Abstract

This paper reports the multiple bandgaps in the two-dimensional semiconductor-dielectric photonic crystals of several compositions: semiconductor (dielectric) thin cylinders in the dielectric (semiconductor) background. We consider both square and triangular lattice arrangements and compute extensive band structures using a plane-wave method within the framework of an efficient standard eigenvalue problem for both E and H polarizations. The whole range of filling fractions has been explored to claim the existence of the lowest (the so-called acoustic bandgap) and multiple higher-frequency bandgaps within the first 30–40 bands for various compositions. The completeness of the existing bandgaps is substantiated through the computation of the band structures via detailed scanning of the principal symmetry directions covering periphery as well as the interior of the irreducible part of the first Brillouin zone and through the computation of the density of states. In general, the composition made up of doped semiconducting cylinders in the insulating background is found to be the optimum case for both geometries. Such semiconductor-dielectric photonic crystals that are shown to possess huge lowest bandgaps below a threshold frequency (the plasma frequency) have an advantage over the dielectric photonic crystals in the emerging technology based on the photonic crystals.

© 2006 Optical Society of America

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  1. E. Yablonovitch, "Inhibited spontaneous emission in solid state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered structures," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. For an extensive review of electronic, photonic, and sonic bandgap crystals, see M. S. Kushwaha, "Classical band structures of periodic elastic composites," Int. J. Mod. Phys. B 10, 977-1094 (1996).
    [CrossRef]
  4. 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]
  5. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
    [CrossRef]
  6. D. F. Sievenpiper, M. E. Sickmiller, and E. Yablonovitch, "3D wire mesh photonic crystals," Phys. Rev. Lett. 76, 2480-2483 (1996).
    [CrossRef] [PubMed]
  7. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
    [CrossRef] [PubMed]
  8. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Phys. Rev. Lett. 78, 3294-3297 (1997).
    [CrossRef]
  9. Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute bandgap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
    [CrossRef]
  10. L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, and J. Zemmouri, "Giant gaps in photonic band structures," Phys. Rev. B 57, R9388-R9391 (1998).
    [CrossRef]
  11. C. S. Kee, J. E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, "Essential parameter in the formation of photonic bandgaps," Phys. Rev. E 59, 4695-4698 (1999).
    [CrossRef]
  12. M. S. Kushwaha and G. Martinez, "Band-gap engineering in two-dimensional periodic photonic crystals," J. Appl. Phys. 88, 2877-2884 (2000).
    [CrossRef]
  13. E. Yablonovitch, "How to be truly photonic," Science 289, 557-559 (2000).
    [CrossRef]
  14. M. S. Kushwaha and P. Halevi, "Band-gap engineering in periodic elastic composites," Appl. Phys. Lett. 64, 1085-1087 (1994).
    [CrossRef]
  15. J. O. Vasseur, L. Dobryznski, B. Djafari-Rouhani, and H. Puszkarski, "Magnon band structure of periodic composites," Phys. Rev. B 54, 1043-1049 (1996).
    [CrossRef]
  16. C. S. Kee, J. E. Kim, and H. Y. Park, "Heliconic band structure of one-dimensional periodic metallic composites," Phys. Rev. E 57, 2327-2330 (1998).
    [CrossRef]
  17. S. John, "Electromagnetic absorption in a disordered medium near a photon mibility edge," Phys. Rev. Lett. 53, 2169-2172 (1984).
    [CrossRef]
  18. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic band-gap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
    [CrossRef] [PubMed]
  19. M. S. Kushwaha and G. Martinez, "Magnetic-field-dependent bandgaps in two-dimensional photonic crystals," Phys. Rev. B 65, 153202 (2002).
    [CrossRef]
  20. D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
    [CrossRef] [PubMed]
  21. M. S. Kushwaha and G. Martinez, "Band gaps, transmission spectra, and Anderson localization in 2D semiconductor-dielectric photonic crystals," (to be published).
  22. T. W. Ebbesen, J. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
    [CrossRef]

2002 (1)

M. S. Kushwaha and G. Martinez, "Magnetic-field-dependent bandgaps in two-dimensional photonic crystals," Phys. Rev. B 65, 153202 (2002).
[CrossRef]

2000 (4)

