Abstract

We propose antireflection coatings at the entrance and exit of arbitrary waveguide bends with graded index photonic crystals. The implementation of the proposed system is validated within the lowest band. The finite element method is employed to simulate the electromagnetic wave propagation of the designed device and analyze the influence of surface termination on transmission efficiency. The results show that the proposed system using antireflection structures exhibits a high-efficiency transmission performance. In addition, the incident waves can smoothly travel through the waveguide bends and keep their original field patterns.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef] [PubMed]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (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, 977–980 (2006).
    [CrossRef] [PubMed]
  4. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
    [CrossRef] [PubMed]
  5. 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,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
    [CrossRef]
  6. H. Y. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
    [CrossRef]
  7. M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).
    [CrossRef] [PubMed]
  8. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
    [CrossRef] [PubMed]
  9. A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32, 3432–3434 (2007).
    [CrossRef] [PubMed]
  10. M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77, 035122(2008).
    [CrossRef]
  11. F. M. Kong, B. I. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 (2007).
    [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 78, 066607 (2008).
    [CrossRef]
  13. 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, 251111 (2008).
    [CrossRef]
  14. B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79, 085103 (2009).
    [CrossRef]
  15. N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express 17, 14872–14879 (2009).
    [CrossRef] [PubMed]
  16. Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105, 104913(2009).
    [CrossRef]
  17. W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96, 041102 (2010).
    [CrossRef]
  18. Y. G. Ma, N. Wang, and C. K. Ong, “Application of inverse, strict conformal transformation to design waveguide devices,” J. Opt. Soc. Am. A 27, 968–972 (2010).
    [CrossRef]
  19. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062(1987).
    [CrossRef] [PubMed]
  20. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef] [PubMed]
  21. E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73, 235119 (2006).
    [CrossRef]
  22. H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15, 1240–1253 (2007).
    [CrossRef] [PubMed]
  23. A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
    [CrossRef]
  24. B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18, 20321–20333 (2010).
    [CrossRef] [PubMed]
  25. H. W. Wang and L. W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
    [CrossRef]
  26. J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
    [CrossRef]
  27. B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal,” Appl. Phys. Lett. 87, 171104 (2005).
    [CrossRef]
  28. S. G. Lee, J. S. Choi, J. E. Kim, H. Y. Park, and C. S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16, 4270–4277 (2008).
    [CrossRef] [PubMed]
  29. T. T. Kim, S. G. Lee, M. W. Kim, H. Y. Park, and J. E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95, 011119 (2009).
    [CrossRef]
  30. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).
  31. A. Sihvola, Electromagnetic Mixing Formulas and Applications (Institution of Electrical Engineers, 1999).
    [CrossRef]
  32. M. Born and E. Wolf, Principles of Optics (Cambridge University, 2002).

2011 (1)

H. W. Wang and L. W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
[CrossRef]

2010 (3)

2009 (5)

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[CrossRef]

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79, 085103 (2009).
[CrossRef]

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

Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105, 104913(2009).
[CrossRef]

T. T. Kim, S. G. Lee, M. W. Kim, H. Y. Park, and J. E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

2008 (7)

S. G. Lee, J. S. Choi, J. E. Kim, H. Y. Park, and C. S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16, 4270–4277 (2008).
[CrossRef] [PubMed]

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77, 035122(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 78, 066607 (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, 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,” Photon. Nanostruct. Fundam. Appl. 6, 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, 11555–11567 (2008).
[CrossRef] [PubMed]

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

2007 (4)

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

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

F. M. Kong, B. I. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15, 1240–1253 (2007).
[CrossRef] [PubMed]

2006 (5)

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73, 235119 (2006).
[CrossRef]

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

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

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

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

2005 (1)

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal,” Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

2004 (1)

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062(1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Adibi, A.

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal,” Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

Albert, J. P.

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73, 235119 (2006).
[CrossRef]

Baehr-Jones, T.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2002).

Caglayan, H.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[CrossRef]

Cakmak, A. O.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[CrossRef]

Cassagne, D.

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73, 235119 (2006).
[CrossRef]

Centeno, E.

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73, 235119 (2006).
[CrossRef]

Chan, C. T.

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

Chen, H. S.

F. M. Kong, B. I. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

Chen, H. Y.

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

Chen, L. W.

H. W. Wang and L. W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
[CrossRef]

Chen, L. X.

W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96, 041102 (2010).
[CrossRef]

Cheng, Q.

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 78, 066607 (2008).
[CrossRef]

Choi, J. S.

Citrin, D. S.

Colak, E.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[CrossRef]

Cui, T. J.

Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105, 104913(2009).
[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 78, 066607 (2008).
[CrossRef]

Cummer, S. 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,” Photon. Nanostruct. Fundam. Appl. 6, 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, 977–980 (2006).
[CrossRef] [PubMed]

Ding, W. Q.

W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96, 041102 (2010).
[CrossRef]

Gajic, R.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18, 20321–20333 (2010).
[CrossRef] [PubMed]

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Hingerl, K.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18, 20321–20333 (2010).
[CrossRef] [PubMed]

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Hochberg, M.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Huangfu, J. T.

F. M. Kong, B. I. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

Isic, G.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18, 20321–20333 (2010).
[CrossRef] [PubMed]

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Jiang, W. X.

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 78, 066607 (2008).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[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, 977–980 (2006).
[CrossRef] [PubMed]

Kee, C. S.

Kildishev, A. V.

Kim, J. E.

T. T. Kim, S. G. Lee, M. W. Kim, H. Y. Park, and J. E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

S. G. Lee, J. S. Choi, J. E. Kim, H. Y. Park, and C. S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16, 4270–4277 (2008).
[CrossRef] [PubMed]

Kim, M. W.

T. T. Kim, S. G. Lee, M. W. Kim, H. Y. Park, and J. E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

Kim, T. T.

T. T. Kim, S. G. Lee, M. W. Kim, H. Y. Park, and J. E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

Kong, F. M.

F. M. Kong, B. I. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

Kong, J. A.

F. M. Kong, B. I. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

Kurt, H.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[CrossRef]

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15, 1240–1253 (2007).
[CrossRef] [PubMed]

Landy, N. I.

Lee, S. G.

T. T. Kim, S. G. Lee, M. W. Kim, H. Y. Park, and J. E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

S. G. Lee, J. S. Choi, J. E. Kim, H. Y. Park, and C. S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16, 4270–4277 (2008).
[CrossRef] [PubMed]

Leonhardt, U.

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

Li, J.

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

Liu, Y.

W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96, 041102 (2010).
[CrossRef]

Ma, Y. G.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

Mei, Z. L.

Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105, 104913(2009).
[CrossRef]

Mock, J. J.

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

Momeni, B.

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal,” Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

Narimanov, E. E.

Ong, C. K.

Ozbay, E.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[CrossRef]

Padilla, W. J.

Park, H. Y.

T. T. Kim, S. G. Lee, M. W. Kim, H. Y. Park, and J. E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

S. G. Lee, J. S. Choi, J. E. Kim, H. Y. Park, and C. S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16, 4270–4277 (2008).
[CrossRef] [PubMed]

Pendry, J. B.

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, 251111 (2008).
[CrossRef]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (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,” Photon. Nanostruct. Fundam. Appl. 6, 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, 11555–11567 (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, 977–980 (2006).
[CrossRef] [PubMed]

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

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

Psaltis, D.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77, 035122(2008).
[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, 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,” Photon. Nanostruct. Fundam. Appl. 6, 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, 251111 (2008).
[CrossRef]

Roberts, D. A.

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, 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,” Photon. Nanostruct. Fundam. Appl. 6, 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, 11555–11567 (2008).
[CrossRef] [PubMed]

Scherer, A.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
[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,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[CrossRef]

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

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

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

Sihvola, A.

A. Sihvola, Electromagnetic Mixing Formulas and Applications (Institution of Electrical Engineers, 1999).
[CrossRef]

Smith, D. R.

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

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,” Photon. Nanostruct. Fundam. Appl. 6, 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, 251111 (2008).
[CrossRef]

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

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

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

Starr, A. F.

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

Sun, X. D.

W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96, 041102 (2010).
[CrossRef]

Tang, D. H.

W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96, 041102 (2010).
[CrossRef]

Tsang, M.

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

Vasic, B.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18, 20321–20333 (2010).
[CrossRef] [PubMed]

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79, 085103 (2009).
[CrossRef]

Wang, H. W.

H. W. Wang and L. W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
[CrossRef]

Wang, N.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

Witzens, J.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2002).

Wu, B. I. I.

F. M. Kong, B. I. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

Xi, S.

