Abstract

We present a new algorithm for calculation of the band structure of photonic crystal slabs. This algorithm combines the plane-wave expansion method with perfectly matched layers for the termination of the computational region in the direction out of the plane. In addition, the effective-medium tensor is applied to improve convergence. A general complex eigenvalue problem is then obtained. Two criteria are presented to distinguish the guided modes from the PML modes. As such, this scheme can accurately determine the band structure both above and below the light cone. The convergence of the algorithm presented has been studied. The results obtained by using this algorithm have been compared with those obtained by the finite-difference time-domain method and found to agree very well.

© 2004 Optical Society of America

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  1. H. Y. Ryu, H. G. Park, Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: Computational design, fabrication, and characterization,” IEEE J. Sel. Top. Quantum Electron. 8, 891–908 (2002).
    [CrossRef]
  2. R. Shimada, A. L. Yablonskii, S. G. Tikhodeev, T. Ishihara, “Transmission properties of a two-dimensional photonic crystal slab with an excitonic resonance,” IEEE J. Quantum Electron. 38, 872–879 (2002).
    [CrossRef]
  3. T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
    [CrossRef]
  4. A. Chutinan, S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
    [CrossRef]
  5. M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, S. Kawakami, “Si-based photonic crystals and photonic-bandgap waveguides,” IEICE Trans. Electron. E85-C, 1025–1032 (2002).
  6. H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
    [CrossRef]
  7. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
    [CrossRef]
  8. A. Scherer, O. Painter, J. Vuckovic, M. Loncar, T. Yoshie, “Photonic crystals for confining, guiding, and emitting light,” IEEE Trans. Nanotech. 1, 4–11 (2002).
    [CrossRef]
  9. M. Loncar, T. Doll, J. Vuckovic, A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
    [CrossRef]
  10. R. D. Meade, A. M. Rappe, K. M. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic bandgap materials,” Phys. Rev. B 48, 8434–8437 (1993).
    [CrossRef]
  11. K. M. Ho, C. T. Chan, C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
    [CrossRef] [PubMed]
  12. S. G. Johnson, J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane wave basis,” Opt. Express 8, 173–180 (2001).
    [CrossRef] [PubMed]
  13. S. G. Johnson, A. Mekis, J. Fan, J. D. Joannopoulos, “Molding the flow of light,” Comput. Sci. Eng. 3, 38–47 (2001).
    [CrossRef]
  14. L. F. Shen, S. L. He, L. Wu, “The application of effective-medium theory in the plane-wave expansion method for analyzing photonic crystals,” Acta Phys. Sin. 51, 1133–1138 (2002).
  15. C. T. Chan, Q. L. Yu, K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995).
    [CrossRef]
  16. S. S. Xiao, L. F. Shen, S. L. He, “A plane-wave expansion method based on the effective medium theory for calculating the band structure of a two-dimensional photonic crystal,” Phys. Lett. A 313, 132–138 (2003).
    [CrossRef]
  17. P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
    [CrossRef]
  18. M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58, 6791–6794 (1998).
    [CrossRef]
  19. M. Qiu, S. L. He, “A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,” J. Appl. Phys. 87, 8268–8275 (2000).
    [CrossRef]
  20. M. Qiu, S. L. He, “FDTD algorithm for computing the off-plane band structure in a two-dimensional photonic crystal with dielectric or metallic inclusions,” Phys. Lett. A 278, 348–354 (2001).
    [CrossRef]
  21. L. Wu, S. L. He, “Revised finite-difference time-domain algorithm in a nonorthogonal coordinate system and its application to the computation of the band structure of a photonic crystal,” J. Appl. Phys. 91, 6499–6506 (2002).
    [CrossRef]
  22. W. Axmann, P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic bandgap materials,” J. Comput. Phys. 150, 467–481 (1999).
    [CrossRef]
  23. D. C. Dobson, “An efficient method for band structure calculations in 2D photonic crystals,” J. Comput. Phys. 149, 363–376 (1999).
    [CrossRef]
  24. D. C. Dobson, J. Gopalakrishnan, J. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161, 668–679 (2000).
    [CrossRef]
  25. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  26. H. Rogier, D. D. Zutter, “Berenger and leaky modes in microstrip substrates terminated by a perfectly matched layer,” IEEE Trans. Microwave Theory Tech. 49, 712–715 (2001).
    [CrossRef]
  27. Q. Cao, P. Lalanne, J.-P. Hugonin, “Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides,” J. Opt. Soc. Am. A 19, 335–338 (2002).
    [CrossRef]
  28. T. Tischler, W. Heinrich, “The perfectly matched layer as lateral boundary in finite-difference transmission-line analysis,” IEEE Trans. Microwave Theory Tech. 48, 2249–2253 (2000).
    [CrossRef]
  29. H. Derudder, F. Olyslager, D. D. Zutter, S. V. D. Berghe, “Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers,” IEEE Trans. Antennas Propag. 49, 185–195 (2001).
    [CrossRef]
  30. Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
    [CrossRef]
  31. D. E. Aspnes, “Effective medium theory,” Am. J. Phys. 50, 704–709 (1982).
    [CrossRef]
  32. A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).
  33. Z. Y. Li, J. Wang, B. Y. Gu, “Creation of partial band gaps in anisotropic photonic-bandgap structures,” Phys. Rev. B 58, 3721–3729 (1998).
    [CrossRef]

