Abstract

Transformation optics provides a promising way to guide waves in the open space. It is shown that a small waveguide coated with transformation medium will behave as a big virtual tunnel connecting two waveguide ports separated faraway. The waves are transmitted and guided smoothly in the open space through this ‘invisible tunnel’. The transformation medium is obtained by squeezing the space between the two ports into a small region. Numerical simulations are performed to illustrate this idea.

©2009 Optical Society of America

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References

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  1. E. J. Post, Formal structure of electromagnetics (Wiley, New York, 1962).
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
    [Crossref] [PubMed]
  3. U. Leonhardt, “Optical Conformal Mapping,” Science 312, 1777–1780 (2006).
    [Crossref] [PubMed]
  4. R. V. Kohn and M. Vogelius, “Identification of an unknown conductivity by means of measurements at the boundary,” In Proc. Symp. Applied Mathematics of the American Mathematical Society and the Society for Industrial and Applied Mathematics, D.W. McLaughlin, ed. (SIAM-AMS Proc. No. 14, Amer. Math. Soc., Providence, 1984), pp. 113–123.
  5. A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas. 24, 413–419 (2003).
    [Crossref] [PubMed]
  6. R. V. Kohn, H. Shen, M. S. Vogelius, and M. I. Weinstein, “Cloaking via change of variables in electric impedance tomography,” Inverse Probl. 24, 015016 (2008).
    [Crossref]
  7. S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
    [Crossref]
  8. 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]
  9. 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]
  10. 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]
  11. F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
    [Crossref] [PubMed]
  12. 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]
  13. Y. Luo, H. S. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
    [Crossref]
  14. Y. Luo, J. Zhang, H. S. Chen, S. Xi, and B-I Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Letts. 93, 033504 (2008).
    [Crossref]
  15. R. Weder, “A rigorous analysis of high-order electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 065207 (2008).
    [Crossref]
  16. R. Weder, “The boundary conditions for point transformed electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 415401 (2008).
    [Crossref]
  17. A. Nicolet, J.-F. Remacle, B. Meys, A. Genon, and W. Legros, “Transformation methods in computational electromagnetism,” J. Appl. Phys. 75, 6036–6038 (1994).
    [Crossref]
  18. A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Optics 43, 773–793 (1996).
    [Crossref]
  19. A. Nicolet, S. Guenneau, and F. Zolla, “Modelling of twisted optical waveguides with edge elements,” Eur. Phys. J. Appl. Phys. 28, 153–157 (2004).
    [Crossref]
  20. A. Nicolet, A. B. Movchan, C. Geuzaine, F. Zolla, and S. Guenneau, “High order asymptotic analysis of twisted electrostatic problems,” Physica B 394, 335–338 (2007).
    [Crossref]
  21. S. Guenneau, B. Gralak, and J. B. Pendry, “Perfect corner reflector,” Opt. Lett. 30, 1204–1206 (2005).
    [Crossref] [PubMed]
  22. A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32, 3432–3434 (2007).
    [Crossref] [PubMed]
  23. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Letts. 90, 241105 (2007).
    [Crossref]
  24. D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16, 18731–18738 (2008).
    [Crossref]
  25. M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).
    [Crossref] [PubMed]
  26. J. Zhang, Y. Luo, H. S. Chen, and B. I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16, 10962–10967 (2008).
    [Crossref] [PubMed]
  27. Y. Luo, J. Zhang, L. Ran, H. S. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antenna. Wireless Propag. Lett. 7, 508–511 (2008).
  28. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008).
    [Crossref]
  29. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [Crossref]
  30. Y. Luo, J. Zhang, H. S. Chen, B-I. Wu, and J. A. Kong, “A new strategy to conceal an object from electromagnetic wave,” arXiv: 0808. 0215 (2008).
  31. T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: Enhancement of scattering with complementary media,” arXiv: 0807.5038 (2008).
  32. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Letts. 85, 3966–3969 (2000).
    [Crossref]
  33. R. Weder, “Dielectric three dimensional electromagnetic tapers with no loss,” IEEE J. Quantum Electron. 24, 775–779 (1988).
    [Crossref]
  34. J. Huangfu, S. Xi, F. Kong, J. Zhang, H. S. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys. 104. 014502 (2008).
    [Crossref]

