Abstract

The existence of uncoupled modes is identified by gaps in the transmission spectra when the density of states is nonzero. We use a group theoretic analysis of the photonic band structure for a simple cubic lattice to tag the symmetry and polarization of each band. The results are compared with transmission spectra calculated by the transfer matrix method.

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References

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  1. C. M. Bowden, J. D. Dowling and H. Everitt, eds. J. Opt. Soc. Am. B 10 (2), (1993).
  2. G. Kurizki and J. W. Haus, eds. J. Mod. Opt. 41 (2), (1994).
    [CrossRef]
  3. J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals, (Princeton Univ. Press, NJ, 1995).
  4. See articles in C. M. Soukoulis, ed. Photonic Band Gaps and Localization, (Plenum, NY, 1993).
  5. J.W. Haus, J. Mod. Opt. 41, 195 (1994).
    [CrossRef]
  6. J.W. Haus, article in Quantum Optics of Confined Systems, M. Ducloy and D. Bloch, eds., (Kluwer Academic, Dordrecht, 1996), pp. 101-142.
    [CrossRef]
  7. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023 (1992).
    [CrossRef] [PubMed]
  8. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe and J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 322 (1993).
    [CrossRef]
  9. K. Sakoda, Phys. Rev. B 51, 4672 (1995).
    [CrossRef]
  10. K. Sakoda, Phys. Rev. B 52, 7982 (1995).
    [CrossRef]
  11. K. Sakoda, Phys. Rev. B 52, 8992 (1995).
    [CrossRef]
  12. M. Wada, K. Sakoda and K. Inoue, Phys. Rev. B 52, 16297 (1995).
    [CrossRef]
  13. M. Wada, Y. Doi, K. Inoue, and J. W. Haus, Phys. Rev. B 55, 10443 (1997).
    [CrossRef]
  14. K. Inoue, M. Wada, K. Sakoda, A. Yamanaka, M. Hayashi and J.W. Haus, Jpn. J. Appl. Phys. 33, L1463 (1994).
    [CrossRef]
  15. K. Inoue, M. Wada, K. Sakoda, M. Hayashi T. Fukushima, and A. Yamanaka, Phys. Rev. B 53, 1010 (1996).
    [CrossRef]
  16. A. Rosenberg, R. J. Tonucci, H-B. Lin, A. J. Campillo, Opt. Lett. 21, 830 (1996).
    [CrossRef] [PubMed]
  17. H-B. Lin,R. J. Tonucci, A. J. Campillo, Appl. Phys. Lett. 68, 2927 (1996).
    [CrossRef]
  18. C. C. Cheng, V. Arbet-Engels, A. Scherer, and E. Yablonovitch, Phys. Scr. T68, 17 (1996).
    [CrossRef]
  19. K. Ohtaka and Y. Tanabe, J. Phys. Soc. Jpn 65, 2670 (1996).
    [CrossRef]
  20. K. Sakoda, Phys. Rev. B 55, 15345 (1997).
    [CrossRef]
  21. H. S. S"oz" uer and J. W. Haus, J. Opt. Soc. Am. B 10, 296 (1993).
    [CrossRef]
  22. H. S. S"oz" uer and J. D. Dowling, J. Mod. Opt. 41, 231 (1994).
    [CrossRef]
  23. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas and M. Sigalas, Solid State Commun. 89, 413 (1994).
    [CrossRef]
  24. E. " Ozbay, E. Michel, G. Tuttle, R. Biswas, M. Sigalas and K. M. Ho, Appl. Phys. Lett. 64, 2059 (1994).
    [CrossRef]
  25. J. B. Pendry, J. Mod. Opt. 41, 208 (1994).
    [CrossRef]
  26. P. M. Bell, J. B. Pendry, L. M. Moreno and A. J. Ward, Comput. Phys. Commun. 85, 306 (1995).
    [CrossRef]
  27. H. S. S"oz" uer, J. W. Haus and R. Inguva, Phys. Rev. B 45, 13962 (1992).
    [CrossRef]

Other

C. M. Bowden, J. D. Dowling and H. Everitt, eds. J. Opt. Soc. Am. B 10 (2), (1993).

G. Kurizki and J. W. Haus, eds. J. Mod. Opt. 41 (2), (1994).
[CrossRef]

J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals, (Princeton Univ. Press, NJ, 1995).

See articles in C. M. Soukoulis, ed. Photonic Band Gaps and Localization, (Plenum, NY, 1993).

