. Opt. A: Pure Appl. Opt. 9, 468-475 (2007).
[CrossRef]

Microw. Opt. Tech. Lett. (1)

J.-Y. Lee and N.-H. Myung, "Locally tensor conformal FDTD method for modelling arbitrary dielectric surfaces," Microw. Opt. Tech. Lett. 23, 245-249 (1999).
[CrossRef]

Nat. Photonics (1)

Q1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (2007).
[CrossRef]

New J. Phys. (1)

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

Opt. Express (5)

Phys. Rev. B (2)

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035122 (2008).
[CrossRef]

Phys. Rev. E (3)

A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

M. G. Silveirinha, A. Alu, and N. Engheta, "Parallel-plate metamaterials for cloaking structures," Phys. Rev. E 75, 036603 (2007).
[CrossRef]

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

Phys. Rev. Lett (1)

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

Phys. Rev. Lett. (3)

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99113903 (2007).
[CrossRef] [PubMed]

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

Proc. R. Soc. A (1)

G. W. Milton, and N. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. A 462, 3027-3059 (2006).
[CrossRef]

Science (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, 977-980 (2006).
[CrossRef] [PubMed]

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

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

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative value of ?? and ??," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (5)

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, "Controlling the emission of electromagnetic sources by coordinate transformation," ArXiv.org:0712.3776v1 (2007).

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, "Electromagnetic cloaking in the visible frequency range," ArXiv.org:0709.2862v2 (2007).

R. Weder, "A rigorous time-domain analysis of fullwave electromagnetic cloaking (Invisibility)," ArXiv.org:0704.0248v4 (2007).

F. B. Hildebrand, Introduction to Numerical Analysis (New York: Mc-Graw-Hill, 1956).

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method 2nd ed. (Norwood, MA: Artech House, 2000).

Supplementary Material (3)

» Media 1: MOV (2756 KB)     
» Media 2: MOV (2840 KB)     
» Media 3: MOV (2763 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

The comparison between the analytical (2) and numerical material parameters (23) for different FDTD spatial resolutions for the case of εr =0.1 (lossless).

Fig. 2.
Fig. 2.

A two-dimensional (2-D) FDTD simulation domain for the case of plane-wave incidence on the cloak.

Fig. 3.
Fig. 3.

(a) Material parameters for an infinite ideal cylindrical cloak [3] where all εr , εϕ and µz are radial dependent. (b), (c) and (d) Field distributions from dispersive FDTD simulations of the cloak: (b) x-component of the electric field, (c) y-component of the electric field and (d) the magnetic field. [Media 1]

Fig. 4.
Fig. 4.

(a) Material parameters for an infinite simplified cylindrical cloak using a linear transformation [4] where only εr is radial dependent. (b), (c) and (d) Field distributions from dispersive FDTD simulations of the cloak: (b) x-component of the electric field, (c) y-component of the electric field and (d) the magnetic field. [Media 2]

Fig. 5.
Fig. 5.

(a) Material parameters for an infinite simplified cylindrical cloak using a high-order transformation [5] where only εr and εϕ are radial dependent. (b), (c) and (d) Field distributions from dispersive FDTD simulations of the cloak: (b) x-component of the electric field, (c) y-component of the electric field and (d) the magnetic field. [Media 3]

Fig. 6.
Fig. 6.

Power flow diagrams for (a) the ideal cloak [3], (b) the simplified cloak based on the linear transformation [4] and (c) the simplified cloak based on the high-order transformation [5]. (d) Comparison of the scattering patterns for different cloaks and for the case of the PEC cylinder without cloak: black solid line - PEC cylinder; yellow dot-dashed line - the simplified cloak based on the linear transformation; blue dashed line - the simplified cloak based on the high-order transformation; red solid line - the ideal cloak.

Equations (52)

