Abstract

It is shown that certain metallic photonic crystals can enable negative refraction and subwavelength imaging without relying on a negative effective index. These metallic structures are very simple in design and appear straightforward for fabrication. Their unusual electromagnetic response should provide an interesting comparison with the metallic left-handed materials.

© 2003 Optical Society of America

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References

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  1. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, �??Extremely low frequency plasmons in metallic structures,�?? Phys. Rev. Lett. 76, 4773-4776 (1996).
    [CrossRef] [PubMed]
  2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, �??Magnetism from conductors and enhanced nonlinear phenomena,�?? IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  3. 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, 4184-4187 (2000).
    [CrossRef] [PubMed]
  4. V. G. Veselago, �??The electrodynamics of substances with simultaneously negative values of ε and μ,�?? Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  5. J. B. Pendry, �??Negative refraction makes a perfect lens,�?? Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  6. R. A. Shelby, D. R. Smith, and S. Schultz, �??Experimental veri.cation of a negative index of refraction,�?? Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  7. D. R. Smith, Left-handed materials home, <a href="http://physics.ucsd.edu/~drs/left home.htm">http://physics.ucsd.edu/~drs/left home.htm</a>
  8. E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059-2062 (1987)
    [CrossRef] [PubMed]
  9. S. John, �??Strong localization of photons in certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  10. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995).
  11. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, �??Superprism phenomena in photonic crystals,�?? Phys. Rev. B 58, R10096-R10099 (1998).
    [CrossRef]
  12. 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]
  13. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, �??All-angle negative refraction without negative e.ective index,�?? Phys. Rev. B 65, 201104-1-201104-4 (2002).
    [CrossRef]
  14. C. Luo, S. G. Johnson, and J. D. Joannopoulos, �??All-angle negative refraction in a three dimensionally periodic photonic crystal,�?? Appl. Phys. Lett. 81, 2352-2354 (2002).
    [CrossRef]
  15. C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, �??Cerenkov radiation in photonic crystals,�?? Science 299, 368-371 (2003).
    [CrossRef] [PubMed]
  16. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, �??Subwavelength imaging in photonic crystals,�?? submitted to Phys. Rev. B .
  17. V. Kuzmiak, A. A. Maradudin, and F. Pincemin, �??Photonic band structures of two-dimensional systems containing metallic components,�?? Phys. Rev. B 50, 16835-16844 (1994).
    [CrossRef]
  18. M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulos, �??Metallic photonic band-gap materials,�?? Phys. Rev. B 52, 11744 (1995).
    [CrossRef]
  19. E. R. Brown and O. B. McMahon, �??Large electromagnetic stop bands in metallodielectric photonic crystals,�?? Appl. Phys. Lett. 67, 2138-2140 (1995).
    [CrossRef]
  20. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, �??Large omnidirectional band gaps in metallodielectric photonic crystals,�?? Phys. Rev. B 54, 11245-11251 (1996).
    [CrossRef]
  21. D. F. Sievenpiper, M. E. Sickmiller, and E. Yablonovitch, �??3D wire mesh photonic crystals,�?? Phys. Rev. Lett. 76, 2480-2483 (1996).
    [CrossRef] [PubMed]
  22. K. A. Mcintosh, L. J. Mahoney, K. M. Molvar, O. B. McMahon, S. Verghese, M. Rothschild, and E. R. Brown, �??Three-dimensional metallodielectric photonic crystals exhibiting resonant infrared stop bands,�?? Appl. Phys. Lett. 70, 2937-2939 (1997).
    [CrossRef]
  23. K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, �??Photonic bands of metallic systems. I. Principle of calculation and accuracy,�?? Phys. Rev. B 64, 045116-1-045116-8 (2001).
    [CrossRef]
  24. J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, �??All-metallic three-dimensional photonic crystals with a large infrared bandgap,�?? Nature (London) 417, 52-55 (2002).
    [CrossRef] [PubMed]
  25. D. R. Smith, D. Schurig, and J. B. Pendry, �??Negative refraction of modulated electromagnetic waves,�?? Appl. Phys. Lett. 81, 2713-2715 (2002).
    [CrossRef]
  26. J. Pacheco, T. M. Grzegorczyk, B.-I. Wu, Y. Zhang, and J. A. Kong, �??Power propagation in homogeneous isotropic frequency-dispersive left-handed media,�?? Phys. Rev. Lett. 89, 257401-1-257401-4 (2002).
    [CrossRef] [PubMed]
  27. S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, Phys. Rev. Lett. 67, 2017-2020 (1991).
    [CrossRef] [PubMed]
  28. H. A. Atwater, private communication.

Appl. Phys. Lett.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, �??All-angle negative refraction in a three dimensionally periodic photonic crystal,�?? Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

E. R. Brown and O. B. McMahon, �??Large electromagnetic stop bands in metallodielectric photonic crystals,�?? Appl. Phys. Lett. 67, 2138-2140 (1995).
[CrossRef]

K. A. Mcintosh, L. J. Mahoney, K. M. Molvar, O. B. McMahon, S. Verghese, M. Rothschild, and E. R. Brown, �??Three-dimensional metallodielectric photonic crystals exhibiting resonant infrared stop bands,�?? Appl. Phys. Lett. 70, 2937-2939 (1997).
[CrossRef]

D. R. Smith, D. Schurig, and J. B. Pendry, �??Negative refraction of modulated electromagnetic waves,�?? Appl. Phys. Lett. 81, 2713-2715 (2002).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, �??Magnetism from conductors and enhanced nonlinear phenomena,�?? IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Nature

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, �??All-metallic three-dimensional photonic crystals with a large infrared bandgap,�?? Nature (London) 417, 52-55 (2002).
[CrossRef] [PubMed]

Phys. Rev . Lett.

