Abstract

We report and analyze hybridization of s-state and p-state modes in photonic crystal one-dimensional defect cavity array. When embedding a nano-strip into a dielectric rod photonic crystal, an effective cavity array is made, where each cavity possesses two cavity modes: s-state and p-state. The two modes are laterally even versus the nano-strip direction, and interact with each other, producing defect bands, of which the group velocity becomes zero within the first Brillouin zone. We could model and describe the phenomena by using the tight-binding method, well agreeing with the plane-wave expansion method analysis. We note that the reported s- and p-state mode interaction corresponds to the hybridization of atomic orbital in solid-state physics. The concept of multiple period s-p hybridization and the proposed model can be useful for analyzing and developing novel photonic crystal waveguides and devices.

© 2005 Optical Society of America

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  1. A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
    [Crossref]
  2. S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
    [Crossref]
  3. N. Stefanou and A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
    [Crossref]
  4. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
    [Crossref]
  5. Y. Xu, R. K. Lee, and A. Yariv, “Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387–400 (2000).
    [Crossref]
  6. E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, “Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures,” IEEE J. Quantum Electron. 38, 837–843 (2002).
    [Crossref]
  7. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large groupvelocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
    [Crossref] [PubMed]
  8. M. Lončar, J. Vučković, and A. Scherer, “Methods for controlling positions of guided modes of photoniccrystal waveguides,” J. Opt. Soc. Am. B 18, 1362–1368 (2001).
    [Crossref]
  9. D. Mori and T. Baba, “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
    [Crossref]
  10. A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
    [Crossref]
  11. L. Brillouin, Wave Propagation in Periodic Structures2nd ed. (Dover Publications, New York, 1953).
  12. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, Philadelphia, 1976).
  13. E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parametrization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
    [Crossref]
  14. J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
    [Crossref]
  15. D. Leuenberger, R. Ferrini, and R. Houdré, “An initio tight-binding approach to photonic-crystal based coupled cavity waveguides,” J. Appl. Phys. 95, 806–809 (2004).
    [Crossref]
  16. V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60, 5359–5365 (1999).
    [Crossref]
  17. V. Yannopapas, A. Modinos, and N. Stefanou, “Waveguides of defect chains in photonic crystals,” Phys. Rev. B 65, 235201 (2002).
    [Crossref]
  18. W. A. Harrison, Electronic Structure and the Properties of Solids (Freeman, San Francisco, 1980).
  19. S. T. Pantelides and W. A. Harrison, “Structure of the valence bands of zinc-blende-type semiconductors,” Phys. Rev. B 11, 3006–3021 (1975).
    [Crossref]
  20. W. T. Lau and S. Fan, “Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs,” Appl. Phys. Lett. 81, 3915–3917 (2002).
    [Crossref]
  21. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, New York, 2001).
  22. The PWE simulations were carried out with BandSOLVE commercial software by RSoft Design Group.
  23. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, 1995).
  24. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991).
    [Crossref]
  25. S. Akiba, M. Usami, and K. Utaka, “1.5-µm λ/4-shifted InGaAsP/InP DFB lasers,” J. Lightwave Technol. LT-5, 1564–1573 (1987).
    [Crossref]
  26. X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
    [Crossref]

2004 (4)

D. Mori and T. Baba, “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
[Crossref]

A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[Crossref]

D. Leuenberger, R. Ferrini, and R. Houdré, “An initio tight-binding approach to photonic-crystal based coupled cavity waveguides,” J. Appl. Phys. 95, 806–809 (2004).
[Crossref]

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

2002 (3)

W. T. Lau and S. Fan, “Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs,” Appl. Phys. Lett. 81, 3915–3917 (2002).
[Crossref]

V. Yannopapas, A. Modinos, and N. Stefanou, “Waveguides of defect chains in photonic crystals,” Phys. Rev. B 65, 235201 (2002).
[Crossref]

E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, “Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures,” IEEE J. Quantum Electron. 38, 837–843 (2002).
[Crossref]

