Abstract

We propose a method to manipulate Bloch waves in curved photonic crystals for achieving transformation optical devices in two dimensions. Instead of starting from an effectively homogeneous medium, we transform a regular photonic crystal into a curved one in the physical space. A scaling law is established to construct the curved photonic crystal with similar unit cells and different scales, which is made of dielectrics only. A wave compressor and a bending waveguide are designed using dielectrics with indices only from 1 to 4. The approach will be useful in constructing low-loss transformation media requiring small indices, or large anisotropy which is particularly difficult for E-polarization using the conventional effective medium approach.

© 2011 OSA

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [CrossRef] [PubMed]
  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).
    [CrossRef] [PubMed]
  5. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
    [CrossRef]
  6. 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]
  7. 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]
  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. V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
    [CrossRef] [PubMed]
  10. N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express 17(17), 14872–14879 (2009).
    [CrossRef] [PubMed]
  11. J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
    [CrossRef]
  12. W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
    [CrossRef] [PubMed]
  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. Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
    [CrossRef] [PubMed]
  15. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
    [CrossRef]
  16. E. E. Narimanov and A. V. Kildishev, “Optical black hole: broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
    [CrossRef]
  17. S. Liu, L. Li, Z. Lin, H. Y. Chen, J. Zi, and C. T. Chan, “Graded index photonic hole: analytical and rigorous full wave solution,” Phys. Rev. B 82(5), 054204 (2010).
    [CrossRef]
  18. H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
    [CrossRef] [PubMed]
  19. P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10(6), 1985–1990 (2010).
    [CrossRef] [PubMed]
  20. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
    [CrossRef] [PubMed]
  21. 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]
  22. Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
    [CrossRef] [PubMed]
  23. H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat Commun 1(3), 21 (2010).
    [CrossRef] [PubMed]
  24. Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” N. J. Phys. 12(6), 063006 (2010).
    [CrossRef]
  25. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
    [CrossRef] [PubMed]
  26. 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]
  27. 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]
  28. J. C. Halimeh, T. Ergin, J. Mueller, N. Stenger, and M. Wegener, “Photorealistic images of carpet cloaks,” Opt. Express 17(22), 19328–19336 (2009).
    [CrossRef] [PubMed]
  29. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
    [CrossRef] [PubMed]
  30. X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
    [CrossRef] [PubMed]
  31. B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
    [CrossRef] [PubMed]
  32. J. Fischer, T. Ergin, and M. Wegener, “Three-dimensional polarization-independent visible-frequency carpet invisibility cloak,” Opt. Lett. 36(11), 2059–2061 (2011).
    [CrossRef] [PubMed]
  33. Y. A. Urzhumov and D. R. Smith, “Transformation optics with photonic band gap media,” Phys. Rev. Lett. 105(16), 163901 (2010).
    [CrossRef] [PubMed]
  34. C. Luo, S. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
    [CrossRef]
  35. V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009).
    [CrossRef] [PubMed]
  36. S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102(20), 203905 (2009).
    [CrossRef] [PubMed]
  37. X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
    [CrossRef] [PubMed]
  38. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

2011 (4)

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
[CrossRef] [PubMed]

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

J. Fischer, T. Ergin, and M. Wegener, “Three-dimensional polarization-independent visible-frequency carpet invisibility cloak,” Opt. Lett. 36(11), 2059–2061 (2011).
[CrossRef] [PubMed]

2010 (9)

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Y. A. Urzhumov and D. R. Smith, “Transformation optics with photonic band gap media,” Phys. Rev. Lett. 105(16), 163901 (2010).
[CrossRef] [PubMed]

S. Liu, L. Li, Z. Lin, H. Y. Chen, J. Zi, and C. T. Chan, “Graded index photonic hole: analytical and rigorous full wave solution,” Phys. Rev. B 82(5), 054204 (2010).
[CrossRef]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[CrossRef] [PubMed]

P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10(6), 1985–1990 (2010).
[CrossRef] [PubMed]

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
[CrossRef] [PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat Commun 1(3), 21 (2010).
[CrossRef] [PubMed]