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ε r = μ r = r R 1 r , ε ϕ = μ ϕ = r r R 1 , ε z = μ z = ( R 2 R 2 R 1 ) 2 r R 1 r ,
ε r ( ω ) = 1 ω p 2 ω 2 j ω γ ,
× E = B t ,
× H = D t ,
B n + 1 = B n Δ t · ˜ × E n + 1 2 ,
D n + 1 = D n + Δ t · ˜ × H n + 1 2 ,
[ ε xx ε xy ε yx ε yy ] = [ ε r cos 2 ϕ + ε ϕ sin 2 ϕ ( ε r ε ϕ ) sin ϕ cos ϕ ( ε r ε ϕ ) sin ϕ cos ϕ ε r sin 2 ϕ + ε ϕ cos 2 ϕ ]
ε 0 [ ε xx ε xy ε yx ε yy ] [ E x E y ] = [ D x D y ] ε 0 [ E x E y ] = [ ε xx ε xy ε yx ε yy ] 1 [ D x D y ] ,
[ ε xx ε xy ε yx ε yy ] 1 = 1 ε r ε ϕ [ ε r sin 2 ϕ + ε ϕ cos 2 ϕ ( ε ϕ ε r ) sin ϕ cos ϕ ( ε ϕ ε r ) sin ϕ cos ϕ ε r cos 2 ϕ + ε ϕ sin 2 ϕ ] .
{ ε r ε ϕ ε 0 E x = ( ε r sin 2 ϕ + ε ϕ cos 2 ϕ ) D x + ( ε ϕ ε r ) sin ϕ cos ϕ D y ε r ε ϕ ε 0 E y = ( ε r cos 2 ϕ + ε ϕ sin 2 ϕ ) D y + ( ε ϕ ε r ) sin ϕ cos ϕ D x ,
{ ε 0 ε ϕ ( ω 2 j ω γ ω p 2 ) E x = [ ( ω 2 j ω γ ω p 2 ) sin 2 ϕ + ε ϕ ( ω 2 j ω γ ) cos 2 ϕ ] D x + [ ε ϕ ( ω 2 j ω γ ) ( ω 2 j ω γ ω p 2 ) ] sin ϕ cos ϕ D y , ε 0 ε ϕ ( ω 2 j ω γ ω p 2 ) E y = [ ( ω 2 j ω γ ω p 2 ) cos 2 ϕ + ε ϕ ( ω 2 j ω γ ) sin 2 ϕ ] D y + [ ε ϕ ( ω 2 j ω γ ) ( ω 2 j ω γ ω p 2 ) ] sin ϕ cos ϕ D x .
j ω t , ω 2 2 t 2 ,
ε 0 ε ϕ ( 2 t 2 + γ t + ω p 2 ) E x = [ ( 2 t 2 + γ t + ω p 2 ) sin 2 ϕ + ε ϕ ( 2 t 2 + γ t ) cos 2 ϕ ] D x
+ [ ε ϕ ( 2 t 2 + γ t ) ( 2 t 2 + γ t + ω p 2 ) ] sin ϕ cos ϕ D y .
2 t 2 δ t 2 ( Δ t ) 2 , t δ t Δ t μ t , ω p 2 ω p 2 μ t 2 ,
δ t F m x , m y , m z n F m x , m y , m z n + 1 2 F m x , m y , m z n 1 2 ,
δ t 2 F m x , m y , m z n F m x , m y , m z n + 1 2 F m x , m y , m z n + F m x , m y , m z n 1 ,
μ t F m x , m y , m z n F m x , m y , m z n + 1 2 + F m x , m y , m z n 1 2 2 ,
μ t 2 F m x , m y , m z n F m x , m y , m z n + 1 + 2 F m x , m y , m z n + F m x , m y , m z n 1 4 .
ε 0 ε ϕ [ δ t 2 ( Δ t ) 2 + γ δ t Δ t μ t + ω p 2 μ t 2 ] E x = { [ δ t 2 ( Δ t ) 2 + γ δ t Δ t μ t + ω p 2 μ t 2 ] sin 2 ϕ
+ ε ϕ [ δ t 2 ( Δ t ) 2 + γ δ t Δ t μ t ] cos 2 ϕ } D x + { ε ϕ [ δ t 2 ( Δ t ) 2 + γ δ t Δ t μ t ]
[ δ t 2 ( Δ t ) 2 + γ δ t Δ t μ t + ω p 2 μ t 2 ] } sin ϕ cos ϕ D y .
ε 0 ε ϕ [ E x n + 1 2 E x n + E x n 1 ( Δ t ) 2 + γ E x n + 1 E x n 1 2 Δ t + ω p 2 E x n + 1 + 2 E x n + E x n 1 4 ]
= sin 2 ϕ [ D x n + 1 2 D x n + D x n 1 ( Δ t ) 2 + γ D x n + 1 D x n 1 2 Δ t + ω p 2 D x n + 1 + 2 D x n + D x n 1 4 ]
+ ε ϕ cos 2 ϕ [ D x n + 1 2 D x n + D x n 1 ( Δ t ) 2 + γ D x n + 1 D x n 1 2 Δ t ]
+ sin ϕ cos ϕ { ε ϕ [ D y n + 1 2 D y n + D y n 1 ( Δ t ) 2 + γ D y n + 1 D y n 1 2 Δ t ]
[ D y n + 1 2 D y n + D y n 1 ( Δ t ) 2 + γ D y n + 1 D y n 1 2 Δ t + ω p 2 D y n + 1 + 2 D y n + D y n 1 4 ] } .