2001 (2)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large groupvelocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

M. Lončar, J. Vučković, and A. Scherer, “Methods for controlling positions of guided modes of photoniccrystal waveguides,” J. Opt. Soc. Am. B 18, 1362–1368 (2001).
[Crossref]

2000 (4)

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[Crossref]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

Y. Xu, R. K. Lee, and A. Yariv, “Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387–400 (2000).
[Crossref]

J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
[Crossref]

1999 (2)

V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60, 5359–5365 (1999).
[Crossref]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[Crossref]

1998 (2)

N. Stefanou and A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[Crossref]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parametrization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[Crossref]

1987 (1)

S. Akiba, M. Usami, and K. Utaka, “1.5-µm λ/4-shifted InGaAsP/InP DFB lasers,” J. Lightwave Technol. LT-5, 1564–1573 (1987).
[Crossref]

1975 (1)

S. T. Pantelides and W. A. Harrison, “Structure of the valence bands of zinc-blende-type semiconductors,” Phys. Rev. B 11, 3006–3021 (1975).
[Crossref]

Akiba, S.

S. Akiba, M. Usami, and K. Utaka, “1.5-µm λ/4-shifted InGaAsP/InP DFB lasers,” J. Lightwave Technol. LT-5, 1564–1573 (1987).
[Crossref]

Albert, J. P.

J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
[Crossref]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, Philadelphia, 1976).

Baba, T.

D. Mori and T. Baba, “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
[Crossref]

Bayindir, M.

E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, “Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures,” IEEE J. Quantum Electron. 38, 837–843 (2002).
[Crossref]

Bertho, D.

J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
[Crossref]

Bonnefont, S.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Boucaud, P.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Brillouin, L.

L. Brillouin, Wave Propagation in Periodic Structures2nd ed. (Dover Publications, New York, 1953).

Bulu, I.

E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, “Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures,” IEEE J. Quantum Electron. 38, 837–843 (2002).
[Crossref]

Cassagne, D.

J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
[Crossref]

Checoury, X.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Chutinan, A.

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[Crossref]

Cubukcu, E.

E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, “Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures,” IEEE J. Quantum Electron. 38, 837–843 (2002).
[Crossref]

Cuisin, C.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Derouin, E.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Drisse, O.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Duan, G. H.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Economou, E. N.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parametrization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[Crossref]

Eich, M.

A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[Crossref]

Fan, S.

W. T. Lau and S. Fan, “Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs,” Appl. Phys. Lett. 81, 3915–3917 (2002).
[Crossref]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

Ferrini, R.

D. Leuenberger, R. Ferrini, and R. Houdré, “An initio tight-binding approach to photonic-crystal based coupled cavity waveguides,” J. Appl. Phys. 95, 806–809 (2004).
[Crossref]

Gauthier-Lafaye, O.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Harrison, W. A.

S. T. Pantelides and W. A. Harrison, “Structure of the valence bands of zinc-blende-type semiconductors,” Phys. Rev. B 11, 3006–3021 (1975).
[Crossref]

W. A. Harrison, Electronic Structure and the Properties of Solids (Freeman, San Francisco, 1980).

Houdré, R.

D. Leuenberger, R. Ferrini, and R. Houdré, “An initio tight-binding approach to photonic-crystal based coupled cavity waveguides,” J. Appl. Phys. 95, 806–809 (2004).
[Crossref]

Joannopoulos, J. D.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

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

Johnson, S. G.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

Jouanin, C.

J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
[Crossref]

Lau, W. T.

W. T. Lau and S. Fan, “Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs,” Appl. Phys. Lett. 81, 3915–3917 (2002).
[Crossref]

Lee, R. K.

Legouezigou, L.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Lelarge, F.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Leuenberger, D.

D. Leuenberger, R. Ferrini, and R. Houdré, “An initio tight-binding approach to photonic-crystal based coupled cavity waveguides,” J. Appl. Phys. 95, 806–809 (2004).
[Crossref]

Lidorikis, E.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parametrization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[Crossref]

Loncar, M.

