Abstract

This paper discusses theoretical calculations of photonic bandgaps found in the one-stage Sierpinski gasket basis in the hexagonal lattice. Dielectric triangles and cylinders as well as air triangles and cylinders are investigated. All of these structures exhibited complete bandgaps, with the largest complete gap having 6.1% fractional width. The largest TE and TM polarization gaps were 23% and 40% fractional width, respectively. Resonators constructed from these crystals with a Q ten to 2000 times greater than resonators constructed using one cylinder in the hex lattice are demonstrated.

© 2007 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 dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature (London) 386, 143-149 (1997).
    [CrossRef]
  4. C. Lopez, "Three-dimensional photonic bandgap materials: semiconductors for light," J. Opt. A 8, R1-R14 (2006).
    [CrossRef]
  5. R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
    [CrossRef]
  6. W. Kuang, Z. Hou, Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A, Pure Appl. Opt. 7, 525-528 (2005).
    [CrossRef]
  7. N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. 91, 3501-3510 (2002).
    [CrossRef]
  8. R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, "Nature of the photonic band gap: some insights from a field analysis," J. Opt. Soc. Am. B 10, 328-332 (1993).
    [CrossRef]
  9. L. Li, Y. C. Xie, Y. Q. Wang, X. Y. Hu, Z. F. Feng, and B. Y. Cheng, "Absolute gap of two-dimensional fractal photonic structure," Chin. Phys. Lett. 20, 1767-1769 (2003).
    [CrossRef]
  10. K. Sakoda, S. Kirihara, Y. Miyamoto, M. W. Takeda, and K. Honda, "Light scattering and transmission spectra of the Menger sponge fractal," Appl. Phys. B: Photophys. Laser Chem. 81, 321-324 (2005).
    [CrossRef]
  11. Z. Liu, J. J. Xu, and Z. F. Lin, "Photonic band gaps in two-dimensional crystals with fractal structure," Chin. Phys. Lett. 20, 516-518 (2003).
    [CrossRef]
  12. P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
    [CrossRef]
  13. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
    [CrossRef]
  14. M. Qiu and B. Jaskorzynska, "Design of a channel drop filter in a two-dimensional triangular photonic crystal," Appl. Phys. Lett. 83, 1074-1076 (2003).
    [CrossRef]
  15. Z. Wang and S. Fan, "Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines," Phys. Rev. E 68, 066616(1)-(4) (2003).
    [CrossRef]
  16. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
    [CrossRef] [PubMed]
  17. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995).
  18. J. N. Winn, R. D. Meade, and J. D. Joannopoulos, "Two-dimensional photonic band-gap materials," J. Mod. Opt. 41, 257-273 (1994).
    [CrossRef]
  19. R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295-310 (1994).
    [CrossRef]
  20. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite Difference Time Domain Method, 3rd Ed. (Artech House, 2005).
  21. FDTD software is available at http://ab-initio.mit.edu/meep, for example.
  22. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
    [CrossRef]
  23. S. Gao and S. Albin, "Numerical techniques for excitation and analysis of defect modes in photonic crystals," Opt. Express 11, 1080 (2003).
    [CrossRef]

2006

C. Lopez, "Three-dimensional photonic bandgap materials: semiconductors for light," J. Opt. A 8, R1-R14 (2006).
[CrossRef]

2005

W. Kuang, Z. Hou, Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A, Pure Appl. Opt. 7, 525-528 (2005).
[CrossRef]

K. Sakoda, S. Kirihara, Y. Miyamoto, M. W. Takeda, and K. Honda, "Light scattering and transmission spectra of the Menger sponge fractal," Appl. Phys. B: Photophys. Laser Chem. 81, 321-324 (2005).
[CrossRef]

2003

Z. Liu, J. J. Xu, and Z. F. Lin, "Photonic band gaps in two-dimensional crystals with fractal structure," Chin. Phys. Lett. 20, 516-518 (2003).
[CrossRef]

M. Qiu and B. Jaskorzynska, "Design of a channel drop filter in a two-dimensional triangular photonic crystal," Appl. Phys. Lett. 83, 1074-1076 (2003).
[CrossRef]