2008 (12)

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

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]

Y. Luo, H. S. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

Y. Luo, J. Zhang, H. S. Chen, S. Xi, and B-I Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Letts. 93, 033504 (2008).
[Crossref]

R. Weder, “A rigorous analysis of high-order electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 065207 (2008).
[Crossref]

R. Weder, “The boundary conditions for point transformed electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 415401 (2008).
[Crossref]

Y. Luo, J. Zhang, L. Ran, H. S. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antenna. Wireless Propag. Lett. 7, 508–511 (2008).

J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008).
[Crossref]

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. S. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys. 104. 014502 (2008).
[Crossref]

J. Zhang, Y. Luo, H. S. Chen, and B. I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16, 10962–10967 (2008).
[Crossref] [PubMed]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).
[Crossref] [PubMed]

D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16, 18731–18738 (2008).
[Crossref]

2007 (4)

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
[Crossref] [PubMed]

A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32, 3432–3434 (2007).
[Crossref] [PubMed]

A. Nicolet, A. B. Movchan, C. Geuzaine, F. Zolla, and S. Guenneau, “High order asymptotic analysis of twisted electrostatic problems,” Physica B 394, 335–338 (2007).
[Crossref]

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Letts. 90, 241105 (2007).
[Crossref]

2006 (6)

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]

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

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]

2005 (1)

2004 (1)

A. Nicolet, S. Guenneau, and F. Zolla, “Modelling of twisted optical waveguides with edge elements,” Eur. Phys. J. Appl. Phys. 28, 153–157 (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]

2000 (1)

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Letts. 85, 3966–3969 (2000).
[Crossref]

1996 (1)

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Optics 43, 773–793 (1996).
[Crossref]

1994 (1)

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

1988 (1)

R. Weder, “Dielectric three dimensional electromagnetic tapers with no loss,” IEEE J. Quantum Electron. 24, 775–779 (1988).
[Crossref]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[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.

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Letts. 90, 241105 (2007).
[Crossref]

Chen, H.

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Letts. 90, 241105 (2007).
[Crossref]

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: Enhancement of scattering with complementary media,” arXiv: 0807.5038 (2008).

Chen, H. S.

Y. Luo, J. Zhang, L. Ran, H. S. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antenna. Wireless Propag. Lett. 7, 508–511 (2008).

Y. Luo, J. Zhang, H. S. Chen, S. Xi, and B-I Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Letts. 93, 033504 (2008).
[Crossref]

J. Zhang, Y. Luo, H. S. Chen, and B. I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16, 10962–10967 (2008).
[Crossref] [PubMed]

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. S. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys. 104. 014502 (2008).
[Crossref]

Y. Luo, H. S. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008).
[Crossref]

Y. Luo, J. Zhang, H. S. Chen, B-I. Wu, and J. A. Kong, “A new strategy to conceal an object from electromagnetic wave,” arXiv: 0808. 0215 (2008).

Cummer, S. A.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “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]

Genon, A.

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

Geuzaine, C.

A. Nicolet, A. B. Movchan, C. Geuzaine, F. Zolla, and S. Guenneau, “High order asymptotic analysis of twisted electrostatic problems,” Physica B 394, 335–338 (2007).
[Crossref]

Gralak, B.

Greenleaf, A.

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, A. B. Movchan, C. Geuzaine, F. Zolla, and S. Guenneau, “High order asymptotic analysis of twisted electrostatic problems,” Physica B 394, 335–338 (2007).
[Crossref]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
[Crossref] [PubMed]

S. Guenneau, B. Gralak, and J. B. Pendry, “Perfect corner reflector,” Opt. Lett. 30, 1204–1206 (2005).
[Crossref] [PubMed]

A. Nicolet, S. Guenneau, and F. Zolla, “Modelling of twisted optical waveguides with edge elements,” Eur. Phys. J. Appl. Phys. 28, 153–157 (2004).
[Crossref]

Huangfu, J.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. S. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys. 104. 014502 (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]

Kildishev, A. V.