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

M. S. Kushwaha and G. Martinez, "Band-gap engineering in two-dimensional periodic photonic crystals," J. Appl. Phys. 88, 2877-2884 (2000).
[CrossRef]

E. Yablonovitch, "How to be truly photonic," Science 289, 557-559 (2000).
[CrossRef]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic band-gap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

1999 (1)

C. S. Kee, J. E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, "Essential parameter in the formation of photonic bandgaps," Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

1998 (4)

C. S. Kee, J. E. Kim, and H. Y. Park, "Heliconic band structure of one-dimensional periodic metallic composites," Phys. Rev. E 57, 2327-2330 (1998).
[CrossRef]

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute bandgap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, and J. Zemmouri, "Giant gaps in photonic band structures," Phys. Rev. B 57, R9388-R9391 (1998).
[CrossRef]

T. W. Ebbesen, J. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

1997 (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Phys. Rev. Lett. 78, 3294-3297 (1997).
[CrossRef]

1996 (4)

J. O. Vasseur, L. Dobryznski, B. Djafari-Rouhani, and H. Puszkarski, "Magnon band structure of periodic composites," Phys. Rev. B 54, 1043-1049 (1996).
[CrossRef]

D. F. Sievenpiper, M. E. Sickmiller, and E. Yablonovitch, "3D wire mesh photonic crystals," Phys. Rev. Lett. 76, 2480-2483 (1996).
[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, 4773-4776 (1996).
[CrossRef] [PubMed]

For an extensive review of electronic, photonic, and sonic bandgap crystals, see M. S. Kushwaha, "Classical band structures of periodic elastic composites," Int. J. Mod. Phys. B 10, 977-1094 (1996).
[CrossRef]

1994 (3)

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]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

M. S. Kushwaha and P. Halevi, "Band-gap engineering in periodic elastic composites," Appl. Phys. Lett. 64, 1085-1087 (1994).
[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 structures," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

1984 (1)

S. John, "Electromagnetic absorption in a disordered medium near a photon mibility edge," Phys. Rev. Lett. 53, 2169-2172 (1984).
[CrossRef]

Akjouj, A.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, and J. Zemmouri, "Giant gaps in photonic band structures," Phys. Rev. B 57, R9388-R9391 (1998).
[CrossRef]

Biswas, R.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Chan, C. T.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic band-gap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Djafari-Rouhani, B.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, and J. Zemmouri, "Giant gaps in photonic band structures," Phys. Rev. B 57, R9388-R9391 (1998).
[CrossRef]

J. O. Vasseur, L. Dobryznski, B. Djafari-Rouhani, and H. Puszkarski, "Magnon band structure of periodic composites," Phys. Rev. B 54, 1043-1049 (1996).
[CrossRef]

Dobryznski, L.

J. O. Vasseur, L. Dobryznski, B. Djafari-Rouhani, and H. Puszkarski, "Magnon band structure of periodic composites," Phys. Rev. B 54, 1043-1049 (1996).
[CrossRef]

Dobrzynski, L.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, and J. Zemmouri, "Giant gaps in photonic band structures," Phys. Rev. B 57, R9388-R9391 (1998).
[CrossRef]

Ebbesen, T. W.

T. W. Ebbesen, J. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Fan, S.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Phys. Rev. Lett. 78, 3294-3297 (1997).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, J. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Gu, B. Y.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute bandgap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

Halevi, P.

M. S. Kushwaha and P. Halevi, "Band-gap engineering in periodic elastic composites," Appl. Phys. Lett. 64, 1085-1087 (1994).
[CrossRef]

Ho, K. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Holden, A. J.

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

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Phys. Rev. Lett. 78, 3294-3297 (1997).
[CrossRef]

John, S.

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

S. John, "Electromagnetic absorption in a disordered medium near a photon mibility edge," Phys. Rev. Lett. 53, 2169-2172 (1984).
[CrossRef]

Kee, C. S.

C. S. Kee, J. E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, "Essential parameter in the formation of photonic bandgaps," Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

C. S. Kee, J. E. Kim, and H. Y. Park, "Heliconic band structure of one-dimensional periodic metallic composites," Phys. Rev. E 57, 2327-2330 (1998).
[CrossRef]

Kim, J. E.

