Abstract

Optical properties of a two-dimensional square-lattice photonic crystal are systematically investigated within the partial bandgap through anisotropic characteristics analysis and numerical simulation of field pattern. Using the plane-wave expansion method and Hellmann–Feynman theorem, the relationships between the incident and refracted angles for both phase and group velocities are calculated to analyze light propagation from air to photonic crystals. Three kinds of flat slab focusing are summarized and demonstrated by numerical simulations using the multiple scattering method.

© 2007 Optical Society of America

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  1. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. B 58, 2059-2062 (1987).
    [CrossRef]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. 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]
  4. C. Luo, S. G. Johnson, J. D. Joannopoulos and J. B. Pendry, "All-negative refraction without negative effective index," Phys. Rev. B 65, 201104(R) (2002).
    [CrossRef]
  5. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  6. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  7. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  8. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
    [CrossRef] [PubMed]
  9. P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
    [CrossRef] [PubMed]
  10. S. Foteinopoulou and C. M. Soukoulis, "Negative refraction and left-handed behavior in two-dimensional photonic crystals," Phys. Rev. B 67, 235107 (2003).
    [CrossRef]
  11. R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, "Negative refraction and superlens behavior in a two-dimensional photonic crystal," Phys. Rev. B 71, 085106 (2005).
    [CrossRef]
  12. X. Ao and S. He, "Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength," Appl. Phys. Lett. 87, 101112 (2005).
    [CrossRef]
  13. R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596-8605 (2005).
    [CrossRef] [PubMed]
  14. Z. Tang, R. Peng, D. Fan, S. Wen, H. Zhang, and L. Qian, "Absolute left-handed behaviors in a triangular elliptical-rod photonic crystal," Opt. Express 13, 9796-9803 (2005).
    [CrossRef] [PubMed]
  15. X. Zhang, "Image resolution depending on slab thickness and object distance in a two-dimensional photonic-crystal-based superlens," Phys. Rev. B 70, 195110 (2004).
    [CrossRef]
  16. C.-H. Kuo and Z. Ye, "Flat lens imaging does not need negative refraction," arxiv.org:http://arxiv.org/abs/cond-mat/0312288.
  17. C.-H. Kuo and Z. Ye, "Negative-refraction-like behavior revealed by arrays of dielectric cylinders," Phys. Rev. E 70, 026608 (2004).
    [CrossRef]
  18. H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, "Direct diffraction without negative refraction," Phys. Rev. B 70, 113101 (2004).
    [CrossRef]
  19. L.-S. Chen, C.-H. Kuo, and Z. Ye, "Guiding optical flows by photonic crystal slabs made of dielectric cylinders," Phys. Rev. E 69, 066612 (2004).
    [CrossRef]
  20. S. Feng, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of an elliptical-rod photonic-crystal slab lens," Phys. Rev. B 72, 075101 (2005).
    [CrossRef]
  21. K. Ren, S. Feng, Z.-F. Feng, Y. Sheng, Z.-Y. Li, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of triangular lattice photonic crystal at the lowest band," Phys. Rev. A 348, 405-409 (2006).
  22. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).
  23. L.-M. Li and Z.-Q. Zhang, "Multiple-scattering approach to finite-sized photonic band-gap materials," Phys. Rev. B 58, 9587-9590 (1998).
    [CrossRef]
  24. H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, "Splitting of triply degenerate refractive indices by photonic crystals," Phys. Rev. B 62, 1477-1480 (2000).
    [CrossRef]

2006 (1)

K. Ren, S. Feng, Z.-F. Feng, Y. Sheng, Z.-Y. Li, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of triangular lattice photonic crystal at the lowest band," Phys. Rev. A 348, 405-409 (2006).

2005 (5)

S. Feng, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of an elliptical-rod photonic-crystal slab lens," Phys. Rev. B 72, 075101 (2005).
[CrossRef]

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, "Negative refraction and superlens behavior in a two-dimensional photonic crystal," Phys. Rev. B 71, 085106 (2005).
[CrossRef]

X. Ao and S. He, "Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength," Appl. Phys. Lett. 87, 101112 (2005).
[CrossRef]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596-8605 (2005).
[CrossRef] [PubMed]

Z. Tang, R. Peng, D. Fan, S. Wen, H. Zhang, and L. Qian, "Absolute left-handed behaviors in a triangular elliptical-rod photonic crystal," Opt. Express 13, 9796-9803 (2005).
[CrossRef] [PubMed]

