Abstract

We propose a method of tunneling electromagnetic (EM) waves through a channel with sub-wavelength cross section. By filling the channel with high-ε isotropic material and implementing two matching layers with uniaxial metamterial substrates, the guided waves can go through the narrow channel without being cut off, as if it has just passed through the original empty waveguide. Both the magnitude and phase information of the EM fields can be effectively restored after passing this channel, regardless of the polarization of the incoming wave. The performance of this sub-wavelength channel, which is designed with coordinate transformation methodology, is studied theoretically and numerically.

© 2010 OSA

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  1. H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006).
    [CrossRef] [PubMed]
  2. M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
    [CrossRef] [PubMed]
  3. R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008).
    [CrossRef] [PubMed]
  4. B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
    [CrossRef] [PubMed]
  5. M. G. Silveirinha and N. Engheta, “Transporting an Image through a Subwavelength Hole,” Phys. Rev. Lett. 102(10), 103902 (2009).
    [CrossRef] [PubMed]
  6. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  7. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [CrossRef] [PubMed]
  8. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
    [CrossRef] [PubMed]
  9. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
    [CrossRef] [PubMed]
  10. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
    [CrossRef] [PubMed]
  11. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon Nanostructure Cloak Operating at Optical Frequencies,” Nat. Photonics 3(8), 461–463 (2009).
    [CrossRef]
  12. H. Chen and C. T. Chan, “Transformation Media that Rotate Electromagnetic Fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
    [CrossRef]
  13. J. Zhang, Y. Luo, H. Chen, and B. I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16(15), 10962–10967 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-15-10962 .
    [CrossRef] [PubMed]
  14. Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antennas Wirel. Propag. Lett. 7, 509–511 (2008).
    [CrossRef]
  15. 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(15), 11555–11567 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-15-11555 .
    [CrossRef] [PubMed]
  16. D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16(23), 18731–18738 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-18731 .
    [CrossRef]
  17. H. Ma, S. Qu, Z. Xu, and J. Wang, “General method for designing wave shape transformers,” Opt. Express 16(26), 22072–22082 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-26-22072 .
    [CrossRef] [PubMed]
  18. Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity Antenna with Small Antenna Aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
    [CrossRef]
  19. Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A Rigorous Analysis of Plane-transformed Invisibility Cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
    [CrossRef]
  20. J. Pendry, “Taking the Wraps off Cloaking,” Physics 2, 95 (2009).
    [CrossRef]

2009 (7)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon Nanostructure Cloak Operating at Optical Frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

M. G. Silveirinha and N. Engheta, “Transporting an Image through a Subwavelength Hole,” Phys. Rev. Lett. 102(10), 103902 (2009).
[CrossRef] [PubMed]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity Antenna with Small Antenna Aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A Rigorous Analysis of Plane-transformed Invisibility Cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

J. Pendry, “Taking the Wraps off Cloaking,” Physics 2, 95 (2009).
[CrossRef]

2008 (8)

J. Zhang, Y. Luo, H. Chen, and B. I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16(15), 10962–10967 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-15-10962 .
[CrossRef] [PubMed]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antennas Wirel. Propag. Lett. 7, 509–511 (2008).
[CrossRef]

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(15), 11555–11567 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-15-11555 .
[CrossRef] [PubMed]

D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16(23), 18731–18738 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-18731 .
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, “General method for designing wave shape transformers,” Opt. Express 16(26), 22072–22082 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-26-22072 .
[CrossRef] [PubMed]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008).
[CrossRef] [PubMed]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

2007 (1)

H. Chen and C. T. Chan, “Transformation Media that Rotate Electromagnetic Fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[CrossRef]

2006 (4)

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006).
[CrossRef] [PubMed]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
[CrossRef] [PubMed]

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

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Alù, A.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon Nanostructure Cloak Operating at Optical Frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Chan, C. T.

H. Chen and C. T. Chan, “Transformation Media that Rotate Electromagnetic Fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[CrossRef]

Chen, H.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity Antenna with Small Antenna Aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A Rigorous Analysis of Plane-transformed Invisibility Cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

J. Zhang, Y. Luo, H. Chen, and B. I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16(15), 10962–10967 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-15-10962 .
[CrossRef] [PubMed]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antennas Wirel. Propag. Lett. 7, 509–511 (2008).
[CrossRef]

H. Chen and C. T. Chan, “Transformation Media that Rotate Electromagnetic Fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[CrossRef]

Cheng, Q.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008).
[CrossRef] [PubMed]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008).
[CrossRef] [PubMed]

Cummer, S. A.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008).
[CrossRef] [PubMed]

Edwards, B.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

Engheta, N.