C. S. Kee, J. E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, "Essential parameter in the formation of photonic bandgaps," Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

C. S. Kee, J. E. Kim, and H. Y. Park, "Heliconic band structure of one-dimensional periodic metallic composites," Phys. Rev. E 57, 2327-2330 (1998).
[CrossRef]

Kim, S. J.

C. S. Kee, J. E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, "Essential parameter in the formation of photonic bandgaps," Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Kroll, N.

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Kushwaha, M. S.

M. S. Kushwaha and G. Martinez, "Magnetic-field-dependent bandgaps in two-dimensional photonic crystals," Phys. Rev. B 65, 153202 (2002).
[CrossRef]

M. S. Kushwaha and G. Martinez, "Band-gap engineering in two-dimensional periodic photonic crystals," J. Appl. Phys. 88, 2877-2884 (2000).
[CrossRef]

For an extensive review of electronic, photonic, and sonic bandgap crystals, see M. S. Kushwaha, "Classical band structures of periodic elastic composites," Int. J. Mod. Phys. B 10, 977-1094 (1996).
[CrossRef]

M. S. Kushwaha and P. Halevi, "Band-gap engineering in periodic elastic composites," Appl. Phys. Lett. 64, 1085-1087 (1994).
[CrossRef]

M. S. Kushwaha and G. Martinez, "Band gaps, transmission spectra, and Anderson localization in 2D semiconductor-dielectric photonic crystals," (to be published).

Kuzmiak, V.

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]

Kwon, Y. S.

C. S. Kee, J. E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, "Essential parameter in the formation of photonic bandgaps," Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Lezec, J. J.

T. W. Ebbesen, J. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Li, Z. Y.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute bandgap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

Lim, H.

C. S. Kee, J. E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, "Essential parameter in the formation of photonic bandgaps," Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Maradudin, A. A.

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]

Martinez, G.

M. S. Kushwaha and G. Martinez, "Magnetic-field-dependent bandgaps in two-dimensional photonic crystals," Phys. Rev. B 65, 153202 (2002).
[CrossRef]

M. S. Kushwaha and G. Martinez, "Band-gap engineering in two-dimensional periodic photonic crystals," J. Appl. Phys. 88, 2877-2884 (2000).
[CrossRef]

M. S. Kushwaha and G. Martinez, "Band gaps, transmission spectra, and Anderson localization in 2D semiconductor-dielectric photonic crystals," (to be published).

Myung, N. H.

C. S. Kee, J. E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, "Essential parameter in the formation of photonic bandgaps," Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Noda, S.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic band-gap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Park, H. Y.

C. S. Kee, J. E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, "Essential parameter in the formation of photonic bandgaps," Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

C. S. Kee, J. E. Kim, and H. Y. Park, "Heliconic band structure of one-dimensional periodic metallic composites," Phys. Rev. E 57, 2327-2330 (1998).
[CrossRef]

Pendry, J. B.

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

Pincemin, F.

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]

Puszkarski, H.

J. O. Vasseur, L. Dobryznski, B. Djafari-Rouhani, and H. Puszkarski, "Magnon band structure of periodic composites," Phys. Rev. B 54, 1043-1049 (1996).
[CrossRef]

Schubert, E. F.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Phys. Rev. Lett. 78, 3294-3297 (1997).
[CrossRef]

Shin, S. Y.

C. S. Kee, J. E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, "Essential parameter in the formation of photonic bandgaps," Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Sickmiller, M. E.

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

Sievenpiper, D. F.

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

Sigalas, M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Smith, D. R.

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Song, H. C.

C. S. Kee, J. E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, "Essential parameter in the formation of photonic bandgaps," Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Soukoulis, C. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Stewart, W. J.

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

Thio, T.

T. W. Ebbesen, J. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic band-gap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Vasseur, J. O.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, and J. Zemmouri, "Giant gaps in photonic band structures," Phys. Rev. B 57, R9388-R9391 (1998).
[CrossRef]

J. O. Vasseur, L. Dobryznski, B. Djafari-Rouhani, and H. Puszkarski, "Magnon band structure of periodic composites," Phys. Rev. B 54, 1043-1049 (1996).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Phys. Rev. Lett. 78, 3294-3297 (1997).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, J. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, "How to be truly photonic," Science 289, 557-559 (2000).
[CrossRef]

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]

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic band-gap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Yang, G. Z.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute bandgap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

Youngs, I.