2004 (4)

X. Zhang, "Image resolution depending on slab thickness and object distance in a two-dimensional photonic-crystal-based superlens," Phys. Rev. B 70, 195110 (2004).
[CrossRef]

C.-H. Kuo and Z. Ye, "Negative-refraction-like behavior revealed by arrays of dielectric cylinders," Phys. Rev. E 70, 026608 (2004).
[CrossRef]

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, "Direct diffraction without negative refraction," Phys. Rev. B 70, 113101 (2004).
[CrossRef]

L.-S. Chen, C.-H. Kuo, and Z. Ye, "Guiding optical flows by photonic crystal slabs made of dielectric cylinders," Phys. Rev. E 69, 066612 (2004).
[CrossRef]

2003 (3)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

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

S. Foteinopoulou and C. M. Soukoulis, "Negative refraction and left-handed behavior in two-dimensional photonic crystals," Phys. Rev. B 67, 235107 (2003).
[CrossRef]

2002 (1)

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

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000 (3)

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, "Splitting of triply degenerate refractive indices by photonic crystals," Phys. Rev. B 62, 1477-1480 (2000).
[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]

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

1998 (1)

L.-M. Li and Z.-Q. Zhang, "Multiple-scattering approach to finite-sized photonic band-gap materials," Phys. Rev. B 58, 9587-9590 (1998).
[CrossRef]

1987 (2)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. B 58, 2059-2062 (1987).
[CrossRef]

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

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Ao, X.

X. Ao and S. He, "Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength," Appl. Phys. Lett. 87, 101112 (2005).
[CrossRef]

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Chen, C.-C.

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, "Direct diffraction without negative refraction," Phys. Rev. B 70, 113101 (2004).
[CrossRef]

Chen, L.-S.

L.-S. Chen, C.-H. Kuo, and Z. Ye, "Guiding optical flows by photonic crystal slabs made of dielectric cylinders," Phys. Rev. E 69, 066612 (2004).
[CrossRef]

Cheng, B.-Y.

K. Ren, S. Feng, Z.-F. Feng, Y. Sheng, Z.-Y. Li, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of triangular lattice photonic crystal at the lowest band," Phys. Rev. A 348, 405-409 (2006).

S. Feng, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of an elliptical-rod photonic-crystal slab lens," Phys. Rev. B 72, 075101 (2005).
[CrossRef]

Chien, H.-T.

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, "Direct diffraction without negative refraction," Phys. Rev. B 70, 113101 (2004).
[CrossRef]

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Fan, D.

Feng, S.

K. Ren, S. Feng, Z.-F. Feng, Y. Sheng, Z.-Y. Li, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of triangular lattice photonic crystal at the lowest band," Phys. Rev. A 348, 405-409 (2006).

S. Feng, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of an elliptical-rod photonic-crystal slab lens," Phys. Rev. B 72, 075101 (2005).
[CrossRef]

Feng, Z.-F.

K. Ren, S. Feng, Z.-F. Feng, Y. Sheng, Z.-Y. Li, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of triangular lattice photonic crystal at the lowest band," Phys. Rev. A 348, 405-409 (2006).

S. Feng, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of an elliptical-rod photonic-crystal slab lens," Phys. Rev. B 72, 075101 (2005).
[CrossRef]

Foteinopoulou, S.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, "Negative refraction and superlens behavior in a two-dimensional photonic crystal," Phys. Rev. B 71, 085106 (2005).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, "Negative refraction and left-handed behavior in two-dimensional photonic crystals," Phys. Rev. B 67, 235107 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Gajic, R.

Guven, K.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, "Negative refraction and superlens behavior in a two-dimensional photonic crystal," Phys. Rev. B 71, 085106 (2005).
[CrossRef]

He, S.

X. Ao and S. He, "Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength," Appl. Phys. Lett. 87, 101112 (2005).
[CrossRef]

Hingerl, K.

Joannopoulos, J. D.

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

John, S.

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

Johnson, S. G.

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

Kawakami, S.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, "Splitting of triply degenerate refractive indices by photonic crystals," Phys. Rev. B 62, 1477-1480 (2000).
[CrossRef]

Kawashima, T.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, "Splitting of triply degenerate refractive indices by photonic crystals," Phys. Rev. B 62, 1477-1480 (2000).
[CrossRef]

Kosaka, H.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, "Splitting of triply degenerate refractive indices by photonic crystals," Phys. Rev. B 62, 1477-1480 (2000).
[CrossRef]

Kuchar, F.

