Abstract

To clarify the nature of photonic band gaps, a series of calculations on two-dimensional photonic crystals is undertaken. Systems that possess a large gap for one polarization and no gap for the other polarization are analyzed. Two features of a photonic crystal that give rise to a large photonic band gap for each polarization, i.e., connectivity and concentration of the dielectric material, are elucidated. The implications for making materials with large photonic band gaps in two and three dimensions are discussed.

© 1993 Optical Society of America

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  1. K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
    [CrossRef] [PubMed]
  2. E. Yablonovitch, T. J. Gmitter, and K. M. Leung, Phys. Rev. Lett. 67, 2295 (1991).
    [CrossRef] [PubMed]
  3. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 13772 (1991).
    [CrossRef]
  4. E. Yablonovitch, T. J. Gmitter, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
    [CrossRef] [PubMed]
  5. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
    [CrossRef]
  6. W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observations of surface photons on periodic dielectric arrays,” Opt. Lett. (to be published).
  7. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  8. J. Martorell and N. Lawandy, Phys. Rev. Lett. 65, 1877 (1990).
    [CrossRef] [PubMed]
  9. E. Yablonovitch and T. J. Gmitter, Phys. Rev. Lett. 63, 1950 (1989).
    [CrossRef] [PubMed]
  10. M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
    [CrossRef]
  11. S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, Phys. Rev. Lett. 67, 2017 (1991).
    [CrossRef] [PubMed]
  12. P. Villeneuve and M. Piche, Phys. Rev. B 46, 4969 (1992).
    [CrossRef]
  13. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
    [CrossRef]
  14. W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 68, 2023 (1992).
    [CrossRef] [PubMed]

1992 (2)

P. Villeneuve and M. Piche, Phys. Rev. B 46, 4969 (1992).
[CrossRef]

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

1991 (7)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, Phys. Rev. Lett. 67, 2295 (1991).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 13772 (1991).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
[CrossRef]

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

1990 (2)

J. Martorell and N. Lawandy, Phys. Rev. Lett. 65, 1877 (1990).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

1989 (1)

E. Yablonovitch and T. J. Gmitter, Phys. Rev. Lett. 63, 1950 (1989).
[CrossRef] [PubMed]

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Arjavalingam, G.

W. 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. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observations of surface photons on periodic dielectric arrays,” Opt. Lett. (to be published).

Brommer, K. D.

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

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 13772 (1991).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observations of surface photons on periodic dielectric arrays,” Opt. Lett. (to be published).

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

Dalichaouch, R.

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

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, Phys. Rev. Lett. 67, 2295 (1991).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

E. Yablonovitch and T. J. Gmitter, Phys. Rev. Lett. 63, 1950 (1989).
[CrossRef] [PubMed]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

Joannopoulos, J. D.

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

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 13772 (1991).
[CrossRef]

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observations of surface photons on periodic dielectric arrays,” Opt. Lett. (to be published).

Lawandy, N.

J. Martorell and N. Lawandy, Phys. Rev. Lett. 65, 1877 (1990).
[CrossRef] [PubMed]

Leung, K. M.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, Phys. Rev. Lett. 67, 2295 (1991).
[CrossRef] [PubMed]

Maradudin, A. A.

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
[CrossRef]

Martorell, J.

J. Martorell and N. Lawandy, Phys. Rev. Lett. 65, 1877 (1990).
[CrossRef] [PubMed]

McCall, S. L.

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

Meade, R. D.

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

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 13772 (1991).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observations of surface photons on periodic dielectric arrays,” Opt. Lett. (to be published).

Piche, M.

P. Villeneuve and M. Piche, Phys. Rev. B 46, 4969 (1992).
[CrossRef]

Platzman, P. M.

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

Plihal, M.

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
[CrossRef]

Rappe, A. M.

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

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 13772 (1991).
[CrossRef]

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observations of surface photons on periodic dielectric arrays,” Opt. Lett. (to be published).

Robertson, W.

W. 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. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observations of surface photons on periodic dielectric arrays,” Opt. Lett. (to be published).

Schultz, S.

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

Shambrook, A.