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” N. J. Phys. 12(6), 063006 (2010).
[CrossRef]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[CrossRef] [PubMed]

2009 (11)

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]

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]

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

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]

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009).
[CrossRef] [PubMed]

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102(20), 203905 (2009).
[CrossRef] [PubMed]

N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express 17(17), 14872–14879 (2009).
[CrossRef] [PubMed]

J. C. Halimeh, T. Ergin, J. Mueller, N. Stenger, and M. Wegener, “Photorealistic images of carpet cloaks,” Opt. Express 17(22), 19328–19336 (2009).
[CrossRef] [PubMed]

2008 (7)

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (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]

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]

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

V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (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]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (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]

2002 (1)

C. Luo, S. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

Barbastathis, G.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
[CrossRef] [PubMed]

Bartal, G.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
[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]

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Cabrini, S.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009).
[CrossRef] [PubMed]

Cai, B. G.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” N. J. Phys. 12(6), 063006 (2010).
[CrossRef]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

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.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[CrossRef] [PubMed]

S. Liu, L. Li, Z. Lin, H. Y. Chen, J. Zi, and C. T. Chan, “Graded index photonic hole: analytical and rigorous full wave solution,” Phys. Rev. B 82(5), 054204 (2010).
[CrossRef]

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

Chang, A. S. P.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009).
[CrossRef] [PubMed]

Chatterjee, R.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102(20), 203905 (2009).
[CrossRef] [PubMed]

Chen, H.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[CrossRef] [PubMed]

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Chen, H. Y.

S. Liu, L. Li, Z. Lin, H. Y. Chen, J. Zi, and C. T. Chan, “Graded index photonic hole: analytical and rigorous full wave solution,” Phys. Rev. B 82(5), 054204 (2010).
[CrossRef]

Chen, X.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

Cheng, Q.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” N. J. Phys. 12(6), 063006 (2010).
[CrossRef]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

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.

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat Commun 1(3), 21 (2010).
[CrossRef] [PubMed]

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” N. J. Phys. 12(6), 063006 (2010).
[CrossRef]

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]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

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]

Dardano, P.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009).
[CrossRef] [PubMed]

Dhuey, S.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009).
[CrossRef] [PubMed]

Ergin, T.

Fischer, J.

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]

García-Vidal, F. J.

P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10(6), 1985–1990 (2010).
[CrossRef] [PubMed]

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]

Halimeh, J. C.

Hang, Z. H.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Harteneck, B.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009).
[CrossRef] [PubMed]

Huang, X.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Huangfu, J.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Huidobro, P. A.

P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10(6), 1985–1990 (2010).
[CrossRef] [PubMed]

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]

Jiang, K.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

Jiang, W. X.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” N. J. Phys. 12(6), 063006 (2010).
[CrossRef]

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

Joannopoulos, J.

C. Luo, S. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

Johnson, S.

C. Luo, S. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kildishev, A. V.

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

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

Kocaman, S.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102(20), 203905 (2009).
[CrossRef] [PubMed]

Kong, F.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Kong, J. A.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Kundtz, N.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[CrossRef] [PubMed]

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]

Kwong, D. L.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102(20), 203905 (2009).
[CrossRef] [PubMed]

Lai, Y.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

Landy, N. I.

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]

Leonhardt, U.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

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]

Li, L.

S. Liu, L. Li, Z. Lin, H. Y. Chen, J. Zi, and C. T. Chan, “Graded index photonic hole: analytical and rigorous full wave solution,” Phys. Rev. B 82(5), 054204 (2010).
[CrossRef]

Lin, Z.

S. Liu, L. Li, Z. Lin, H. Y. Chen, J. Zi, and C. T. Chan, “Graded index photonic hole: analytical and rigorous full wave solution,” Phys. Rev. B 82(5), 054204 (2010).
[CrossRef]

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]

Liu, S.

S. Liu, L. Li, Z. Lin, H. Y. Chen, J. Zi, and C. T. Chan, “Graded index photonic hole: analytical and rigorous full wave solution,” Phys. Rev. B 82(5), 054204 (2010).
[CrossRef]

Liu, X.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
[CrossRef] [PubMed]

Liu, Y.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
[CrossRef] [PubMed]

Luo, C.