E x n + 1 = [ a x D x n + 1 + b x D x n + c x D x n 1 + d x D y ¯ n + 1 + e x D y ¯ n + f x D y ¯ n 1 ( g x E x n + h x E x n 1 ) ] l x .
a x = sin 2 ϕ [ 1 ( Δ t ) 2 + γ 2 Δ t + ω p 2 4 ] + ε ϕ cos 2 ϕ [ 1 ( Δ t ) 2 + γ 2 Δ t ] ,
b x = sin 2 ϕ [ 2 ( Δ t ) 2 + ω p 2 2 ] ε ϕ cos 2 ϕ 2 ( Δ t ) 2 ,
c x = sin 2 ϕ [ 1 ( Δ t ) 2 γ 2 Δ t + ω p 2 4 ] + ε ϕ cos 2 ϕ [ 1 ( Δ t ) 2 γ 2 Δ t ] ,
d x = { ε ϕ [ 1 ( Δ t ) 2 + γ 2 Δ t ] [ 1 ( Δ t ) 2 + γ 2 Δ t + ω p 2 4 ] } sin ϕ cos ϕ ,
e x = { ε ϕ [ 2 ( Δ t ) 2 ] [ 2 ( Δ t ) 2 + ω p 2 2 ] } sin ϕ cos ϕ ,
f x = { ε ϕ [ 1 ( Δ t ) 2 γ 2 Δ t ] [ 1 ( Δ t ) 2 γ 2 Δ t + ω p 2 4 ] } sin ϕ cos ϕ ,
g x = ε 0 ε ϕ [ 2 ( Δ t ) 2 + ω p 2 2 ] ,       h x = ε 0 ε ϕ [ 1 ( Δ t ) 2 γ 2 Δ t + ω p 2 4 ] ,       l x = ε 0 ε ϕ [ 1 ( Δ t ) 2 + γ 2 Δ t + ω p 2 4 ] .
E y n + 1 = [ a y D y n + 1 + b y D y n + c y D y n 1 + d y D x ¯ n + 1 + e y D x ¯ n + f y D x ¯ n 1 ( g y E y n + h y E y n 1 ) ] l y .
a y = cos 2 ϕ [ 1 ( Δ t ) 2 + γ 2 Δ t + ω p 2 4 ] + ε ϕ sin 2 ϕ [ 1 ( Δ t ) 2 + γ 2 Δ t ] ,
b y = cos 2 ϕ [ 2 ( Δ t ) 2 + ω p 2 2 ] ε ϕ sin 2 ϕ 2 ( Δ t ) 2 ,
c y = cos 2 ϕ [ 1 ( Δ t ) 2 γ 2 Δ t + ω p 2 4 ] + ε ϕ sin 2 ϕ [ 1 ( Δ t ) 2 γ 2 Δ t ] ,
d y = { ε ϕ [ 1 ( Δ t ) 2 + γ 2 Δ t ] [ 1 ( Δ t ) 2 + γ 2 Δ t + ω p 2 4 ] } sin ϕ cos ϕ ,
e y = { ε ϕ [ 2 ( Δ t ) 2 ] [ 2 ( Δ t ) 2 + ω p 2 2 ] } sin ϕ cos ϕ ,
f y = { ε ϕ [ 1 ( Δ t ) 2 γ 2 Δ t ] [ 1 ( Δ t ) 2 γ 2 Δ t + ω p 2 4 ] } sin ϕ cos ϕ ,
g y = ε 0 ε ϕ [ 2 ( Δ t ) 2 + ω p 2 2 ] , h y = ε 0 ε ϕ [ 1 ( Δ t ) 2 γ 2 Δ t + ω p 2 4 ] , l y = ε 0 ε ϕ [ 1 ( Δ t ) 2 + γ 2 Δ t + ω p 2 4 ] .
D x ¯ ( i , j ) = D x ( i , j ) + D x ( i , j + 1 ) + D x ( i 1 , j ) + D x ( i 1 , j + 1 ) 4 ,
D y ¯ ( i , j ) = D y ( i , j ) + D y ( i + 1 , j ) + D y ( i , j 1 ) + D y ( i + 1 , j 1 ) 4 ,
μ z ( ω ) = A ( 1 ω pm 2 ω 2 j ω γ m ) ,
H z n + 1 = 1 A { [ 1 μ 0 ( Δ t ) 2 + γ m 2 μ 0 Δ t ] B z n + 1 2 μ 0 ( Δ t ) 2 B z n + [ 1 μ 0 ( Δ t ) 2 γ m 2 μ 0 Δ t ] B z n 1 + A [ 2 ( Δ t ) 2 ω pm 2 2 ] H 2 n A [ 1 ( Δ t ) 2 γ m 2 Δ t + ω pm 2 4 ] H z n 1 } [ 1 ( Δ t ) 2 + γ m 2 Δ t + ω pm 2 4 ] . .
E n = E e j n ω Δ t , D n = D e j n ω Δ t ,
ε r ~ = ε 0 [ 1 ω p 2 ( Δ t ) 2 cos 2 ω Δ t 2 2 sin ω Δ t 2 ( 2 sin ω Δ t 2 j γ Δ t cos ω Δ t 2 ) ] .
ω p 2 ~ = 2 sin ω Δ t 2 [ 2 ( ε r 1 ) sin ω Δ t 2 ε r γ Δ t cos ω Δ t 2 ] ( Δ t ) 2 cos 2 ω Δ t 2 , γ ~ = 2 ε r sin ω Δ t 2 ( ε r 1 ) Δ t cos ω Δ t 2 .
ε r = ( R 2 R 2 R 1 ) 2 ( r R 1 r ) 2 , ε ϕ = ( R 2 R 2 R 1 ) 2 , μ z = 1 .
ε r = ( r r ) 2 , ε ϕ = [ g ( r ) r ] 2 , μ z = 1 .

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