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

Zemmouri, J.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, and J. Zemmouri, "Giant gaps in photonic band structures," Phys. Rev. B 57, R9388-R9391 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

M. S. Kushwaha and P. Halevi, "Band-gap engineering in periodic elastic composites," Appl. Phys. Lett. 64, 1085-1087 (1994).
[CrossRef]

Int. J. Mod. Phys. B (1)

For an extensive review of electronic, photonic, and sonic bandgap crystals, see M. S. Kushwaha, "Classical band structures of periodic elastic composites," Int. J. Mod. Phys. B 10, 977-1094 (1996).
[CrossRef]

J. Appl. Phys. (1)

M. S. Kushwaha and G. Martinez, "Band-gap engineering in two-dimensional periodic photonic crystals," J. Appl. Phys. 88, 2877-2884 (2000).
[CrossRef]

Nature (1)

T. W. Ebbesen, J. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Phys. Rev. B (4)

M. S. Kushwaha and G. Martinez, "Magnetic-field-dependent bandgaps in two-dimensional photonic crystals," Phys. Rev. B 65, 153202 (2002).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Schematics of a unit cell of square (left panel) and triangular (right panel) lattices of lattice constant a. The cylindrical inclusions of radius r 0 and the cylindrical rods (or holes) are oriented along the z axis. Propagation is confined to the xy plane.

Fig. 2
Fig. 2

Full spectrum of the multiple gap windows as a function of filling fraction, the band structure in the principle symmetry directions, the band structure in the entire irreducible part of the first Brillouin zone, and the density of states, respectively, in the first, second, third, and fourth panels, counting from the left, for the doped GaAs cylinders in vacuum background for the E polarization for a square lattice. The filling fraction for the second, third, and fourth panels is f = 47.5 % .

Fig. 3
Fig. 3

Full spectrum of the multiple gap windows as a function of filling fraction, the band structure in the principle symmetry directions, the band structure in the entire irreducible part of the first Brillouin zone, and the density of states, respectively, in the first, second, third, and fourth panels, counting from the left, for the cylindrical holes in doped GaAs background for the E polarization for a square lattice. The filling fraction for the second, third, and fourth panels is f = 40 % .

Fig. 4
Fig. 4

Full spectrum of the multiple gap windows as a function of filling fraction, the band structure in the principle symmetry directions, the band structure in the entire irreducible part of the first Brillouin zone, and the density of states, respectively, in the first, second, third, and fourth panels, counting from the left, for the doped GaAs cylinders in vacuum background for the H polarization for a square lattice. The filling fraction for the second, third, and fourth panels is f = 47.5 % .

Fig. 5
Fig. 5

Full spectrum of the multiple gap windows as a function of filling fraction, the band structure in the principle symmetry directions, the band structure in the entire irreducible part of the first Brillouin zone, and the density of states, respectively, in the first, second, third, and fourth panels, counting from the left, for the cylindrical holes in doped GaAs background for the H polarization for a square lattice. The filling fraction for the second, third, and fourth panels is f = 40 % .

Fig. 6
Fig. 6

Demonstration that only the highest gap (light grey region) for the H polarization in Fig. 4 lies within the second (counting from the top) gap (dark grey region) for the E polarization in Fig. 2, for the filling fraction f = 47.5 % . Thus the highest gap of Fig. 4 is the only complete gap for the doped GaAs cylinders in vacuum background for a square lattice arrangement, within the frequency range 0 Ω 1.5 .

Fig. 7
Fig. 7

Full spectrum of the multiple gap windows as a function of filling fraction, the band structure in the principle symmetry directions, the band structure in the entire irreducible part of the first Brillouin zone, and the density of states, respectively, in the first, second, third, and fourth panels, counting from the left, for the doped GaAs cylinders in vacuum background for the E polarization for a triangular lattice. The filling fraction for the second, third, and fourth panels is f = 52.5 % .

