Abstract

Numerical studies on a graded negative index lens made by a slab of graded photonic crystal (PC) are reported. The graded negative index lens is capable of focusing plane waves and can also be made highly insensitive to frequency, enabling broadband negative index imaging. We provide a simple model for the graded PC lens and predict its superior focusing properties such as low chromatic aberrations and broadband operation. Those properties were also confirmed and analyzed by the finite-difference time-domain simulations. We believe the negative index graded PCs will expand the utility of PC lenses and enable new applications in optoelectronic systems.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  4. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (1-4) (2002).
    [CrossRef]
  5. P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
    [CrossRef] [PubMed]
  6. E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (1-6) (2006).
    [CrossRef]
  7. E. Schonbrun, Q. Wu, W. Park, T, Yamashita, C. J. Summers, M. Abashin and Y. Fainman, "Wave front evolution of negatively refracted waves in a photonic crystal," Appl. Phys. Lett. 90, 041113 (1-3) (2007).
    [CrossRef]
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    [CrossRef]
  9. B. D. F. Casse, W. T. Lu, Y. J. Huang and S. Sridhar, "Nano-optical microlens with ultrashort focal length using negative refraction," Appl. Phys. Lett. 93, 053111 (1-3) (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (1-3) (2005).
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  22. X. Wang, Z. F. Ren, and K. Kempa, "Unrestricted superlensing in a triangular two-dimensional photonic crystal," Opt. Express 12, 2919-2924 (2004).
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2008

B. D. F. Casse, W. T. Lu, Y. J. Huang and S. Sridhar, "Nano-optical microlens with ultrashort focal length using negative refraction," Appl. Phys. Lett. 93, 053111 (1-3) (2008).
[CrossRef]

2007

2006

Q. Wu, E. Schonbrun, and W. Park, "Tunable superlensing by a mechanically controlled photonic crystal," J. Opt. Soc. Am. B 23, 479-484 (2006).
[CrossRef]

H. Chien and C. Chen, "Focusing of electromagnetic waves by periodic arrays of air holes with gradually varying radii," Opt. Express 14, 10759-10764 (2006).
[CrossRef] [PubMed]

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (1-6) (2006).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffractionlimited optical imaging with silver superlens," Science 308, 534-537 (2006).
[CrossRef]

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-spacemicrowave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (1-3) (2006).
[CrossRef]

Q1. E. Centeno, D. Cassagne, and J. P. Albert, "Mirage and superbending effect in two-dimensional graded photonic crystals," Phys. Rev. B 73, 235119-235119 (2006).
[CrossRef]

F. S. Roux and I. De Leon, "Planar photonic crystal gradient index lens, simulated with a finite difference time domain method," Phys. Rev. B 74, 113103 (1-4) (2006).
[CrossRef]

2005

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (1-3) (2005).
[CrossRef]

E. Centeno and D. Cassagne, "Graded photonic crystals," Opt. Lett. 74, 2278-2280 (2005).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609 (1-4) (2005).
[CrossRef]

2004

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter and M. H. Tanielian, "Performance of a negative index of refraction lens, " Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

X. Wang, Z. F. Ren, and K. Kempa, "Unrestricted superlensing in a triangular two-dimensional photonic crystal," Opt. Express 12, 2919-2924 (2004).
[CrossRef] [PubMed]

2003

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

2002

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (1-4) (2002).
[CrossRef]

2000

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

1994

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Abashin, M.

E. Schonbrun, Q. Wu, W. Park, T, Yamashita, C. J. Summers, M. Abashin and Y. Fainman, "Wave front evolution of negatively refracted waves in a photonic crystal," Appl. Phys. Lett. 90, 041113 (1-3) (2007).
[CrossRef]

Albert, J. P.

Q1. E. Centeno, D. Cassagne, and J. P. Albert, "Mirage and superbending effect in two-dimensional graded photonic crystals," Phys. Rev. B 73, 235119-235119 (2006).
[CrossRef]

Basov, D. N.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-spacemicrowave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (1-3) (2006).
[CrossRef]

Berenger, J. P.

