Abstract

We demonstrate unrestricted superlensing in a triangular two-dimensional photonic crystal. We investigate simple two-point light sources imaged by a slab lenses made of this photonic crystal, and show that the refraction of light follows simple rules of geometric optics with the Snell’s-law refraction at each interface, and an effective isotropic refractive index n=-1 for light propagating inside the crystal. We contrast this behavior with that of a square two-dimensional photonic crystal in the first photonic band, where the effective dielectric response is anisotropic. This leads to a restricted superlensing, which does not follow the geometric optics.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  4. J.B. Pendry, A.J. Holden, W.J. Stewart, and I. Youngs, ???Extremely Low Frequency Plasmons in Metallic Mesostructures,??? Phys. Rev. Lett. 76, 4773 (1996).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. R.A. Shelby, D.R. Smith, and S. Schultz, ???Experimental Verification of a Negative Index of Refraction,??? Science 292, 77 (2001).
    [CrossRef] [PubMed]
  7. G. Shvets, ???Photonic approach to making a material with a negative index of refraction,??? Phys. Rev. B 67, 035109 (2003).
    [CrossRef]
  8. A. Grbic and G. V. Eleftheriades, ???Experimental verification of backward-wave radiation from a negative refractive index metamaterial,??? J. Appl. Phys. 92, 5930 (2002).
    [CrossRef]
  9. 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, 10 696 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
  11. S. Foteinopoulou and C. M. Soukoulis, ???Negative refraction and left-handed behavior in two-dimensional photonic crystals,??? Phys. Rev. B 67, 235107 (2003).
    [CrossRef]
  12. 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 (2002).
    [CrossRef]
  13. P. V. Parimi, W. T. Lu, P. Vodo and S. Sridhar, ???Photonic crystals: Imaging by flat lens using negative refraction,??? Nature (London) 426, 404 (2003).
    [CrossRef]
  14. C. Luo, S. G. Johnson, J. D. Joannopoulos and J. B. Pendry, ???Subwavelength imaging in photonic crystals,??? Phys. Rev. B 68, 045115 (2003).
    [CrossRef]
  15. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, ???Electromagnetic waves: Negative refraction by photonic crystals,??? Nature (London) 423, 604 (2003).
    [CrossRef]
  16. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, ???Subwavelength Resolution in a Two-Dimensional Photonic-Crystal-Based Superlens,??? Phys. Rev. Lett. 91, 207401 (2003).
    [CrossRef] [PubMed]
  17. Zhi-Yuan Li and Lan-Lan Lin, ???Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,??? Phys. Rev. B 68, 245110 (2003).
    [CrossRef]
  18. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995).
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    [CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, ???Numerical solution of initial boundary value problems involving Maxwell???s equations in isotropic media,??? IEEE Trans. Antennas Propag. 14, 302 (1966).
[CrossRef]

IEEE Trans. Microwave Theory Technol. (1)

J.B. Pendry, A.J. Holden, D.J. Robbins, and W.J. Stewart, ???Magnetism from conductors and enhanced nonlinear phenomena,??? IEEE Trans. Microwave Theory Technol. 47, 2075 (1999).
[CrossRef]

J. Appl. Phys. (1)

A. Grbic and G. V. Eleftheriades, ???Experimental verification of backward-wave radiation from a negative refractive index metamaterial,??? J. Appl. Phys. 92, 5930 (2002).
[CrossRef]

J. Comput. Phys. (1)

J. Berenger, ???A Perfectly Matched Layer for the Absorption of Electromagnetic Waves,??? J. Comput. Phys. 114, 185 (1994).
[CrossRef]

J. Phys.: Condens. Matter (1)

J. B. Pendry and S. A. Ramakrishna, ???Near-field lenses in two dimensions,??? J. Phys.: Condens. Matter 14, 8463 (2002).
[CrossRef]

Nature (2)

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

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, ???Electromagnetic waves: Negative refraction by photonic crystals,??? Nature (London) 423, 604 (2003).
[CrossRef]

Phys. Rev. B (6)

Zhi-Yuan Li and Lan-Lan Lin, ???Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,??? Phys. Rev. B 68, 245110 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos and J. B. Pendry, ???Subwavelength imaging in photonic crystals,??? Phys. Rev. B 68, 045115 (2003).
[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]

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 (2002).
[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, 10 696 (2000).
[CrossRef]

G. Shvets, ???Photonic approach to making a material with a negative index of refraction,??? Phys. Rev. B 67, 035109 (2003).
[CrossRef]

Phys. Rev. Lett. (5)

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, ???Refraction in Media with a Negative Refractive Index,??? Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

J. B. Pendry, ???Negative Refraction Makes a Perfect Lens,??? Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

J.B. Pendry, A.J. Holden, W.J. Stewart, and I. Youngs, ???Extremely Low Frequency Plasmons in Metallic Mesostructures,??? Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, and S. Schultz, ???Composite Medium with Simultaneously Negative Permeability and Permittivity,??? Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, ???Subwavelength Resolution in a Two-Dimensional Photonic-Crystal-Based Superlens,??? Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

Science (1)

R.A. Shelby, D.R. Smith, and S. Schultz, ???Experimental Verification of a Negative Index of Refraction,??? Science 292, 77 (2001).
[CrossRef] [PubMed]

Other (2)

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

A.Taflove, Computational Electrodynamics???the Finite-Difference Time-Domain Method (Artech House, Norwood, MA, 1995).

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Figures (5)

Fig. 1.
Fig. 1.

Calculated photonic band structures for (a) square 2DPC with air-holes of radius r=0.35a, in a dielectric matrix with ε=12, and (b) triangular 2DPC with air-holes of radius r=0.4a, in a dielectric matrix with ε=12.96. Insets: constant frequency contours for (a) ω 1=0.192 and (b) ω 2=0.305.

Fig. 2.
Fig. 2.

(a) The propagation map (magnetic field distribution across space) for a slab of the square 2D-PC (the corresponding band structure in Fig.1a), for two thicknesses of the slab, and the point source frequency ω 1=0.192. (b) The corresponding sketches of geometric optics analysis, showing that for a thicker slab (lower panel) the image must be further away from the crystal edge.

Fig. 3.
Fig. 3.

The propagation map (electric field distribution across space) for a slab of the triangular 2D-PC (the corresponding band structure in Fig.1b), for varying source positions and thickness of the slab. The point source frequency is ω 2=0.305. Positions of the images follow the geometric optics analysis, in which the PC is considered a metamedium with n=-1, and Snell’s-law refraction occurs at each interface.

Fig. 4.
Fig. 4.

The propagation map (electric field distribution across space) for a slab of the triangular 2D-PC, for a two point source in a vertical (a), and horizontal (b) positions.

Fig. 5.
Fig. 5.

Light intensity across the image of two vertical point sources for three different distances between sources.

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