J.W. Haus, J. Mod. Opt. 41, 195 (1994).
[CrossRef]

J.W. Haus, article in Quantum Optics of Confined Systems, M. Ducloy and D. Bloch, eds., (Kluwer Academic, Dordrecht, 1996), pp. 101-142.
[CrossRef]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023 (1992).
[CrossRef] [PubMed]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe and J. D. Joannopoulos, J. Opt. Soc. Am. B 10, 322 (1993).
[CrossRef]

K. Sakoda, Phys. Rev. B 51, 4672 (1995).
[CrossRef]

K. Sakoda, Phys. Rev. B 52, 7982 (1995).
[CrossRef]

K. Sakoda, Phys. Rev. B 52, 8992 (1995).
[CrossRef]

M. Wada, K. Sakoda and K. Inoue, Phys. Rev. B 52, 16297 (1995).
[CrossRef]

M. Wada, Y. Doi, K. Inoue, and J. W. Haus, Phys. Rev. B 55, 10443 (1997).
[CrossRef]

K. Inoue, M. Wada, K. Sakoda, A. Yamanaka, M. Hayashi and J.W. Haus, Jpn. J. Appl. Phys. 33, L1463 (1994).
[CrossRef]

K. Inoue, M. Wada, K. Sakoda, M. Hayashi T. Fukushima, and A. Yamanaka, Phys. Rev. B 53, 1010 (1996).
[CrossRef]

A. Rosenberg, R. J. Tonucci, H-B. Lin, A. J. Campillo, Opt. Lett. 21, 830 (1996).
[CrossRef] [PubMed]

H-B. Lin,R. J. Tonucci, A. J. Campillo, Appl. Phys. Lett. 68, 2927 (1996).
[CrossRef]

C. C. Cheng, V. Arbet-Engels, A. Scherer, and E. Yablonovitch, Phys. Scr. T68, 17 (1996).
[CrossRef]

K. Ohtaka and Y. Tanabe, J. Phys. Soc. Jpn 65, 2670 (1996).
[CrossRef]

K. Sakoda, Phys. Rev. B 55, 15345 (1997).
[CrossRef]

H. S. S"oz" uer and J. W. Haus, J. Opt. Soc. Am. B 10, 296 (1993).
[CrossRef]

H. S. S"oz" uer and J. D. Dowling, J. Mod. Opt. 41, 231 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

E. " Ozbay, E. Michel, G. Tuttle, R. Biswas, M. Sigalas and K. M. Ho, Appl. Phys. Lett. 64, 2059 (1994).
[CrossRef]

J. B. Pendry, J. Mod. Opt. 41, 208 (1994).
[CrossRef]

P. M. Bell, J. B. Pendry, L. M. Moreno and A. J. Ward, Comput. Phys. Commun. 85, 306 (1995).
[CrossRef]

H. S. S"oz" uer, J. W. Haus and R. Inguva, Phys. Rev. B 45, 13962 (1992).
[CrossRef]

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Figures (7)

Figure 1.
Figure 1.

Photonic band structure of the infinite simple cubic lattice of air-holes. The E-method calculations use 729 plane waves for each polarization and the cubic symmetry was deformed by 1 % for direct comparison with the transmittance. The scaled radius of the air-holes is 0.495 and the dielectric constant is 13. The color and corresponding line-type scheme is discussed in the text.

Figure 2.
Figure 2.

The P- and S-polarization transmittances along the Γ - M direction for the simple cubic lattice of air-holes for a sample that is 32 periods thick. The scaled radius of the air-holes is 0.495 and the dielectric constant is 13.

Figure 3.
Figure 3.

The convergence of the E- and H-methods versus N -1/3 for bands calculated at the M-point of the Brillouin zone, where N is the number of plane waves in the truncated expansion for each polarization. The radius of the air-holes is 0.495 and the dielectric constant of the host is 13.

Figure 4.
Figure 4.

Photonic band structure of the infinite simple cubic lattice of dielectric spheres. The E-method calculations use 729 plane waves for each polarization. The scaled radius of the spheres is 0.495 and the dielectric constant is 13. The color and line-type scheme is identical to Fig. 1.

Figure 5.
Figure 5.

The P- and S-polarization transmittance of the simple cubic lattice of dielectric spheres along the Γ - M direction for a 32 periods thick sample. The scaled radius of the speheres is 0.495 and the dielctric constant is 13.

Figure 6.
Figure 6.

Photonic band structure of the infinite simple cubic lattice of dielectric spheres. The E-method calculations use 729 plane waves for each polarization. The scaled radius of the spheres is 0.297 and the dielectric constant is 13.

Figure 7.
Figure 7.

The P- and S-polarization transmittance of the simple cubic lattice along the Γ - M direction of dielectric spheres for a 32 periods thick sample. The scaled radius of the speheres is 0.297 and the dielectric constant is 13.

Tables (1)

Tables Icon

Table 1. Gaps identified from the band structure calculations and the corresponding gaps determined by the transfer matrix computations.

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