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Cassagne, D.

Q1. E. Centeno, D. Cassagne, and J. P. Albert, "Mirage and superbending effect in two-dimensional graded photonic crystals," Phys. Rev. B 73, 235119-235119 (2006).
[CrossRef]

E. Centeno and D. Cassagne, "Graded photonic crystals," Opt. Lett. 74, 2278-2280 (2005).
[CrossRef]

Casse, B. D. F.

B. D. F. Casse, W. T. Lu, Y. J. Huang and S. Sridhar, "Nano-optical microlens with ultrashort focal length using negative refraction," Appl. Phys. Lett. 93, 053111 (1-3) (2008).
[CrossRef]

Centeno, E.

Q1. E. Centeno, D. Cassagne, and J. P. Albert, "Mirage and superbending effect in two-dimensional graded photonic crystals," Phys. Rev. B 73, 235119-235119 (2006).
[CrossRef]

E. Centeno and D. Cassagne, "Graded photonic crystals," Opt. Lett. 74, 2278-2280 (2005).
[CrossRef]

Chen, C.

Chien, H.

Citrin, D. S.

De Leon, I.

F. S. Roux and I. De Leon, "Planar photonic crystal gradient index lens, simulated with a finite difference time domain method," Phys. Rev. B 74, 113103 (1-4) (2006).
[CrossRef]

Driscoll, T.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-spacemicrowave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (1-3) (2006).
[CrossRef]

Fainman, Y.

E. Schonbrun, Q. Wu, W. Park, T, Yamashita, C. J. Summers, M. Abashin and Y. Fainman, "Wave front evolution of negatively refracted waves in a photonic crystal," Appl. Phys. Lett. 90, 041113 (1-3) (2007).
[CrossRef]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffractionlimited optical imaging with silver superlens," Science 308, 534-537 (2006).
[CrossRef]

Greegor, R. B.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (1-3) (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter and M. H. Tanielian, "Performance of a negative index of refraction lens, " Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Huang, Y. J.

B. D. F. Casse, W. T. Lu, Y. J. Huang and S. Sridhar, "Nano-optical microlens with ultrashort focal length using negative refraction," Appl. Phys. Lett. 93, 053111 (1-3) (2008).
[CrossRef]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (1-4) (2002).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (1-4) (2002).
[CrossRef]

Kempa, K.

Kurt, H.

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffractionlimited optical imaging with silver superlens," Science 308, 534-537 (2006).
[CrossRef]

Li, K.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter and M. H. Tanielian, "Performance of a negative index of refraction lens, " Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Lu, W. T.

B. D. F. Casse, W. T. Lu, Y. J. Huang and S. Sridhar, "Nano-optical microlens with ultrashort focal length using negative refraction," Appl. Phys. Lett. 93, 053111 (1-3) (2008).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (1-4) (2002).
[CrossRef]

Mock, J. J.

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609 (1-4) (2005).
[CrossRef]

Nemat-Nasser, S.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-spacemicrowave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (1-3) (2006).
[CrossRef]

Nielsen, J. A.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (1-3) (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter and M. H. Tanielian, "Performance of a negative index of refraction lens, " Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Notomi, M.

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

Parazzoli, C. G.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (1-3) (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter and M. H. Tanielian, "Performance of a negative index of refraction lens, " Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Park, W.

Q. Wu, E. Schonbrun, and W. Park, "Image inversion and magnification by negative index prisms," J. Opt. Soc. Am. A 24, A45-A51 (2007).
[CrossRef]

E. Schonbrun, Q. Wu, W. Park, T, Yamashita, C. J. Summers, M. Abashin and Y. Fainman, "Wave front evolution of negatively refracted waves in a photonic crystal," Appl. Phys. Lett. 90, 041113 (1-3) (2007).
[CrossRef]

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (1-6) (2006).
[CrossRef]

Q. Wu, E. Schonbrun, and W. Park, "Tunable superlensing by a mechanically controlled photonic crystal," J. Opt. Soc. Am. B 23, 479-484 (2006).
[CrossRef]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (1-4) (2002).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Pinchuk, A. O.