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
[CrossRef]

Sheng, P.

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
[CrossRef]

Smith, D.

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

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

Villeneuve, P.

P. Villeneuve and M. Piche, Phys. Rev. B 46, 4969 (1992).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, Phys. Rev. Lett. 67, 2295 (1991).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

E. Yablonovitch and T. J. Gmitter, Phys. Rev. Lett. 63, 1950 (1989).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. Plihal, A. Shambrook, A. A. Maradudin, and P. Sheng, Opt. Commun. 80, 199 (1991).
[CrossRef]

Phys. Rev. B (4)

P. Villeneuve and M. Piche, Phys. Rev. B 46, 4969 (1992).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 13772 (1991).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

Phys. Rev. Lett. (8)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

J. Martorell and N. Lawandy, Phys. Rev. Lett. 65, 1877 (1990).
[CrossRef] [PubMed]

E. Yablonovitch and T. J. Gmitter, Phys. Rev. Lett. 63, 1950 (1989).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, Phys. Rev. Lett. 67, 2295 (1991).
[CrossRef] [PubMed]

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

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

Other (1)

W. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observations of surface photons on periodic dielectric arrays,” Opt. Lett. (to be published).

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Figures (5)

Fig. 1
Fig. 1

Photonic band structures, showing the relationship between frequency and wave vector for the lowest-frequency prorpagating electromagnetic modes. Solid curves represent TM modes, with fields along (Ez, Hx, Hy), and dashed curves represent TE modes, with fields along (Hz, Ex, Ey). The left-hand inset of each figure shows the high-symmetry points within the two-dimensional Brillouin zone. The right-hand insets show a cross-sectional view of the dielectric function, with the shaded area representing high dielectric constant. (a) Modes inside a square array of high-dielectric ( = 8.9) cylinders. (b) Modes inside a square array of square holes in a high-dielectric material.

Fig. 2
Fig. 2

Displacement fields of X-point TM states inside a square array of high-dielectric ( = 8.9) cylinders. TM modes have D normal to the plane, D(r) = d(r) z ^. The height of the surface represents the size of the z component of the displacement field. Positive peaks represent displacement fields pointing up the cylinders, and negative peaks show displacement fields pointing down the cylinders. (a) Dielectric-band state; (b) air-band state.

Fig. 3
Fig. 3

Displacement fields of X-point TE states inside a square array of high-dielectric ( = 8.9) cylinders. TE modes have D in the plane D(r) · z ^= 0, and the figure shows the field lines of D. Cylinders of high-dielectric material are enclosed by dotted circles, and the displacement field lines are shown as solid curves. (a) Dielectric-band state; (b) air-band state.

Fig. 4
Fig. 4

Displacement fields of X-point TM states inside a square array of square holes in a high-dielectric ( = 8.9) material. TM modes have D normal to the plane, D(r) = d(r) z ^. The height of the surface represents the size of the z component of the displacement field. Positive peaks represent displacement fields pointing up the veins between square holes, and negative peaks show displacement fields pointing down the veins between square holes. (a) Dielectric-band state; (b) air-band state.

Fig. 5
Fig. 5

Displacement fields of X-point TE states inside a square array of square holes in a high-dielectric ( = 8.9) constant. TE modes have D in the plane D(r) · z ^= 0, and the figure shows the field lines of D. The regions of high-dielectric strength are enclosed by dotted curves, and the displacement field lines are shown as solid curves. (a) Dielectric-band state; (b) air-band state.

Tables (2)

Tables Icon

Table 1 Fill Factors for the Lattice of Dielectric Rodsa

Tables Icon

Table 2 Fill Factors for the Lattice of Square Holesa

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

× ( 1 ( r ) × H ) = ω 2 c 2 H .
( G λ ) Θ ( G λ ) , ( G λ ) k h ( G λ ) = ω 2 h ( G λ ) ,
Θ ( G λ ) , ( G λ ) k = [ ( k + G ) × e λ ] · [ ( k + G ) × e λ ] - 1 ( G , G ) .
f = V = 8.9 E * ( r ) · D ( r ) d 3 r E * ( r ) · D ( r ) d 3 r .

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