Z. Wang and S. Fan, "Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines," Phys. Rev. E 68, 066616(1)-(4) (2003).
[CrossRef]

L. Li, Y. C. Xie, Y. Q. Wang, X. Y. Hu, Z. F. Feng, and B. Y. Cheng, "Absolute gap of two-dimensional fractal photonic structure," Chin. Phys. Lett. 20, 1767-1769 (2003).
[CrossRef]

S. Gao and S. Albin, "Numerical techniques for excitation and analysis of defect modes in photonic crystals," Opt. Express 11, 1080 (2003).
[CrossRef]

2002

N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. 91, 3501-3510 (2002).
[CrossRef]

2001

R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

1998

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

1997

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature (London) 386, 143-149 (1997).
[CrossRef]

1996

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

1994

J. N. Winn, R. D. Meade, and J. D. Joannopoulos, "Two-dimensional photonic band-gap materials," J. Mod. Opt. 41, 257-273 (1994).
[CrossRef]

R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295-310 (1994).
[CrossRef]

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

1993

1987

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]

Albin, S.

Berenger, J. P.

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Brommer, K. D.

Cheng, B. Y.

L. Li, Y. C. Xie, Y. Q. Wang, X. Y. Hu, Z. F. Feng, and B. Y. Cheng, "Absolute gap of two-dimensional fractal photonic structure," Chin. Phys. Lett. 20, 1767-1769 (2003).
[CrossRef]

Fan, S.

Z. Wang and S. Fan, "Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines," Phys. Rev. E 68, 066616(1)-(4) (2003).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature (London) 386, 143-149 (1997).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

Feng, Z. F.

L. Li, Y. C. Xie, Y. Q. Wang, X. Y. Hu, Z. F. Feng, and B. Y. Cheng, "Absolute gap of two-dimensional fractal photonic structure," Chin. Phys. Lett. 20, 1767-1769 (2003).
[CrossRef]

Gao, S.

Gerard, J. M.

R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295-310 (1994).
[CrossRef]

Gu, B. Y.

R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite Difference Time Domain Method, 3rd Ed. (Artech House, 2005).

Haus, H. A.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

Honda, K.

K. Sakoda, S. Kirihara, Y. Miyamoto, M. W. Takeda, and K. Honda, "Light scattering and transmission spectra of the Menger sponge fractal," Appl. Phys. B: Photophys. Laser Chem. 81, 321-324 (2005).
[CrossRef]

Hou, Z.

W. Kuang, Z. Hou, Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A, Pure Appl. Opt. 7, 525-528 (2005).
[CrossRef]

Hu, X. Y.

L. Li, Y. C. Xie, Y. Q. Wang, X. Y. Hu, Z. F. Feng, and B. Y. Cheng, "Absolute gap of two-dimensional fractal photonic structure," Chin. Phys. Lett. 20, 1767-1769 (2003).
[CrossRef]

Jaskorzynska, B.

M. Qiu and B. Jaskorzynska, "Design of a channel drop filter in a two-dimensional triangular photonic crystal," Appl. Phys. Lett. 83, 1074-1076 (2003).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature (London) 386, 143-149 (1997).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

J. N. Winn, R. D. Meade, and J. D. Joannopoulos, "Two-dimensional photonic band-gap materials," J. Mod. Opt. 41, 257-273 (1994).
[CrossRef]

R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, "Nature of the photonic band gap: some insights from a field analysis," J. Opt. Soc. Am. B 10, 328-332 (1993).
[CrossRef]

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

John, S.

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

Johnson, S. G.

Kirihara, S.

K. Sakoda, S. Kirihara, Y. Miyamoto, M. W. Takeda, and K. Honda, "Light scattering and transmission spectra of the Menger sponge fractal," Appl. Phys. B: Photophys. Laser Chem. 81, 321-324 (2005).
[CrossRef]

Kuang, W.

W. Kuang, Z. Hou, Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A, Pure Appl. Opt. 7, 525-528 (2005).
[CrossRef]

Li, H.

W. Kuang, Z. Hou, Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A, Pure Appl. Opt. 7, 525-528 (2005).
[CrossRef]

Li, L.