M. G. Silveirinha and N. Engheta, “Transporting an Image through a Subwavelength Hole,” Phys. Rev. Lett. 102(10), 103902 (2009).
[CrossRef] [PubMed]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
[CrossRef] [PubMed]

Gabrielli, L. H.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon Nanostructure Cloak Operating at Optical Frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Hand, T.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008).
[CrossRef] [PubMed]

Huangfu, J.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity Antenna with Small Antenna Aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[CrossRef]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Kong, J. A.

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A Rigorous Analysis of Plane-transformed Invisibility Cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antennas Wirel. Propag. Lett. 7, 509–511 (2008).
[CrossRef]

Kurokawa, Y.

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006).
[CrossRef] [PubMed]

Kwon, D. H.

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

Lipson, M.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon Nanostructure Cloak Operating at Optical Frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008).
[CrossRef] [PubMed]

Luo, Y.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity Antenna with Small Antenna Aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A Rigorous Analysis of Plane-transformed Invisibility Cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

J. Zhang, Y. Luo, H. Chen, and B. I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16(15), 10962–10967 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-15-10962 .
[CrossRef] [PubMed]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antennas Wirel. Propag. Lett. 7, 509–511 (2008).
[CrossRef]

Ma, H.

Miyazaki, H. T.

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006).
[CrossRef] [PubMed]

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008).
[CrossRef] [PubMed]

Pendry, J.

J. Pendry, “Taking the Wraps off Cloaking,” Physics 2, 95 (2009).
[CrossRef]

Pendry, J. B.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (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(15), 11555–11567 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-15-11555 .
[CrossRef] [PubMed]

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

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon Nanostructure Cloak Operating at Optical Frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Qu, S.

Rahm, M.

Ran, L.

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A Rigorous Analysis of Plane-transformed Invisibility Cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity Antenna with Small Antenna Aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[CrossRef]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antennas Wirel. Propag. Lett. 7, 509–511 (2008).
[CrossRef]

Roberts, D. A.

Schurig, D.

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

Silveirinha, M.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
[CrossRef] [PubMed]

Silveirinha, M. G.

M. G. Silveirinha and N. Engheta, “Transporting an Image through a Subwavelength Hole,” Phys. Rev. Lett. 102(10), 103902 (2009).
[CrossRef] [PubMed]

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (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(15), 11555–11567 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-15-11555 .
[CrossRef] [PubMed]

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

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Wang, J.

Werner, D. H.

Wu, B. I.

Wu, B.-I.

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A Rigorous Analysis of Plane-transformed Invisibility Cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

Xu, Z.

Young, M. E.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Zhang, J.

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A Rigorous Analysis of Plane-transformed Invisibility Cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity Antenna with Small Antenna Aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[CrossRef]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antennas Wirel. Propag. Lett. 7, 509–511 (2008).
[CrossRef]

J. Zhang, Y. Luo, H. Chen, and B. I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16(15), 10962–10967 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-15-10962 .
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

H. Chen and C. T. Chan, “Transformation Media that Rotate Electromagnetic Fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity Antenna with Small Antenna Aperture,” Appl. Phys. Lett. 95(19), 193506 (2009).
[CrossRef]

IEEE Antennas Wirel. Propag. Lett. (1)

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “New Concept Conformal Antennas Utilizing Metamaterial and Transformation Optics,” IEEE Antennas Wirel. Propag. Lett. 7, 509–511 (2008).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A Rigorous Analysis of Plane-transformed Invisibility Cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

Nat. Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Nat. Photonics (1)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon Nanostructure Cloak Operating at Optical Frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Opt. Express (4)

Phys. Rev. Lett. (6)

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006).
[CrossRef] [PubMed]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
[CrossRef] [PubMed]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008).
[CrossRef] [PubMed]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

M. G. Silveirinha and N. Engheta, “Transporting an Image through a Subwavelength Hole,” Phys. Rev. Lett. 102(10), 103902 (2009).
[CrossRef] [PubMed]

Physics (1)

J. Pendry, “Taking the Wraps off Cloaking,” Physics 2, 95 (2009).
[CrossRef]

Science (3)

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

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) A coordinate transformation that compresses a trapezoiform region along the y axis into a narrow channel-shaped region.