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, 015016 (2008).
[Crossref]

R. V. Kohn and M. Vogelius, “Identification of an unknown conductivity by means of measurements at the boundary,” In Proc. Symp. Applied Mathematics of the American Mathematical Society and the Society for Industrial and Applied Mathematics, D.W. McLaughlin, ed. (SIAM-AMS Proc. No. 14, Amer. Math. Soc., Providence, 1984), pp. 113–123.

Kong, F.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. S. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys. 104. 014502 (2008).
[Crossref]

Kong, J. A.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. S. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys. 104. 014502 (2008).
[Crossref]

Y. Luo, H. S. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008).
[Crossref]

Y. Luo, J. Zhang, L. Ran, H. S. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antenna. Wireless Propag. Lett. 7, 508–511 (2008).

Y. Luo, J. Zhang, H. S. Chen, B-I. Wu, and J. A. Kong, “A new strategy to conceal an object from electromagnetic wave,” arXiv: 0808. 0215 (2008).

Kwon, D. H.

Lassas, M.

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 electromagnetism,” J. Appl. Phys. 75, 6036–6038 (1994).
[Crossref]

Leonhardt, U.

U. Leonhardt, “Optical Conformal Mapping,” Science 312, 1777–1780 (2006).
[Crossref] [PubMed]

Luo, X.

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: Enhancement of scattering with complementary media,” arXiv: 0807.5038 (2008).

Luo, Y.

Y. Luo, J. Zhang, L. Ran, H. S. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antenna. Wireless Propag. Lett. 7, 508–511 (2008).

Y. Luo, J. Zhang, H. S. Chen, S. Xi, and B-I Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Letts. 93, 033504 (2008).
[Crossref]

J. Zhang, Y. Luo, H. S. Chen, and B. I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16, 10962–10967 (2008).
[Crossref] [PubMed]

J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008).
[Crossref]

Y. Luo, H. S. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

Y. Luo, J. Zhang, H. S. Chen, B-I. Wu, and J. A. Kong, “A new strategy to conceal an object from electromagnetic wave,” arXiv: 0808. 0215 (2008).

Ma, H.

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: Enhancement of scattering with complementary media,” arXiv: 0807.5038 (2008).

Meys, B.

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

Milton, G. W.

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]

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]

Movchan, A. B.

A. Nicolet, A. B. Movchan, C. Geuzaine, F. Zolla, and S. Guenneau, “High order asymptotic analysis of twisted electrostatic problems,” Physica B 394, 335–338 (2007).
[Crossref]

Narimanov, E. E.

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, A. B. Movchan, C. Geuzaine, F. Zolla, and S. Guenneau, “High order asymptotic analysis of twisted electrostatic problems,” Physica B 394, 335–338 (2007).
[Crossref]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
[Crossref] [PubMed]

A. Nicolet, S. Guenneau, and F. Zolla, “Modelling of twisted optical waveguides with edge elements,” Eur. Phys. J. Appl. Phys. 28, 153–157 (2004).
[Crossref]

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

Pendry, J. B.

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).
[Crossref] [PubMed]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
[Crossref] [PubMed]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “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]

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]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

S. Guenneau, B. Gralak, and J. B. Pendry, “Perfect corner reflector,” Opt. Lett. 30, 1204–1206 (2005).
[Crossref] [PubMed]

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Letts. 85, 3966–3969 (2000).
[Crossref]

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Optics 43, 773–793 (1996).
[Crossref]

Popa, B.-I.

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

Post, E. J.

E. J. Post, Formal structure of electromagnetics (Wiley, New York, 1962).

Rahm, M.

Ran, L.