Kuo, C.-H.

C.-H. Kuo and Z. Ye, "Negative-refraction-like behavior revealed by arrays of dielectric cylinders," Phys. Rev. E 70, 026608 (2004).
[CrossRef]

L.-S. Chen, C.-H. Kuo, and Z. Ye, "Guiding optical flows by photonic crystal slabs made of dielectric cylinders," Phys. Rev. E 69, 066612 (2004).
[CrossRef]

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, "Direct diffraction without negative refraction," Phys. Rev. B 70, 113101 (2004).
[CrossRef]

C.-H. Kuo and Z. Ye, "Flat lens imaging does not need negative refraction," arxiv.org:http://arxiv.org/abs/cond-mat/0312288.

Li, L.-M.

L.-M. Li and Z.-Q. Zhang, "Multiple-scattering approach to finite-sized photonic band-gap materials," Phys. Rev. B 58, 9587-9590 (1998).
[CrossRef]

Li, Z.-Y.

K. Ren, S. Feng, Z.-F. Feng, Y. Sheng, Z.-Y. Li, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of triangular lattice photonic crystal at the lowest band," Phys. Rev. A 348, 405-409 (2006).

S. Feng, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of an elliptical-rod photonic-crystal slab lens," Phys. Rev. B 72, 075101 (2005).
[CrossRef]

Lu, W. T.

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

Luo, C.

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

Meisels, R.

Moussa, R.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, "Negative refraction and superlens behavior in a two-dimensional photonic crystal," Phys. Rev. B 71, 085106 (2005).
[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]

Ozbay, E.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, "Negative refraction and superlens behavior in a two-dimensional photonic crystal," Phys. Rev. B 71, 085106 (2005).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Parimi, P. V.

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

Pendry, J. B.

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

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

Peng, R.

Qian, L.

Ren, K.

K. Ren, S. Feng, Z.-F. Feng, Y. Sheng, Z.-Y. Li, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of triangular lattice photonic crystal at the lowest band," Phys. Rev. A 348, 405-409 (2006).

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).

Sato, T.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, "Splitting of triply degenerate refractive indices by photonic crystals," Phys. Rev. B 62, 1477-1480 (2000).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sheng, Y.

K. Ren, S. Feng, Z.-F. Feng, Y. Sheng, Z.-Y. Li, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of triangular lattice photonic crystal at the lowest band," Phys. Rev. A 348, 405-409 (2006).

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, "Negative refraction and superlens behavior in a two-dimensional photonic crystal," Phys. Rev. B 71, 085106 (2005).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, "Negative refraction and left-handed behavior in two-dimensional photonic crystals," Phys. Rev. B 67, 235107 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Sridhar, S.

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

Tang, H.-T.

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, "Direct diffraction without negative refraction," Phys. Rev. B 70, 113101 (2004).
[CrossRef]

Tang, Z.

Tomita, A.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, "Splitting of triply degenerate refractive indices by photonic crystals," Phys. Rev. B 62, 1477-1480 (2000).
[CrossRef]

Tuttle, G.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, "Negative refraction and superlens behavior in a two-dimensional photonic crystal," Phys. Rev. B 71, 085106 (2005).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vodo, P.

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

Wen, S.

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. B 58, 2059-2062 (1987).
[CrossRef]

Ye, Z.

L.-S. Chen, C.-H. Kuo, and Z. Ye, "Guiding optical flows by photonic crystal slabs made of dielectric cylinders," Phys. Rev. E 69, 066612 (2004).
[CrossRef]

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, "Direct diffraction without negative refraction," Phys. Rev. B 70, 113101 (2004).
[CrossRef]

C.-H. Kuo and Z. Ye, "Negative-refraction-like behavior revealed by arrays of dielectric cylinders," Phys. Rev. E 70, 026608 (2004).
[CrossRef]

C.-H. Kuo and Z. Ye, "Flat lens imaging does not need negative refraction," arxiv.org:http://arxiv.org/abs/cond-mat/0312288.

Zhang, D.-Z.

K. Ren, S. Feng, Z.-F. Feng, Y. Sheng, Z.-Y. Li, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of triangular lattice photonic crystal at the lowest band," Phys. Rev. A 348, 405-409 (2006).

S. Feng, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of an elliptical-rod photonic-crystal slab lens," Phys. Rev. B 72, 075101 (2005).
[CrossRef]

Zhang, H.