C. Luo, S. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

Luo, Y.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
[CrossRef] [PubMed]

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

Ma, H. F.

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat Commun 1(3), 21 (2010).
[CrossRef] [PubMed]

Ma, Y. G.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

Martín-Moreno, L.

P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10(6), 1985–1990 (2010).
[CrossRef] [PubMed]

McMillan, J. F.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102(20), 203905 (2009).
[CrossRef] [PubMed]

Mocella, V.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009).
[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]

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]

Moretti, L.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009).
[CrossRef] [PubMed]

Mueller, J.

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]

Nesterov, M. L.

P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10(6), 1985–1990 (2010).
[CrossRef] [PubMed]

Olynick, D.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009).
[CrossRef] [PubMed]

Ong, C. K.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

Osgood, R. M.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102(20), 203905 (2009).
[CrossRef] [PubMed]

Padilla, W. J.

Panoiu, N. C.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102(20), 203905 (2009).
[CrossRef] [PubMed]

Pendry, J.

C. Luo, S. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

Pendry, J. B.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[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]

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. 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, 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. 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]

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]

Rahm, M.

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, 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]

Ran, L.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Rendina, I.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009).
[CrossRef] [PubMed]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of 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]

Schurig, D.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(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]

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

Shalaev, V. M.

V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
[CrossRef] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[CrossRef] [PubMed]

Smith, D. R.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[CrossRef] [PubMed]

Y. A. Urzhumov and D. R. Smith, “Transformation optics with photonic band gap media,” Phys. Rev. Lett. 105(16), 163901 (2010).
[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]

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]

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]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Stenger, N.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

J. C. Halimeh, T. Ergin, J. Mueller, N. Stenger, and M. Wegener, “Photorealistic images of carpet cloaks,” Opt. Express 17(22), 19328–19336 (2009).
[CrossRef] [PubMed]

Tyc, T.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[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]

Urzhumov, Y. A.

Y. A. Urzhumov and D. R. Smith, “Transformation optics with photonic band gap media,” Phys. Rev. Lett. 105(16), 163901 (2010).
[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, D.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Wegener, M.

Wong, C. W.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102(20), 203905 (2009).
[CrossRef] [PubMed]

Wu, B.-I.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Xi, S.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Yang, X. M.

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

Yu, M. B.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102(20), 203905 (2009).
[CrossRef] [PubMed]

Zentgraf, T.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
[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]

Zhang, B.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
[CrossRef] [PubMed]

Zhang, J.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

Zhang, S.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

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

Zhang, X.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
[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]

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

Zhang, Z. Q.

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

Zheng, H.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Zhou, X. Y.

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

Zi, J.

S. Liu, L. Li, Z. Lin, H. Y. Chen, J. Zi, and C. T. Chan, “Graded index photonic hole: analytical and rigorous full wave solution,” Phys. Rev. B 82(5), 054204 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

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

J. Appl. Phys. (1)

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).
[CrossRef]

N. J. Phys. (1)

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” N. J. Phys. 12(6), 063006 (2010).
[CrossRef]

Nano Lett. (2)

P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10(6), 1985–1990 (2010).
[CrossRef] [PubMed]

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
[CrossRef] [PubMed]

Nat Commun (2)

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat Commun 1(3), 21 (2010).
[CrossRef] [PubMed]

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

Nat. Mater. (5)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[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]

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[CrossRef] [PubMed]

Nat. Photonics (2)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

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 (3)

Opt. Lett. (1)

Photonics Nanostruct. Fundam. Appl. (1)

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

Phys. Rev. B (2)

S. Liu, L. Li, Z. Lin, H. Y. Chen, J. Zi, and C. T. Chan, “Graded index photonic hole: analytical and rigorous full wave solution,” Phys. Rev. B 82(5), 054204 (2010).
[CrossRef]

C. Luo, S. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(6), 066607 (2008).
[CrossRef] [PubMed]

Phys. Rev. Lett. (8)