2003 (1)

S. S. Xiao, L. F. Shen, S. L. He, “A plane-wave expansion method based on the effective medium theory for calculating the band structure of a two-dimensional photonic crystal,” Phys. Lett. A 313, 132–138 (2003).
[CrossRef]

2002 (9)

L. F. Shen, S. L. He, L. Wu, “The application of effective-medium theory in the plane-wave expansion method for analyzing photonic crystals,” Acta Phys. Sin. 51, 1133–1138 (2002).

M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, S. Kawakami, “Si-based photonic crystals and photonic-bandgap waveguides,” IEICE Trans. Electron. E85-C, 1025–1032 (2002).

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

H. Y. Ryu, H. G. Park, Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: Computational design, fabrication, and characterization,” IEEE J. Sel. Top. Quantum Electron. 8, 891–908 (2002).
[CrossRef]

R. Shimada, A. L. Yablonskii, S. G. Tikhodeev, T. Ishihara, “Transmission properties of a two-dimensional photonic crystal slab with an excitonic resonance,” IEEE J. Quantum Electron. 38, 872–879 (2002).
[CrossRef]

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, T. Yoshie, “Photonic crystals for confining, guiding, and emitting light,” IEEE Trans. Nanotech. 1, 4–11 (2002).
[CrossRef]

L. Wu, S. L. He, “Revised finite-difference time-domain algorithm in a nonorthogonal coordinate system and its application to the computation of the band structure of a photonic crystal,” J. Appl. Phys. 91, 6499–6506 (2002).
[CrossRef]

Q. Cao, P. Lalanne, J.-P. Hugonin, “Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides,” J. Opt. Soc. Am. A 19, 335–338 (2002).
[CrossRef]

2001 (5)

H. Derudder, F. Olyslager, D. D. Zutter, S. V. D. Berghe, “Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers,” IEEE Trans. Antennas Propag. 49, 185–195 (2001).
[CrossRef]

M. Qiu, S. L. He, “FDTD algorithm for computing the off-plane band structure in a two-dimensional photonic crystal with dielectric or metallic inclusions,” Phys. Lett. A 278, 348–354 (2001).
[CrossRef]

H. Rogier, D. D. Zutter, “Berenger and leaky modes in microstrip substrates terminated by a perfectly matched layer,” IEEE Trans. Microwave Theory Tech. 49, 712–715 (2001).
[CrossRef]

S. G. Johnson, J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane wave basis,” Opt. Express 8, 173–180 (2001).
[CrossRef] [PubMed]

S. G. Johnson, A. Mekis, J. Fan, J. D. Joannopoulos, “Molding the flow of light,” Comput. Sci. Eng. 3, 38–47 (2001).
[CrossRef]

2000 (5)

M. Loncar, T. Doll, J. Vuckovic, A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
[CrossRef]

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

D. C. Dobson, J. Gopalakrishnan, J. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161, 668–679 (2000).
[CrossRef]

M. Qiu, S. L. He, “A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,” J. Appl. Phys. 87, 8268–8275 (2000).
[CrossRef]

T. Tischler, W. Heinrich, “The perfectly matched layer as lateral boundary in finite-difference transmission-line analysis,” IEEE Trans. Microwave Theory Tech. 48, 2249–2253 (2000).
[CrossRef]

1999 (3)

W. Axmann, P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic bandgap materials,” J. Comput. Phys. 150, 467–481 (1999).
[CrossRef]

D. C. Dobson, “An efficient method for band structure calculations in 2D photonic crystals,” J. Comput. Phys. 149, 363–376 (1999).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

1998 (2)

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58, 6791–6794 (1998).
[CrossRef]

Z. Y. Li, J. Wang, B. Y. Gu, “Creation of partial band gaps in anisotropic photonic-bandgap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

1995 (3)

Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

C. T. Chan, Q. L. Yu, K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995).
[CrossRef]

P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

1994 (1)

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

1993 (1)

R. D. Meade, A. M. Rappe, K. M. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic bandgap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

1982 (1)

D. E. Aspnes, “Effective medium theory,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

Alerhand, O. L.

R. D. Meade, A. M. Rappe, K. M. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic bandgap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, “Effective medium theory,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

Axmann, W.

W. Axmann, P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic bandgap materials,” J. Comput. Phys. 150, 467–481 (1999).
[CrossRef]

Baba, T.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

Bell, P. M.

P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Berenger, J. P.