Lourtioz, J-M.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Lozes, F.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Meade, R. D.

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

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, Philadelphia, 1976).

Modinos, A.

V. Yannopapas, A. Modinos, and N. Stefanou, “Waveguides of defect chains in photonic crystals,” Phys. Rev. B 65, 235201 (2002).
[Crossref]

V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60, 5359–5365 (1999).
[Crossref]

N. Stefanou and A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[Crossref]

Mori, D.

D. Mori and T. Baba, “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
[Crossref]

Mulin, D.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Noda, S.

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[Crossref]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large groupvelocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Ozbay, E.

E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, “Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures,” IEEE J. Quantum Electron. 38, 837–843 (2002).
[Crossref]

Pantelides, S. T.

S. T. Pantelides and W. A. Harrison, “Structure of the valence bands of zinc-blende-type semiconductors,” Phys. Rev. B 11, 3006–3021 (1975).
[Crossref]

Petrov, A. Y.

A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[Crossref]

Poingt, F.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Pommereau, F.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, New York, 2001).

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991).
[Crossref]

Scherer, A.

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large groupvelocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Sigalas, M. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parametrization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[Crossref]

Soukoulis, C. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parametrization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[Crossref]

Stefanou, N.

V. Yannopapas, A. Modinos, and N. Stefanou, “Waveguides of defect chains in photonic crystals,” Phys. Rev. B 65, 235201 (2002).
[Crossref]

V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60, 5359–5365 (1999).
[Crossref]

N. Stefanou and A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[Crossref]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large groupvelocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large groupvelocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Talneau, A.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991).
[Crossref]

Usami, M.

S. Akiba, M. Usami, and K. Utaka, “1.5-µm λ/4-shifted InGaAsP/InP DFB lasers,” J. Lightwave Technol. LT-5, 1564–1573 (1987).
[Crossref]

Utaka, K.

S. Akiba, M. Usami, and K. Utaka, “1.5-µm λ/4-shifted InGaAsP/InP DFB lasers,” J. Lightwave Technol. LT-5, 1564–1573 (1987).
[Crossref]

Valentin, J.

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

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S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

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Winn, J. N.

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

Xu, Y.

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large groupvelocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Yannopapas, V.

V. Yannopapas, A. Modinos, and N. Stefanou, “Waveguides of defect chains in photonic crystals,” Phys. Rev. B 65, 235201 (2002).
[Crossref]

V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60, 5359–5365 (1999).
[Crossref]

Yariv, A.

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large groupvelocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

D. Mori and T. Baba, “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
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W. T. Lau and S. Fan, “Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs,” Appl. Phys. Lett. 81, 3915–3917 (2002).
[Crossref]

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 µm,” Appl. Phys. Lett. 85, 5502–5504(2004).
[Crossref]

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E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, “Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures,” IEEE J. Quantum Electron. 38, 837–843 (2002).
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D. Leuenberger, R. Ferrini, and R. Houdré, “An initio tight-binding approach to photonic-crystal based coupled cavity waveguides,” J. Appl. Phys. 95, 806–809 (2004).
[Crossref]

J. Lightwave Technol. (1)

S. Akiba, M. Usami, and K. Utaka, “1.5-µm λ/4-shifted InGaAsP/InP DFB lasers,” J. Lightwave Technol. LT-5, 1564–1573 (1987).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Lett. (1)

Phys. Rev. B (7)

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[Crossref]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

N. Stefanou and A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[Crossref]

S. T. Pantelides and W. A. Harrison, “Structure of the valence bands of zinc-blende-type semiconductors,” Phys. Rev. B 11, 3006–3021 (1975).
[Crossref]

J. P. Albert, C. Jouanin, D. Cassagne, and D. Bertho, “Generalized Wannier function method for photonic crystals,” Phys. Rev. B 61, 4381–4384 (2000).
[Crossref]

V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60, 5359–5365 (1999).
[Crossref]

V. Yannopapas, A. Modinos, and N. Stefanou, “Waveguides of defect chains in photonic crystals,” Phys. Rev. B 65, 235201 (2002).
[Crossref]

Phys. Rev. Lett. (2)

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parametrization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[Crossref]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large groupvelocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Other (7)

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, New York, 2001).