L. Li, Y. C. Xie, Y. Q. Wang, X. Y. Hu, Z. F. Feng, and B. Y. Cheng, "Absolute gap of two-dimensional fractal photonic structure," Chin. Phys. Lett. 20, 1767-1769 (2003).
[CrossRef]

Lin, Z. F.

Z. Liu, J. J. Xu, and Z. F. Lin, "Photonic band gaps in two-dimensional crystals with fractal structure," Chin. Phys. Lett. 20, 516-518 (2003).
[CrossRef]

Liu, Y.

W. Kuang, Z. Hou, Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A, Pure Appl. Opt. 7, 525-528 (2005).
[CrossRef]

Liu, Z.

Z. Liu, J. J. Xu, and Z. F. Lin, "Photonic band gaps in two-dimensional crystals with fractal structure," Chin. Phys. Lett. 20, 516-518 (2003).
[CrossRef]

Lopez, C.

C. Lopez, "Three-dimensional photonic bandgap materials: semiconductors for light," J. Opt. A 8, R1-R14 (2006).
[CrossRef]

Marzin, J. Y.

R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295-310 (1994).
[CrossRef]

Meade, R. D.

J. N. Winn, R. D. Meade, and J. D. Joannopoulos, "Two-dimensional photonic band-gap materials," J. Mod. Opt. 41, 257-273 (1994).
[CrossRef]

R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, "Nature of the photonic band gap: some insights from a field analysis," J. Opt. Soc. Am. B 10, 328-332 (1993).
[CrossRef]

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

Miyamoto, Y.

K. Sakoda, S. Kirihara, Y. Miyamoto, M. W. Takeda, and K. Honda, "Light scattering and transmission spectra of the Menger sponge fractal," Appl. Phys. B: Photophys. Laser Chem. 81, 321-324 (2005).
[CrossRef]

Padjen, R.

R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295-310 (1994).
[CrossRef]

Qiu, M.

M. Qiu and B. Jaskorzynska, "Design of a channel drop filter in a two-dimensional triangular photonic crystal," Appl. Phys. Lett. 83, 1074-1076 (2003).
[CrossRef]

Rappe, A. M.

Sakoda, K.

K. Sakoda, S. Kirihara, Y. Miyamoto, M. W. Takeda, and K. Honda, "Light scattering and transmission spectra of the Menger sponge fractal," Appl. Phys. B: Photophys. Laser Chem. 81, 321-324 (2005).
[CrossRef]

Susa, N.

N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. 91, 3501-3510 (2002).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite Difference Time Domain Method, 3rd Ed. (Artech House, 2005).

Takeda, M. W.

K. Sakoda, S. Kirihara, Y. Miyamoto, M. W. Takeda, and K. Honda, "Light scattering and transmission spectra of the Menger sponge fractal," Appl. Phys. B: Photophys. Laser Chem. 81, 321-324 (2005).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature (London) 386, 143-149 (1997).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

Wang, R.

R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

Wang, X. H.

R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

Wang, Y. Q.

L. Li, Y. C. Xie, Y. Q. Wang, X. Y. Hu, Z. F. Feng, and B. Y. Cheng, "Absolute gap of two-dimensional fractal photonic structure," Chin. Phys. Lett. 20, 1767-1769 (2003).
[CrossRef]

Wang, Z.

Z. Wang and S. Fan, "Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines," Phys. Rev. E 68, 066616(1)-(4) (2003).
[CrossRef]

Winn, J. N.

J. N. Winn, R. D. Meade, and J. D. Joannopoulos, "Two-dimensional photonic band-gap materials," J. Mod. Opt. 41, 257-273 (1994).
[CrossRef]

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

Xie, Y. C.

L. Li, Y. C. Xie, Y. Q. Wang, X. Y. Hu, Z. F. Feng, and B. Y. Cheng, "Absolute gap of two-dimensional fractal photonic structure," Chin. Phys. Lett. 20, 1767-1769 (2003).
[CrossRef]

Xu, J. J.

Z. Liu, J. J. Xu, and Z. F. Lin, "Photonic band gaps in two-dimensional crystals with fractal structure," Chin. Phys. Lett. 20, 516-518 (2003).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yang, G. Z.

