Abstract

We demonstrate that a transformation device can be emulated using a gradient-index waveguide. The effective index of the waveguide is spatially varied by tailoring a gradient thickness dielectric waveguide. Based on this technology, we demonstrate a transformation device guiding visible light around a sharp corner, with low scattering loss and reflection loss. The experimental results are in good agreement with the numerical results.

© 2012 OSA

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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  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(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  4. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
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  5. X. D. Luo, T. Yang, Y. W. Gu, H. Y. Chen, and H. R. Ma, “Conceal an entrance by means of superscatterer,” Appl. Phys. Lett. 94(22), 223513 (2009).
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  6. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
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  7. E. E. Narimanov and A. V. Kildishev, “Optical black hole: broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
    [CrossRef]
  8. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations,” Photonics Nanostruct. Fundam. Appl.. 6(1), 87–95 (2008).
    [CrossRef]
  9. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
    [CrossRef]
  10. H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
    [CrossRef] [PubMed]
  11. 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(6), 063903 (2008).
    [CrossRef] [PubMed]
  12. D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
    [CrossRef]
  13. 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).
    [CrossRef] [PubMed]
  14. Z. L. Mei and T. J. Cui, “Experimental realization of a broadband bend structure using gradient index metamaterials,” Opt. Express 17(20), 18354–18363 (2009).
    [CrossRef] [PubMed]
  15. B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105(4), 044905 (2009).
    [CrossRef]
  16. M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
    [CrossRef]
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  20. 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]
  21. 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]
  22. E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
    [CrossRef]
  23. K. V. Do, X. Le Roux, D. Marris-Morini, L. Vivien, and E. Cassan, “Experimental demonstration of light bending at optical frequencies using a non-homogenizable graded photonic crystal,” Opt. Express 20(4), 4776–4783 (2012).
    [CrossRef] [PubMed]
  24. T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
    [CrossRef] [PubMed]
  25. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, 1964).
  26. I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102(21), 213901 (2009).
    [CrossRef] [PubMed]
  27. V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Maxwell fish-eye and Eaton lenses emulated by microdroplets,” Opt. Lett. 35(20), 3396–3398 (2010).
    [CrossRef] [PubMed]

2012 (1)

2011 (1)

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[CrossRef] [PubMed]

2010 (1)

2009 (12)

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102(21), 213901 (2009).
[CrossRef] [PubMed]

X. D. Luo, T. Yang, Y. W. Gu, H. Y. Chen, and H. R. Ma, “Conceal an entrance by means of superscatterer,” Appl. Phys. Lett. 94(22), 223513 (2009).
[CrossRef]

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

E. E. Narimanov and A. V. Kildishev, “Optical black hole: broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
[CrossRef]

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105(4), 044905 (2009).
[CrossRef]

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]

H. Ma, S. Qu, Z. Xu, and J. Wang, “Wave-shape-keeping media,” Opt. Lett. 34(2), 127–129 (2009).
[CrossRef] [PubMed]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17(19), 16535–16542 (2009).
[CrossRef] [PubMed]

T. R. Zhai, Y. Zhou, J. Zhou, and D. H. Liu, “Polarization controller based on embedded optical transformation,” Opt. Express 17(20), 17206–17213 (2009).
[CrossRef] [PubMed]

Z. L. Mei and T. J. Cui, “Experimental realization of a broadband bend structure using gradient index metamaterials,” Opt. Express 17(20), 18354–18363 (2009).
[CrossRef] [PubMed]

2008 (6)

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[CrossRef]

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(6), 063903 (2008).
[CrossRef] [PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[CrossRef]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations,” Photonics Nanostruct. Fundam. Appl.. 6(1), 87–95 (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).
[CrossRef] [PubMed]

2007 (2)

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
[CrossRef] [PubMed]

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[CrossRef]

2006 (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]

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Akmansoy, E.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

Alu, A.

B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105(4), 044905 (2009).
[CrossRef]

Ao, X.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[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]

Cassagne, D.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

Cassan, E.

Centeno, E.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

Chan, C. T.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[CrossRef]

Chen, H.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[CrossRef]

Chen, H. Y.

X. D. Luo, T. Yang, Y. W. Gu, H. Y. Chen, and H. R. Ma, “Conceal an entrance by means of superscatterer,” Appl. Phys. Lett. 94(22), 223513 (2009).
[CrossRef]

Chen, S.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

Cui, T. J.

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(6), 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations,” Photonics Nanostruct. Fundam. Appl.. 6(1), 87–95 (2008).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Do, K. V.

Edwards, B.

B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105(4), 044905 (2009).
[CrossRef]

Engheta, N.

B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105(4), 044905 (2009).
[CrossRef]

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]

Genov, D. A.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
[CrossRef] [PubMed]

Gu, Y. W.

X. D. Luo, T. Yang, Y. W. Gu, H. Y. Chen, and H. R. Ma, “Conceal an entrance by means of superscatterer,” Appl. Phys. Lett. 94(22), 223513 (2009).
[CrossRef]

Hou, B.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kildishev, A. V.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Maxwell fish-eye and Eaton lenses emulated by microdroplets,” Opt. Lett. 35(20), 3396–3398 (2010).
[CrossRef] [PubMed]

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102(21), 213901 (2009).
[CrossRef] [PubMed]

E. E. Narimanov and A. V. Kildishev, “Optical black hole: broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
[CrossRef]

Kundtz, N.

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
[CrossRef] [PubMed]

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
[CrossRef] [PubMed]

Le Roux, X.

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]

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, D. H.

Liu, Y.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[CrossRef] [PubMed]

Lourtioz, J. M.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

Luo, X. D.