Fig. 8
Fig. 8

Full spectrum of the multiple gap windows as a function of filling fraction, the band structure in the principle symmetry directions, the band structure in the entire irreducible part of the first Brillouin zone, and the density of states, respectively, in the first, second, third, and fourth panels, counting from the left, for the cylindrical holes in doped GaAs background for the E polarization for a triangular lattice. The filling fraction for the second, third, and fourth panels is f = 56 % .

Fig. 9
Fig. 9

Full spectrum of the multiple gap windows as a function of filling fraction, the band structure in the principle symmetry directions, the band structure in the entire irreducible part of the first Brillouin zone, and the density of states, respectively, in the first, second, third, and fourth panels, counting from the left, for the doped GaAs cylinders in vacuum background for the H polarization for a triangular lattice. The filling fraction for the second, third, and fourth panels is f = 52.5 % .

Fig. 10
Fig. 10

Full spectrum of the multiple gap windows as a function of filling fraction, the band structure in the principle symmetry directions, the band structure in the entire irreducible part of the first Brillouin zone, and the density of states, respectively, in the first, second, third, and fourth panels, counting from the left, for the cylindrical holes in doped GaAs background for the H polarization for a triangular lattice. The filling fraction for the second, third, and fourth panels is f = 56 % .

Fig. 11
Fig. 11

Demonstration that only the highest gap (light grey region) for the H polarization in Fig. 9 slightly overlaps with the third (counting from the top) gap (dark grey region) for the E polarization in Fig. 7, for the filling fraction f = 52.5 % . This figure shows that the hatched region represents the only complete gap for the doped GaAs cylinders in vacuum background for a triangular lattice arrangement, within the frequency range 0 Ω 1.5 .

Equations (25)

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× ( × E ) q 0 2 ϵ     E = 0 ,
[ q 0 2 ϵ + y 2 + z 2 x y x z y x q 0 2 ϵ + x 2 + z 2 y z z x z y q 0 2 ϵ x 2 + y 2 ] [ E x E y E z ] = [ 0 0 0 ] .
2 E z + q 0 2 ϵ E z = 0 ,
( q 0 2 ϵ + y 2 ) E x x y E y = 0 ,
x y E x + ( q 0 2 ϵ + x 2 ) E y = 0 ,
g A g , g E z ( g ) = Ω 2 E z ( g ) ,
A = B 1 C
B g , g = P δ g , g + R F ( g g ) ( 1 δ g , g ) ,
C g , g = [ Q + k + g 2 ] δ g , g + S F ( g g ) ( 1 δ g , g ) ,
P = ϵ L i f + ϵ L b ( 1 f ) ,
Q = ϵ L i Ω p i 2 f + ϵ L b Ω p b 2 ( 1 f ) ,
R = ϵ L i ϵ L b ,
S = ϵ L i Ω p i 2 ϵ L b Ω p b 2 ,
A 1 ( g , g ) E x ( g ) + A 2 ( g , g ) E y ( g ) = 0 ,
A 3 ( g , g ) E x ( g ) + A 4 ( g , g ) E y ( g ) = 0 ,
A 1 ( i , j ) = A ( i , j ) Ω 2 [ B ( i , j ) + ( k + g ) y ( k + g ) y δ i j ] ,
A 2 ( i , j ) = ( k + g ) x ( k + g ) y δ i j ,
A 3 ( i , j ) = ( k + g ) x ( k + g ) y δ i j ,
A 4 ( i , j ) = A ( i , j ) Ω 2 [ B ( i , j ) + ( k + g ) x ( k + g ) x δ i j ] .
A ( g ) = { ϵ L i f + ϵ L b ( 1 f ) , if g = 0 ( ϵ L i ϵ L b ) F ( g ) , if g 0 } ,
B ( g ) = { ϵ L i Ω p i 2 f + ϵ L b Ω p b 2 ( 1 f ) , if g = 0 ( ϵ L i Ω p i 2 ϵ L b Ω p b 2 ) F ( g ) , if g 0 } .
[ C 1 Ω 2 + C 2 ] E = 0 ,
C 1 = [ A 0 0 A ] ,
C 2 = [ B ( k + g ) y ( k + g ) y δ i j ( k + g ) x ( k + g ) y δ i j ( k + g ) x ( k + g ) y δ i j B ( k + g ) x ( k + g ) x δ i j ] .
M G = λ G ,

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