Y. Luo, J. Zhang, L. Ran, H. S. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antenna. Wireless Propag. Lett. 7, 508–511 (2008).

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. S. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys. 104. 014502 (2008).
[Crossref]

J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008).
[Crossref]

Y. Luo, H. S. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

Remacle, J.-F.

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

Roberts, D. A.

Schurig, D.

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]

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, D. R. Smith, and J. B. Pendry, “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]

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, 015016 (2008).
[Crossref]

Smith, D. R.

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (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. 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, D. R. Smith, and J. B. Pendry, “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]

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]

Uhlmann, G.

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

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

Vogelius, M.

R. V. Kohn and M. Vogelius, “Identification of an unknown conductivity by means of measurements at the boundary,” In Proc. Symp. Applied Mathematics of the American Mathematical Society and the Society for Industrial and Applied Mathematics, D.W. McLaughlin, ed. (SIAM-AMS Proc. No. 14, Amer. Math. Soc., Providence, 1984), pp. 113–123.

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, 015016 (2008).
[Crossref]

Wang, D.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. S. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys. 104. 014502 (2008).
[Crossref]

Ward, A. J.

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Optics 43, 773–793 (1996).
[Crossref]

Weder, R.

R. Weder, “The boundary conditions for point transformed electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 415401 (2008).
[Crossref]

R. Weder, “A rigorous analysis of high-order electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 065207 (2008).
[Crossref]

R. Weder, “Dielectric three dimensional electromagnetic tapers with no loss,” IEEE J. Quantum Electron. 24, 775–779 (1988).
[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, 015016 (2008).
[Crossref]

Werner, D. H.

Willis, J. R.

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.

Wu, B.-I.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. S. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys. 104. 014502 (2008).
[Crossref]

J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008).
[Crossref]

Wu, B-I

Y. Luo, J. Zhang, H. S. Chen, S. Xi, and B-I Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Letts. 93, 033504 (2008).
[Crossref]

Wu, B-I.

Y. Luo, J. Zhang, H. S. Chen, B-I. Wu, and J. A. Kong, “A new strategy to conceal an object from electromagnetic wave,” arXiv: 0808. 0215 (2008).

Xi, S.

J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008).
[Crossref]

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. S. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys. 104. 014502 (2008).
[Crossref]

Y. Luo, J. Zhang, H. S. Chen, S. Xi, and B-I Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Letts. 93, 033504 (2008).
[Crossref]

Yang, T.

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: Enhancement of scattering with complementary media,” arXiv: 0807.5038 (2008).

Zhang, J.

Y. Luo, J. Zhang, L. Ran, H. S. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antenna. Wireless Propag. Lett. 7, 508–511 (2008).

Y. Luo, J. Zhang, H. S. Chen, S. Xi, and B-I Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Letts. 93, 033504 (2008).
[Crossref]

J. Zhang, Y. Luo, H. S. Chen, and B. I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16, 10962–10967 (2008).
[Crossref] [PubMed]

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. S. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys. 104. 014502 (2008).
[Crossref]

J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008).
[Crossref]

Y. Luo, H. S. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

Y. Luo, J. Zhang, H. S. Chen, B-I. Wu, and J. A. Kong, “A new strategy to conceal an object from electromagnetic wave,” arXiv: 0808. 0215 (2008).

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]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
[Crossref] [PubMed]

A. Nicolet, A. B. Movchan, C. Geuzaine, F. Zolla, and S. Guenneau, “High order asymptotic analysis of twisted electrostatic problems,” Physica B 394, 335–338 (2007).
[Crossref]

A. Nicolet, S. Guenneau, and F. Zolla, “Modelling of twisted optical waveguides with edge elements,” Eur. Phys. J. Appl. Phys. 28, 153–157 (2004).
[Crossref]

Appl. Phys. Letts. (2)

Y. Luo, J. Zhang, H. S. Chen, S. Xi, and B-I Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Letts. 93, 033504 (2008).
[Crossref]

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Letts. 90, 241105 (2007).
[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. 28, 153–157 (2004).
[Crossref]

IEEE Antenna. Wireless Propag. Lett. (1)

Y. Luo, J. Zhang, L. Ran, H. S. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antenna. Wireless Propag. Lett. 7, 508–511 (2008).