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, Phys. Rev. Lett. 67, 2017-2020 (1991).
[CrossRef] [PubMed]

Phys. Rev. B

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, �??Superprism phenomena in photonic crystals,�?? Phys. Rev. B 58, R10096-R10099 (1998).
[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 e.ective index,�?? Phys. Rev. B 65, 201104-1-201104-4 (2002).
[CrossRef]

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, �??Photonic bands of metallic systems. I. Principle of calculation and accuracy,�?? Phys. Rev. B 64, 045116-1-045116-8 (2001).
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, �??Large omnidirectional band gaps in metallodielectric photonic crystals,�?? Phys. Rev. B 54, 11245-11251 (1996).
[CrossRef]

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, �??Photonic band structures of two-dimensional systems containing metallic components,�?? Phys. Rev. B 50, 16835-16844 (1994).
[CrossRef]

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulos, �??Metallic photonic band-gap materials,�?? Phys. Rev. B 52, 11744 (1995).
[CrossRef]

Phys. Rev. Lett.

D. F. Sievenpiper, M. E. Sickmiller, and E. Yablonovitch, �??3D wire mesh photonic crystals,�?? Phys. Rev. Lett. 76, 2480-2483 (1996).
[CrossRef] [PubMed]

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]

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, 4184-4187 (2000).
[CrossRef] [PubMed]

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

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, �??Extremely low frequency plasmons in metallic structures,�?? Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

J. Pacheco, T. M. Grzegorczyk, B.-I. Wu, Y. Zhang, and J. A. Kong, �??Power propagation in homogeneous isotropic frequency-dispersive left-handed media,�?? Phys. Rev. Lett. 89, 257401-1-257401-4 (2002).
[CrossRef] [PubMed]

Science

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

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, �??Cerenkov radiation in photonic crystals,�?? Science 299, 368-371 (2003).
[CrossRef] [PubMed]

Sov. Phys. Usp.

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

Other

D. R. Smith, Left-handed materials home, <a href="http://physics.ucsd.edu/~drs/left home.htm">http://physics.ucsd.edu/~drs/left home.htm</a>

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

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, �??Subwavelength imaging in photonic crystals,�?? submitted to Phys. Rev. B .

H. A. Atwater, private communication.

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Figures (4)

Fig. 1.
Fig. 1.

The first few bands of a 2D square lattice of metallic cylinders in dielectric computed by FDTD. The photonic dispersion relations are indicated by black circles and connected by red lines. The broken line is the light line centered on the M point. The green AANR region is the frequency range of negative refraction for all incident angles. The left inset is a schematic illustration of the photonic crystal (yellow stands for dielectric and blue stands for metal). The right inset is a portrayal of the Brillouin zone and the refraction in wavevector space. Air modes and photonic-crystal modes are indicated by black and red colors, respectively. The long and thin arrows indicate the phase velocity k, and the short and thick arrows indicate the group (energy) velocity ∂ω/∂k. The green region is the phase space corresponding to the AANR frequency range.

Fig. 2.
Fig. 2.

FDTD simulation of negative refraction. Shown is the pattern for the electric field E perpendicular to the plane (red for positive and blue for negative values). The dielectric and metallic boundaries are in black. The arrows and texts illustrate the various beam directions. The inset shows two possible ways of constructing phase fronts from the field pattern. We choose the set of phase fronts with the maximum wavelength (a maximum 4-wavelength distance d 1 of that set is shown in red) to be the phase fronts of the refracted beam.

Fig. 3.
Fig. 3.

Bound photon modes inside a slab of metallic photonic crystal plotted on top of the projected surface band structure. The black circles and lines indicate the bulk-guided modes. The colored circles and lines represent the surface-guided modes for two different slab thicknesses. The lightly red region is the bulk band structure projected to the surface direction, and the lightly blue region is the light cone. Inset is a schematic illustrations of the photonic-crystals slab of finite thickness h.

Fig. 4.
Fig. 4.

FDTD simulation of superlensing with metallic photonic crystal. Each column correspond to the results for a CW point source placed at 0.207a away from the left surface of the slab, for the frequency value indicated at the top. (a): Intensity distribution in the system marked with the directions of coordinate axes x and z. The intensity is calculated as the averaged square of the electric field value between 2174 and 2416 periods. A lighter color represents a higher intensity value. The point source is placed at (z,x)=(-6.21a, 0). (b): Intensity distribution data plotted along the surface direction in the image space (x=0, z>0). (c): Intensity distribution data measured at the z value of the intensity peak in (b), plotted along the transverse direction (x).

Tables (1)

Tables Icon

Table 1. AANR frequency range for various cylinder radii (TM polarization)

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