F. M. Kong, B. I. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 (2007).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062(1987).
[CrossRef] [PubMed]

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 78, 066607 (2008).
[CrossRef]

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 78, 066607 (2008).
[CrossRef]

Appl. Phys. Lett. (6)

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

F. M. Kong, B. I. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 (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, 251111 (2008).
[CrossRef]

W. Q. Ding, D. H. Tang, Y. Liu, L. X. Chen, and X. D. Sun, “Arbitrary waveguide bends using isotropic and homogeneous metamaterial,” Appl. Phys. Lett. 96, 041102 (2010).
[CrossRef]

T. T. Kim, S. G. Lee, M. W. Kim, H. Y. Park, and J. E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett. 95, 011119 (2009).
[CrossRef]

B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystal,” Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

J. Appl. Phys. (3)

Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105, 104913(2009).
[CrossRef]

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[CrossRef]

H. W. Wang and L. W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (6)

Opt. Lett. (1)

Photon. 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,” Photon. Nanostruct. Fundam. Appl. 6, 87–95 (2008).
[CrossRef]

Phys. Rev. B (3)

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

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79, 085103 (2009).
[CrossRef]

E. Centeno, D. Cassagne, and J. P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73, 235119 (2006).
[CrossRef]

Phys. Rev. E (2)

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
[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 78, 066607 (2008).
[CrossRef]

Phys. Rev. Lett. (3)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062(1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

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

Science (3)

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

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

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

Other (3)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

A. Sihvola, Electromagnetic Mixing Formulas and Applications (Institution of Electrical Engineers, 1999).
[CrossRef]

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Scheme of the arbitrary waveguide bends with an angle of θ. b and c are the inner and outer radii of the circular waveguide bends, respectively.

Fig. 2
Fig. 2

Distribution of the refractive index for the waveguide bend structure when A = 1 , b = 0.35 m , c = 0.7 m , and θ = π / 2 .

Fig. 3
Fig. 3

(a) Dispersion curves along the Γ - X direction of PCs for different radii. (b) Effective refractive indices of PCs for different radii as a function of normalized frequency.

Fig. 4
Fig. 4

(a) Scheme of the waveguide bend with GRIN PCs composed of a square array of dielectric cylinders by spatially varying radii. Cylinders with the same radius are introduced into the entrance and exit as the ARC structures. R a r c is the radius of ARC cylinders, and δ a r c is the distance between the GRIN PCs and the ARC cylinders. (b) ARC made from cylinders whose radius varies in space is considered. h is the optical thickness of the ARC layer, and δ a r c is the distance relative to the bend entrance and exit. (c) Approximate refractive indices of each cell along the radial direction in the GRIN PCs. The dashed curve represents the refractive indices based on the theoretical description.

Fig. 5
Fig. 5

Electric field distributions for (a) waveguide bend based on the theoretical description and (b) one with GRIN PCs at a frequency of 0.1 ( ω a / 2 π c ). A Gaussian beam from the bottom is incident on the entrance of the waveguide bend.

Fig. 6
Fig. 6

Transmission spectra of the waveguide bend ( θ = π / 2 ) based on the theoretical description and the one with GRIN PCs.

Fig. 7
Fig. 7

Transmission spectra of the waveguide bends ( θ = π / 2 ) with GRIN PCs (a) for various R a r c when the distance between the GRIN PCs and the ARC cylinders is fixed at δ a r c = 1 a and (b) for various δ a r c when the radius of ARC cylinders is fixed at R a r c = 0.19 a .

Fig. 8
Fig. 8

Transmission spectra of the waveguide bends ( θ = π / 2 ) with GRIN PCs (a) for various h at δ a r c = 1 a and (b) for various δ a r c when the optical thickness is fixed at h = 1 a .

Fig. 9
Fig. 9

(a) Transmission spectra of the waveguide bends with and without the ARC structures. (b) Electric field distributions for the waveguide bends with ARC structures at a frequency of 0.1 ( ω a / 2 π c ). The bending angle is θ = π / 4 .

Fig. 10
Fig. 10

(a) Transmission spectra of the waveguide bends with and without the ARC structures. (b) Electric field distributions for the waveguide bends with the ARC structures at a frequency of 0.1 ( ω a / 2 π c ). The bending angle is θ = π / 2 .

Fig. 11
Fig. 11

(a) Transmission spectra of the waveguide bends with and without the ARC structures. (b) Electric field distributions for the waveguide bends with ARC structures at a frequency of 0.1 ( ω a / 2 π c ). The bending angle is θ = 3 π / 4 .

Fig. 12
Fig. 12

(a) Transmission spectra of the waveguide bends with and without ARC structures. (b) Electric field distributions for the waveguide bends with the ARC structures at a frequency of 0.1 ( ω a / 2 π c ). The bending angle is θ = π .

Equations (4)

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

z = exp ( w A ) ,
n = | d w d z | = A x 2 + y 2 ,
r i j = a n i j 2 ε b π ( ε r ε b ) ,
P = 1 2 Re ( s E × H * · d s ) , T = P out / P in ,

Metrics