Ren, Z. F.

Roux, F. S.

F. S. Roux and I. De Leon, "Planar photonic crystal gradient index lens, simulated with a finite difference time domain method," Phys. Rev. B 74, 113103 (1-4) (2006).
[CrossRef]

Rye, P. M.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-spacemicrowave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (1-3) (2006).
[CrossRef]

Schatz, G. C.

Schonbrun, E.

E. Schonbrun, Q. Wu, W. Park, T, Yamashita, C. J. Summers, M. Abashin and Y. Fainman, "Wave front evolution of negatively refracted waves in a photonic crystal," Appl. Phys. Lett. 90, 041113 (1-3) (2007).
[CrossRef]

Q. Wu, E. Schonbrun, and W. Park, "Image inversion and magnification by negative index prisms," J. Opt. Soc. Am. A 24, A45-A51 (2007).
[CrossRef]

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (1-6) (2006).
[CrossRef]

Q. Wu, E. Schonbrun, and W. Park, "Tunable superlensing by a mechanically controlled photonic crystal," J. Opt. Soc. Am. B 23, 479-484 (2006).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

Schurig, D.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-spacemicrowave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (1-3) (2006).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609 (1-4) (2005).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

Smith, D. R.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-spacemicrowave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (1-3) (2006).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609 (1-4) (2005).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (1-3) (2005).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

Sridhar, S.

B. D. F. Casse, W. T. Lu, Y. J. Huang and S. Sridhar, "Nano-optical microlens with ultrashort focal length using negative refraction," Appl. Phys. Lett. 93, 053111 (1-3) (2008).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Starr, A. F.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-spacemicrowave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (1-3) (2006).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609 (1-4) (2005).
[CrossRef]

Summers, C. J.

E. Schonbrun, Q. Wu, W. Park, T, Yamashita, C. J. Summers, M. Abashin and Y. Fainman, "Wave front evolution of negatively refracted waves in a photonic crystal," Appl. Phys. Lett. 90, 041113 (1-3) (2007).
[CrossRef]

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (1-6) (2006).
[CrossRef]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffractionlimited optical imaging with silver superlens," Science 308, 534-537 (2006).
[CrossRef]

Tanielian, M. H.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (1-3) (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter and M. H. Tanielian, "Performance of a negative index of refraction lens, " Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Thompson, M. A.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (1-3) (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter and M. H. Tanielian, "Performance of a negative index of refraction lens, " Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Vetter, A. M.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter and M. H. Tanielian, "Performance of a negative index of refraction lens, " Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
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Q. Wu, E. Schonbrun, and W. Park, "Image inversion and magnification by negative index prisms," J. Opt. Soc. Am. A 24, A45-A51 (2007).
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E. Schonbrun, Q. Wu, W. Park, T, Yamashita, C. J. Summers, M. Abashin and Y. Fainman, "Wave front evolution of negatively refracted waves in a photonic crystal," Appl. Phys. Lett. 90, 041113 (1-3) (2007).
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Q. Wu, E. Schonbrun, and W. Park, "Tunable superlensing by a mechanically controlled photonic crystal," J. Opt. Soc. Am. B 23, 479-484 (2006).
[CrossRef]

Yamashita, T,

E. Schonbrun, Q. Wu, W. Park, T, Yamashita, C. J. Summers, M. Abashin and Y. Fainman, "Wave front evolution of negatively refracted waves in a photonic crystal," Appl. Phys. Lett. 90, 041113 (1-3) (2007).
[CrossRef]

Yamashita, T.

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (1-6) (2006).
[CrossRef]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffractionlimited optical imaging with silver superlens," Science 308, 534-537 (2006).
[CrossRef]

Appl. Phys. Lett.