R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

Appl. Phys. B: Photophys. Laser Chem.

K. Sakoda, S. Kirihara, Y. Miyamoto, M. W. Takeda, and K. Honda, "Light scattering and transmission spectra of the Menger sponge fractal," Appl. Phys. B: Photophys. Laser Chem. 81, 321-324 (2005).
[CrossRef]

Appl. Phys. Lett.

M. Qiu and B. Jaskorzynska, "Design of a channel drop filter in a two-dimensional triangular photonic crystal," Appl. Phys. Lett. 83, 1074-1076 (2003).
[CrossRef]

Chin. Phys. Lett.

Z. Liu, J. J. Xu, and Z. F. Lin, "Photonic band gaps in two-dimensional crystals with fractal structure," Chin. Phys. Lett. 20, 516-518 (2003).
[CrossRef]

L. Li, Y. C. Xie, Y. Q. Wang, X. Y. Hu, Z. F. Feng, and B. Y. Cheng, "Absolute gap of two-dimensional fractal photonic structure," Chin. Phys. Lett. 20, 1767-1769 (2003).
[CrossRef]

J. Appl. Phys.

N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. 91, 3501-3510 (2002).
[CrossRef]

R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

J. Comput. Phys.

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

J. Mod. Opt.

J. N. Winn, R. D. Meade, and J. D. Joannopoulos, "Two-dimensional photonic band-gap materials," J. Mod. Opt. 41, 257-273 (1994).
[CrossRef]

R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295-310 (1994).
[CrossRef]

J. Opt. A

C. Lopez, "Three-dimensional photonic bandgap materials: semiconductors for light," J. Opt. A 8, R1-R14 (2006).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

W. Kuang, Z. Hou, Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A, Pure Appl. Opt. 7, 525-528 (2005).
[CrossRef]

J. Opt. Soc. Am. B

Nature (London)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature (London) 386, 143-149 (1997).
[CrossRef]

Opt. Express

Phys. Rev. B

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

Phys. Rev. E

Z. Wang and S. Fan, "Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines," Phys. Rev. E 68, 066616(1)-(4) (2003).
[CrossRef]

Phys. Rev. Lett.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).
[CrossRef]

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]

Other

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite Difference Time Domain Method, 3rd Ed. (Artech House, 2005).

FDTD software is available at http://ab-initio.mit.edu/meep, for example.

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

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Figures (6)

Fig. 1
Fig. 1

(a)–(c) Construction of Sierpinski gasket. (d) Three triangle basis and Brillouin zone for hexagonal lattice.

Fig. 2
Fig. 2

Band structure of three triangle basis with largest complete gap. Fractional area is 0.14. Complete gap of 6.1% is just above a frequency of 1.

Fig. 3
Fig. 3

(a) Dielectric and (b) air bands for TM polarization at M point. Z component of the E field is shown.

Fig. 4
Fig. 4

Gap map versus filling fraction for one cylinder in hexagonal lattice with a dielectric constant of 12.

Fig. 5
Fig. 5

Resonator modes for three dielectric cylinders in hex lattice with (a) two and (b) four rows of the crystal basis around the resonator.

Fig. 6
Fig. 6

Resonator Q versus the number of crystal basis cells around resonator for three dielectric cylinder Sierpinski basis and three air cylinders. Both are in hexagonal lattice.

Tables (2)

Tables Icon

Table 1 TE, TM, and Complete Bandgaps for Each of the Four Basis Types Considered a

Tables Icon

Table 2 Fraction of D Field Energy in Dielectric and Air Bands, with Indication Whether the Dielectric Band Energy is Greater or Less Then the Air Band Energy

Equations (7)

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

× E = 1 c B t ,
× H = 1 c D t ,
× E ( r ) = i ω c H ( r ) ,
× H ( r ) = i ω c ϵ ( r ) E ( r ) .
× ( 1 ϵ × H ( r ) ) = ( ω c ) 2 H ( r ) .
E f ( H ) = ( 1 2 ( H , H ) ) d r 1 ϵ ω c D 2 .
Q = ω 0 ( N 1 N 0 ) Δ t 2 ln ( H 1 H 0 ) ,

Metrics