The PWE simulations were carried out with BandSOLVE commercial software by RSoft Design Group.

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

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991).
[Crossref]

W. A. Harrison, Electronic Structure and the Properties of Solids (Freeman, San Francisco, 1980).

L. Brillouin, Wave Propagation in Periodic Structures2nd ed. (Dover Publications, New York, 1953).

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, Philadelphia, 1976).

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Figures (7)

Fig. 1.
Fig. 1.

Two-dimensional NEPC: (a) dielectric rod photonic crystal with nano-strip embedding, (b) projected band diagram, red and blue lines: NEPC defect bands, (c) conceptual interpretation of NEPC: one-dimensional defect cavity array.

Fig. 2.
Fig. 2.

Effective defect cavity of NEPC: (a) elementary effective defect cavity, (b) s-state cavity mode field distribution, (c) p-state cavity mode field distribution.

Fig. 3.
Fig. 3.

Multiple period s-p hybridization in NEPC: solid lines; PWE results, circles; tight-binding model results for (a) nearest neighbor interaction only, (b) up to third-nearest neighbor interactions, (c) up to fourth-nearest neighbor interactions.

Fig. 4.
Fig. 4.

Mode profiles for (a) k=0 (amplitude), (b) k=0.25 (intensity), (c) k=0.4 (intensity), (d) k=0.5 (amplitude), left side; tight-binding model, right side; PWE analysis, upper side; upper band mode, lower side; lower band mode.

Fig. 5.
Fig. 5.

Relative amplitudes of the s-state (solid line) and p-state (dashed line) cavity modes for (a) lower defect band, (b) upper defect band.

Fig. 6.
Fig. 6.

Effective cavity fitting for tight-binding model convergence to the PWE method: blue line; PWE method, red dashed line; tight-binding method (nano-strip with length of a), red crosses; tight-binding method (nano-strip with increased length of 1.2a), red circles; tight-binding method (nano-strip with increased length of 1.2a and increased refractive index of 3.9).

Fig. 7.
Fig. 7.

Mode field profile comparison for (a) k=0 (amplitude), (b) k=0.32 (intensity), (c) k=0.5 (amplitude), left side; tight-binding model, right side; the PWE method.

Equations (11)

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E k ( r , t ) = exp ( i ω k t ) n exp ( i n k a ) l A l E Ω l ( r n a e ̂ z ) .
× × E k = ε ( r ) ω k 2 c 2 E k
d r ε o ( r ) E Ω l ( r ) · E Ω m ( r ) = δ l , m ,
l A l Ω l 2 [ δ m , l + n 0 exp ( i n k a ) β m , l n ] = ω k 2 l A l [ δ m , l + Δ α m , l + n 0 exp ( i n k a ) α m , l n ]
α m , l n = d r ε ( r ) E Ω m ( r ) · E Ω l ( r n a e ̂ z ) ,
β m , l n = d r ε o ( r n a e ̂ z ) E Ω m ( r ) · E Ω l ( r n a e ̂ z ) ,
Δ α m , l = d r [ ε ( r ) ε o ( r ) ] E Ω m ( r ) · E Ω l ( r ) .
A m [ ω k 2 { 1 + Δ α m , m + n 0 2 α m , m n cos ( n k a ) } + Ω m 2 { 1 + n 0 2 β m , m n cos ( n k a ) } ]
i A l [ ω k 2 n 0 2 α m , l n sin ( n k a ) + Ω l 2 n 0 2 β m , l n sin ( n k a ) ] = 0 ,
κ m , l n = β m , l n α m , l n
= d r [ ε o ( r n a e ̂ z ) ε ( r n a e ̂ z ) ] E Ω m ( r ) · E Ω l ( r n a e ̂ z )

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