E. Schonbrun, Q. Wu, W. Park, T, Yamashita, C. J. Summers, M. Abashin and Y. Fainman, "Wave front evolution of negatively refracted waves in a photonic crystal," Appl. Phys. Lett. 90, 041113 (1-3) (2007).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter and M. H. Tanielian, "Performance of a negative index of refraction lens, " Appl. Phys. Lett. 84, 3232-3234 (2004).
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B. D. F. Casse, W. T. Lu, Y. J. Huang and S. Sridhar, "Nano-optical microlens with ultrashort focal length using negative refraction," Appl. Phys. Lett. 93, 053111 (1-3) (2008).
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T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-spacemicrowave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (1-3) (2006).
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Appl. Phys. Lett.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (1-3) (2005).
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[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

E. Centeno and D. Cassagne, "Graded photonic crystals," Opt. Lett. 74, 2278-2280 (2005).
[CrossRef]

Phys. Rev. B

Q1. E. Centeno, D. Cassagne, and J. P. Albert, "Mirage and superbending effect in two-dimensional graded photonic crystals," Phys. Rev. B 73, 235119-235119 (2006).
[CrossRef]

F. S. Roux and I. De Leon, "Planar photonic crystal gradient index lens, simulated with a finite difference time domain method," Phys. Rev. B 74, 113103 (1-4) (2006).
[CrossRef]

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (1-6) (2006).
[CrossRef]

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (1-4) (2002).
[CrossRef]

Phys. Rev. E

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609 (1-4) (2005).
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Phys. Rev. Lett.

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Science

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffractionlimited optical imaging with silver superlens," Science 308, 534-537 (2006).
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R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
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A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Boston: Artech House, 2000).

S. Sinzinger and J. Jahns, Microoptics, 2nd ed. (Wiley, New York, 2003).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a) Photonic band structures of PCs composed of a triangular lattice of air-holes. The first and second photonic bands are shown by the black and red curves, respectively. The solid and dashed curves correspond to PCs with air-hole radii of 0.25a and 0.40a, respectively. The horizontal line is drawn at a normalized frequency of 0.26 (c/a) and the arrows indicate the wave vectors of the two PCs along the Γ-M direction at this frequency. (b) A schematic of graded index lens made by a PC with graded air-hole size. The optical axis is along the z axis and the transverse direction of the lens is along the y axis.

Fig. 2.
Fig. 2.

(a) Phase profile of EM waves (red solid) along the back interface of the graded PC lens at a frequency of 0.26 (c/a). The x axis is the transverse coordinate in unit of a. The blue dashed curve is the phase profile of a cylindrical wave that best fits the red curve. (b) Phase profiles along the back interfaces of different graded PC lenses. The red, blue and purple solid curves correspond to PCs with parabolic, 1.4th power function and linear grading profiles. The black dashed line represents the same cylindrical wave phase profile as in (a).

Fig. 3.
Fig. 3.

(a) FDTD simulations of the electric field intensity distribution through the graded PC lenses, (top) linear grading, (middle) 1.4th power and (bottom) quadratic grading at a frequency of 0.26 (c/a). (b) The intensity distribution at the back focal planes of the three different graded PC lenses.

Fig. 4.
Fig. 4.

(a) Phase profiles of EM waves along the back interface of the graded PC lens with 1.4th power grading of air hole radius. Different colored curves represent different operating frequencies from 0.22 to 0.32 (c/a). (b) FDTD simulations of the intensity distribution along optical axis after the graded PC lens. Different colored curves correspond to various operating frequencies and the peak of each curve represents the back focal points.

Fig. 5.
Fig. 5.

(a) FDTD simulations of the electric field intensity distribution after a graded PC lens at different frequencies of 0.265, 0.275, 0.285 and 0.295 (c/a). (b) Electric field intensity distribution after a uniform negative index PC excited by a point source at the same frequencies.

Fig. 6.
Fig. 6.

Frequency dependence of the back focal length of different graded PC lenses and a uniform negative index PC lens. Their linear fitting curves are shown by the dashed black lines.

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