IEEE J. Quantum Electron. (1)

R. Weder, “Dielectric three dimensional electromagnetic tapers with no loss,” IEEE J. Quantum Electron. 24, 775–779 (1988).
[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, 015016 (2008).
[Crossref]

J. Appl. Phys. (2)

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

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. S. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys. 104. 014502 (2008).
[Crossref]

J. Mod. Optics (1)

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Optics 43, 773–793 (1996).
[Crossref]

J. Phys. A: Math. Theor. (2)

R. Weder, “A rigorous analysis of high-order electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 065207 (2008).
[Crossref]

R. Weder, “The boundary conditions for point transformed electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 415401 (2008).
[Crossref]

New J. Phys. (1)

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 Lett. (1)

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]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. B (1)

Y. Luo, H. S. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

Phys. Rev. E (1)

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

Phys. Rev. Letts. (1)

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Letts. 85, 3966–3969 (2000).
[Crossref]

Physica B (1)

A. Nicolet, A. B. Movchan, C. Geuzaine, F. Zolla, and S. Guenneau, “High order asymptotic analysis of twisted electrostatic problems,” Physica B 394, 335–338 (2007).
[Crossref]

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]

Prog. Electromagn. Res. (1)

J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. 81, 437–446 (2008).
[Crossref]

Science (3)

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]

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]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

Other (4)

Y. Luo, J. Zhang, H. S. Chen, B-I. Wu, and J. A. Kong, “A new strategy to conceal an object from electromagnetic wave,” arXiv: 0808. 0215 (2008).

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: Enhancement of scattering with complementary media,” arXiv: 0807.5038 (2008).

R. V. Kohn and M. Vogelius, “Identification of an unknown conductivity by means of measurements at the boundary,” In Proc. Symp. Applied Mathematics of the American Mathematical Society and the Society for Industrial and Applied Mathematics, D.W. McLaughlin, ed. (SIAM-AMS Proc. No. 14, Amer. Math. Soc., Providence, 1984), pp. 113–123.

E. J. Post, Formal structure of electromagnetics (Wiley, New York, 1962).

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic of a waveguide in free space whose two ports A and B are far away from each other. (b) With the transformation medium, we can build an invisible tunnel between the two ports to transmit waves in the open space. The dashed sphere with radius D denotes the original space before transformation, and the dark blue sphere with radius R 1 represents the transformed space. The light blue annulus region is designed to meet the impedance matching requirement.

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Fig. 2
Fig. 2 (a) Electric field distribution when the TE polarized wave is transmitted by the 2D waveguide (b) Two waveguide ports placed face to face. The EM wave is transmitted from the left port and a large portion of the energy is dispersed in the open space. (c) Electric field distribution of the system when a small waveguide coated with a transformation medium is placed between the two open waveguide ports, behaving as a large invisible tunnel connecting the two ports.

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Fig. 3
Fig. 3 (a) Field distribution when a small waveguide coated with transformation medium is placed between two big waveguide ports which are separated faraway. (b) Field distribution of the above case when the transformation medium is shifted to the side of the waveguides ports.

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Fig. 4.
Fig. 4. The electric field distribution of the case where a small bent waveguide (0.02m wide) coated with transformation medium works as a tunnel connecting two orthogonally located waveguide ports (0.2m wide).

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Equations (2)

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

ε ρρ = μ ρρ = f ( ρ ) ρf ′ ( ρ ) , ε φφ = μ φφ = ρf ( ρ ) f ( ρ ) , ε zz = μ zz = f ′ ( ρ ) f ( ρ ) ρ ,
f ( ρ ) = { D R 1 ρ , for ρ < R 1 R 2 − D R 2 − R 1 ( ρ − R 1 ) + D , for R 1 < ρ < R 2 .

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