Fig. 2
Fig. 2

The electric field distribution inside planar waveguides under the TE1 mode excitation in five different conditions. In all the cases, the width of the planar waveguide is 0.1m, while the width of the channel is 0.01m. (a) an empty waveguide (b) a sub-wavelength channel is embedded inside the waveguide. (c) a waveguide with the embedded channel filled with metamaterial substrate characterized by Eq. (2). (d) a waveguide with the same matched layers at both sides with those in (c), but high-ε isotropic material in the central channel (e) a waveguide with only high-ε isotropic material in the central channel.

Fig. 3
Fig. 3

Schematic figure showing (a) an EM wave with electric field polarized along z direction is incident upon the interface of an isotropic (left) and an anisotropic media (right). (b) a triangular anisotropic medium with free space on the left side, high-ε medium on the right side.

Fig. 4
Fig. 4

The electric field distribution for planar waveguides under TEM mode excitation in four different conditions. In all the cases, the widths of the planar waveguide and the channel are 0.06m and 0.01m, respectively. (a) an empty waveguide. (b) a sub-wavelength channel is embedded in the waveguide. (c) the sub-wavelength channel is filled with ENZ metamaterial [2]. (d) the sub-wavelength channel is filled with transformation media characterized by Eqs. (2-)a), (2-b), and (3).

Fig. 5
Fig. 5

The electric field distribution for planar waveguides under TM3 mode excitation in five different conditions. In all the cases, the widths of the waveguide and the channel are 0.3m and 0.02m, respectively. (a) an empty waveguide. (b) a narrow channel is embedded in the waveguide. (c) the sub-wavelength channel is filled with transformation media characterized by Eqs. (2-)a), (2-b), and (3). (d) the sub-wavelength channel is filled with ENZ metamaterial.

Equations (12)

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x = x ,   y = h 2 h 1 h 2 y + h 1 d ( l + d + x ) ,   z = z         for  ( l + d ) < x < l ,
x = x ,   y = h 2 h 1 h 2 y + h 1 d ( l + d x ) ,   z = z         for  l < x < l + d ,
x = x ,   y = h 2 h 1 h 2 y + h 1 ,   z = z         for  l < x < l .
ε z z = μ z z = h 2 h 2 h 1 ,   ε x x = μ x x = h 2 h 2 h 1 , ε y y = μ y y = h 2 h 1 h 2 + h 2 h 2 h 1 ( h 1 d ) 2 ,                   ε x y = μ x y = h 1 h 2 ( h 2 h 1 ) d     for  ( l + d ) < x < l ,
ε z z = μ z z = h 2 h 2 h 1 ,   ε x x = μ x x = h 2 h 2 h 1 , ε y y = μ y y = h 2 h 1 h 2 + h 2 h 2 h 1 ( h 1 d ) 2 ,                   ε x y = μ x y = h 1 h 2 ( h 2 h 1 ) d     for  l < x < ( l + d ) ,
ε z z = μ z z = h 2 h 2 h 1 ,   ε x x = μ x x = h 2 h 2 h 1 , ε y y = μ y y = h 2 h 1 h 2   for  l < x < l .
ε z z = μ z z = ( h 2 h 2 h 1 ) 2 , ε x x = μ x x = 1 , ε y y = μ y y = 1     for  l < x < l .
μ y y 2 y 2 E z + μ x x 2 x 2 E z + ( μ x y + μ y x ) 2 x y E z + ε z z ( μ x x μ y y μ x y μ y x ) k 0 2 E z = 0.
E ¯ i = z ^ E 0 e i k x x + i k y y , E ¯ R = z ^ R E 0 e i k x x + i k y y , E ¯ T = z ^ T E 0 e k x x + i k y y .
1 + R = T ,   and    1 R = μ 1 ( μ y x k y + μ x x k x ) k x ( μ x x μ y y μ x y μ y x ) T .
μ 1 μ x x ε z z k 0 2 k y 2 ( μ 1 ε 1 k 0 2 k y 2 ) ( μ x x μ y y μ x y 2 ) = 1.
μ x x μ y y μ x y 2 = 1 ,   μ x x ε z z = ε 1 .

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