X. D. Luo, T. Yang, Y. W. Gu, H. Y. Chen, and H. R. Ma, “Conceal an entrance by means of superscatterer,” Appl. Phys. Lett. 94(22), 223513 (2009).
[CrossRef]

Ma, H.

Ma, H. R.

X. D. Luo, T. Yang, Y. W. Gu, H. Y. Chen, and H. R. Ma, “Conceal an entrance by means of superscatterer,” Appl. Phys. Lett. 94(22), 223513 (2009).
[CrossRef]

Marris-Morini, D.

Mei, Z. L.

Mikkelsen, M. H.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[CrossRef] [PubMed]

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Narimanov, E. E.

E. E. Narimanov and A. V. Kildishev, “Optical black hole: broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
[CrossRef]

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(6), 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations,” Photonics Nanostruct. Fundam. Appl.. 6(1), 87–95 (2008).
[CrossRef]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (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).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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(5801), 977–980 (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]

Qiu, M.

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[CrossRef]

Qu, S.

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(6), 063903 (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).
[CrossRef] [PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[CrossRef]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations,” Photonics Nanostruct. Fundam. Appl.. 6(1), 87–95 (2008).
[CrossRef]

Roberts, D. A.

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17(19), 16535–16542 (2009).
[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).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations,” Photonics Nanostruct. Fundam. Appl.. 6(1), 87–95 (2008).
[CrossRef]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[CrossRef]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations,” Photonics Nanostruct. Fundam. Appl.. 6(1), 87–95 (2008).
[CrossRef]

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(6), 063903 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Maxwell fish-eye and Eaton lenses emulated by microdroplets,” Opt. Lett. 35(20), 3396–3398 (2010).
[CrossRef] [PubMed]

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102(21), 213901 (2009).
[CrossRef] [PubMed]

Silveirinha, M. G.

B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105(4), 044905 (2009).
[CrossRef]

Smith, D. R.

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17(19), 16535–16542 (2009).
[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).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations,” Photonics Nanostruct. Fundam. Appl.. 6(1), 87–95 (2008).
[CrossRef]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[CrossRef]

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(6), 063903 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Smolyaninov, I. I.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Maxwell fish-eye and Eaton lenses emulated by microdroplets,” Opt. Lett. 35(20), 3396–3398 (2010).
[CrossRef] [PubMed]

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102(21), 213901 (2009).
[CrossRef] [PubMed]

Smolyaninova, V. N.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Maxwell fish-eye and Eaton lenses emulated by microdroplets,” Opt. Lett. 35(20), 3396–3398 (2010).
[CrossRef] [PubMed]

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102(21), 213901 (2009).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
[CrossRef] [PubMed]

Valentine, J.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[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]

Vivien, L.

Vynck, K.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

Wang, J.

Wen, W.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

Xu, Z.

Yan, M.

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[CrossRef]

Yan, W.

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[CrossRef]

Yang, T.

X. D. Luo, T. Yang, Y. W. Gu, H. Y. Chen, and H. R. Ma, “Conceal an entrance by means of superscatterer,” Appl. Phys. Lett. 94(22), 223513 (2009).
[CrossRef]

Zentgraf, T.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[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]

Zhai, T. R.

Zhang, S.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

Zhang, X.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[CrossRef] [PubMed]

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

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]

Zhou, J.

Zhou, Y.

Appl. Phys. Lett. (5)

X. D. Luo, T. Yang, Y. W. Gu, H. Y. Chen, and H. R. Ma, “Conceal an entrance by means of superscatterer,” Appl. Phys. Lett. 94(22), 223513 (2009).
[CrossRef]

E. E. Narimanov and A. V. Kildishev, “Optical black hole: broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
[CrossRef]

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[CrossRef]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[CrossRef]

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

J. Appl. Phys. (1)

B. Edwards, A. Alu, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105(4), 044905 (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. Nanotechnol. (1)

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[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]

Nat. Phys. (1)

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Photonics Nanostruct. Fundam. Appl.. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations,” Photonics Nanostruct. Fundam. Appl.. 6(1), 87–95 (2008).
[CrossRef]

Phys. Rev. B (1)

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[CrossRef]

Phys. Rev. Lett. (4)

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
[CrossRef] [PubMed]

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102(21), 213901 (2009).
[CrossRef] [PubMed]

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[CrossRef] [PubMed]

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(6), 063903 (2008).
[CrossRef] [PubMed]

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]

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Other (1)

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, 1964).

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Figures (5)

Fig. 1
Fig. 1

Schematic picture of graded-index waveguide around a right-angled corner.

Fig. 2
Fig. 2

Structure fabrication (a) – (d). Schematic diagram of the fabrication process.

Fig. 3
Fig. 3

Microscopy interference pattern of the sample illuminated by white light (a) and by a laser at 633 nm (b); (c) FIB image of a cross-section near the sharp corner; (d) thickness profile around the corner retrieved from (b) and (c).

Fig. 4
Fig. 4

(a) Schematic picture of waveguide; (b) thickness dependence of effective mode index; (c) effective mode index profile of the structure; (d) numerical simulation results of light propagating around the corner.

Fig. 5
Fig. 5

Fluorescence image of light propagation in the waveguide. (a) light propagation along the boundary of waveguide; (b) light bending around the sharp corner; (c) mode splitting in thick waveguide; (d) radiation of a point source around the sharp corner; (e) magnified bending area taken from the frame in (b).

Equations (1)

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exp[2i( θ 12 θ 23 κ 2 d )]= exp[2 γ 3 t+2i( θ 34 θ 23 )]+1 exp[2 γ 3 t+2i( θ 34 + θ 23 )]+1 ,

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