Zhang, L.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, "Negative refraction and superlens behavior in a two-dimensional photonic crystal," Phys. Rev. B 71, 085106 (2005).
[CrossRef]

Zhang, X.

X. Zhang, "Image resolution depending on slab thickness and object distance in a two-dimensional photonic-crystal-based superlens," Phys. Rev. B 70, 195110 (2004).
[CrossRef]

Zhang, Z.-Q.

L.-M. Li and Z.-Q. Zhang, "Multiple-scattering approach to finite-sized photonic band-gap materials," Phys. Rev. B 58, 9587-9590 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

X. Ao and S. He, "Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength," Appl. Phys. Lett. 87, 101112 (2005).
[CrossRef]

Nature (2)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

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

Opt. Express (2)

Phys. Rev. A (1)

K. Ren, S. Feng, Z.-F. Feng, Y. Sheng, Z.-Y. Li, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of triangular lattice photonic crystal at the lowest band," Phys. Rev. A 348, 405-409 (2006).

Phys. Rev. B (10)

L.-M. Li and Z.-Q. Zhang, "Multiple-scattering approach to finite-sized photonic band-gap materials," Phys. Rev. B 58, 9587-9590 (1998).
[CrossRef]

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, "Splitting of triply degenerate refractive indices by photonic crystals," Phys. Rev. B 62, 1477-1480 (2000).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, "Negative refraction and left-handed behavior in two-dimensional photonic crystals," Phys. Rev. B 67, 235107 (2003).
[CrossRef]

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis, "Negative refraction and superlens behavior in a two-dimensional photonic crystal," Phys. Rev. B 71, 085106 (2005).
[CrossRef]

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. B 58, 2059-2062 (1987).
[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-negative refraction without negative effective index," Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

X. Zhang, "Image resolution depending on slab thickness and object distance in a two-dimensional photonic-crystal-based superlens," Phys. Rev. B 70, 195110 (2004).
[CrossRef]

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, "Direct diffraction without negative refraction," Phys. Rev. B 70, 113101 (2004).
[CrossRef]

S. Feng, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, "Imaging properties of an elliptical-rod photonic-crystal slab lens," Phys. Rev. B 72, 075101 (2005).
[CrossRef]

Phys. Rev. E (2)

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Figures (8)

Fig. 1
Fig. 1

(a) Photonic band structure and (b) EFCs for the 2D PhC studied in this paper.

Fig. 2
Fig. 2

Schematics of anisotropy analyses for four Bloch modes such as f = 0.18 , 0.19 , 0.198 , and 0.21 (a) Phase indices n p . (b) Group indices n g . (c) Angles between the Bloch wave vector k and its corresponding group velocity ν g .

Fig. 3
Fig. 3

Schematics of the incident angle in free space and its corresponding refracted angle in PhC for (a) phase velocities and (b) group velocities.

Fig. 4
Fig. 4

Refractions of a slit beam with an incident angle β = 30 ° at the normalized frequencies: (a) f = 0.18 , (b) f = 0.19 , (c) f = 0.198 , and (d) f = 0.21 . Blue dashed lines and red dashed and black arrows indicate the equiphase surfaces, phase velocities, and energy flows, respectively.

Fig. 5
Fig. 5

Distributions of (a) electric field amplitude and (b) intensity for a nine-layer PhC slab excited by a point source at f = 0.18 .

Fig. 6
Fig. 6

Propagation maps for (a) 9-layer and (b) 19-layer PhC slabs excited by a point source at f = 0.19 . (a1) and (b1) are the snapshots of the electric field amplitude. (a2) and (b2) display the corresponding intensity distributions.

Fig. 7
Fig. 7

Distributions of (a) electric field amplitude and (b) intensity for a 29-layer PhC slab excited by a point source at f = 0.198 .

Fig. 8
Fig. 8

Imaging analysis for the PhC slabs at f = 0.21 . A point source is located at (a) d o = 1.5 a and (b) d o = 6 a before a 17-layer slab, (c) Point source located at d o = 1.5 a before a 29-layer slab. (a1), (b1), and (c1) are the snapshots of the electric field amplitude. (a2), (b2), and (c2) display the corresponding intensity distributions.

Equations (3)

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n p = k k 0 = sgn ( k ν g ) k k 0 ,
ν g = k ω ( k ) .
n g = c ν g = c k ω ( k ) ,

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