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102(13), 133902 (2009).
[CrossRef] [PubMed]

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102(20), 203905 (2009).
[CrossRef] [PubMed]

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
[CrossRef] [PubMed]

Y. A. Urzhumov and D. R. Smith, “Transformation optics with photonic band gap media,” Phys. Rev. Lett. 105(16), 163901 (2010).
[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]

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]

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (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 (6)

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]

V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
[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]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Other (1)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

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Figures (4)

Fig. 1
Fig. 1

Transforming (a) a regular PhC in virtual space to (b) a curved PhC in physical space. The black dashed lines outline the boundary of the unit cells of the PhC; the black solid lines outline specific structures within each unit cell. The blue arrows indicate the wave propagation paths.

Fig. 2
Fig. 2

Transforming (a) a regular unit cell to (b) the curved unit cell. The lattice constant of the regular PhC unit cell is a. The curved PhC unit cell (composed of isotropic dielectric materials) spans an angle of Δ θ = π / 3 with an inner radius r 1 = 0.455 a and an outer radius r 2 = 1.455 a . The curved unit cell has a circular cylinder with radius r d = 0.2 a and permittivity 12.5 ε b in background permittivity ε b = 1 . The color map shows the E-field pattern at a normalized frequency ω a / ( 2 π c ) = 0.59 .

Fig. 3
Fig. 3

(a) A curved PhC bending waveguide with inner radius 3.66a and outer radius 6.87a. Each unit cell of the outermost layer spans an angle of Δ θ = 9 o with thickness a in the r-direction. It consists of a circular cylinder with radius r d = 0.275 a and permittivity 4 ε b in the background permittivity ε b = 1 . The scale factor is s = 1.17 . (b) EFC (black line) of the regular PhC at normalized frequency ω a / ( 2 π c ) = 0.686 . The red dashed line represents the EFC of the corresponding isotropic effective medium. (c) H-field pattern at the same normalized frequency for a plane wave incident on the upper port. (d) H-field pattern for the corresponding effective medium ε e f f = n r e g a 2 / ( r Δ θ ) 2 and μ e f f = n r e g , where n r e g = 0.146 . All length scales are normalized to a.

Fig. 4
Fig. 4

(a) Transforming a regular PhC with flat EFC to achieve a wave compressor. (b) Index profile of the wave compressor. The compressor has inner radius R 1 = 10.5 a and outer radius R 2 = 19.6 a ; see text for details of the configuration. (c) EFC of the regular PhC at normalized frequency ω a / ( 2 π c ) = 0.58 . (d) E-field pattern when a Gaussian beam of width 10.3a is incident from the left. The beam is compressed to a width of 5.5a at the exit. (e) E-filed pattern of the same compressor with the corresponding effective medium, ε e f f = n r e g a 2 / ( r Δ θ ) 2 , μ θ ( e f f ) = n r e g , and μ r ( e f f ) = , where n r e g = 0.261 . (f) The normalized E-field amplitude distribution of the beam along the y-direction. The blue solid line represents the distribution of the incident beam. The black dashed line represents the ideal exit beam profile with compressed ratio R 2 / R 1 , and the red solid line represents the actual distribution of the exit beam from the simulation. All length scales are normalized to a.

Equations (6)

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

x ' = g ( r ) , y ' = R θ , z ' = z ,
μ x ' ( x ' , y ' ) = 1 μ y ' ( x ' , y ' ) = g ( r ) r R , ε z ' ( x ' , y ' ) = r / R g ( r ) ε ( r , θ ) .
ω Δ r ε b 2 π c = constant,
ε x ' ( x ' , y ' ) ε ( r , θ ) = ε ( r , θ ) ε y ' ( x ' , y ' ) = g ( r ) r R , μ z ' ( x ' , y ' ) = r / R g ( r )
ε e f f = n r e g a 2 / ( r Δ θ ) 2 , μ e f f = n r e g .
ε e f f = n r e g a 2 / ( r Δ θ ) 2 , μ r ( e f f ) = , μ θ ( e f f ) = n r e g .

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