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

Berghe, S. V. D.

H. Derudder, F. Olyslager, D. D. Zutter, S. V. D. Berghe, “Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers,” IEEE Trans. Antennas Propag. 49, 185–195 (2001).
[CrossRef]

Biswas, R.

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58, 6791–6794 (1998).
[CrossRef]

Brommer, K. M.

R. D. Meade, A. M. Rappe, K. M. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic bandgap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Cao, Q.

Chan, C. T.

C. T. Chan, Q. L. Yu, K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

Chutinan, A.

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

Derudder, H.

H. Derudder, F. Olyslager, D. D. Zutter, S. V. D. Berghe, “Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers,” IEEE Trans. Antennas Propag. 49, 185–195 (2001).
[CrossRef]

Dobson, D. C.

D. C. Dobson, J. Gopalakrishnan, J. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161, 668–679 (2000).
[CrossRef]

D. C. Dobson, “An efficient method for band structure calculations in 2D photonic crystals,” J. Comput. Phys. 149, 363–376 (1999).
[CrossRef]

Doll, T.

Fan, J.

S. G. Johnson, A. Mekis, J. Fan, J. D. Joannopoulos, “Molding the flow of light,” Comput. Sci. Eng. 3, 38–47 (2001).
[CrossRef]

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Fukaya, N.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

Gopalakrishnan, J.

D. C. Dobson, J. Gopalakrishnan, J. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161, 668–679 (2000).
[CrossRef]

Gu, B. Y.

Z. Y. Li, J. Wang, B. Y. Gu, “Creation of partial band gaps in anisotropic photonic-bandgap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

Hagness, S. C.

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

He, S. L.

S. S. Xiao, L. F. Shen, S. L. He, “A plane-wave expansion method based on the effective medium theory for calculating the band structure of a two-dimensional photonic crystal,” Phys. Lett. A 313, 132–138 (2003).
[CrossRef]

L. F. Shen, S. L. He, L. Wu, “The application of effective-medium theory in the plane-wave expansion method for analyzing photonic crystals,” Acta Phys. Sin. 51, 1133–1138 (2002).

L. Wu, S. L. He, “Revised finite-difference time-domain algorithm in a nonorthogonal coordinate system and its application to the computation of the band structure of a photonic crystal,” J. Appl. Phys. 91, 6499–6506 (2002).
[CrossRef]

M. Qiu, S. L. He, “FDTD algorithm for computing the off-plane band structure in a two-dimensional photonic crystal with dielectric or metallic inclusions,” Phys. Lett. A 278, 348–354 (2001).
[CrossRef]

M. Qiu, S. L. He, “A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,” J. Appl. Phys. 87, 8268–8275 (2000).
[CrossRef]

Heinrich, W.

T. Tischler, W. Heinrich, “The perfectly matched layer as lateral boundary in finite-difference transmission-line analysis,” IEEE Trans. Microwave Theory Tech. 48, 2249–2253 (2000).
[CrossRef]

Ho, K. M.

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58, 6791–6794 (1998).
[CrossRef]

C. T. Chan, Q. L. Yu, K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

Hugonin, J.-P.

Huh, J.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Hwang, J. K.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Ishihara, T.

R. Shimada, A. L. Yablonskii, S. G. Tikhodeev, T. Ishihara, “Transmission properties of a two-dimensional photonic crystal slab with an excitonic resonance,” IEEE J. Quantum Electron. 38, 872–879 (2002).
[CrossRef]

Iwai, T.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson, A. Mekis, J. Fan, J. D. Joannopoulos, “Molding the flow of light,” Comput. Sci. Eng. 3, 38–47 (2001).
[CrossRef]

S. G. Johnson, J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane wave basis,” Opt. Express 8, 173–180 (2001).
[CrossRef] [PubMed]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

R. D. Meade, A. M. Rappe, K. M. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic bandgap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Johnson, S. G.

S. G. Johnson, A. Mekis, J. Fan, J. D. Joannopoulos, “Molding the flow of light,” Comput. Sci. Eng. 3, 38–47 (2001).
[CrossRef]

S. G. Johnson, J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane wave basis,” Opt. Express 8, 173–180 (2001).
[CrossRef] [PubMed]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Kawakami, S.

M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, S. Kawakami, “Si-based photonic crystals and photonic-bandgap waveguides,” IEICE Trans. Electron. E85-C, 1025–1032 (2002).

Kawashima, T.

M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, S. Kawakami, “Si-based photonic crystals and photonic-bandgap waveguides,” IEICE Trans. Electron. E85-C, 1025–1032 (2002).

Kim, J. S.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Kim, S. H.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Kingsland, D. M.

Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

Kuchment, P.

W. Axmann, P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic bandgap materials,” J. Comput. Phys. 150, 467–481 (1999).
[CrossRef]

Kuramochi, E.

M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, S. Kawakami, “Si-based photonic crystals and photonic-bandgap waveguides,” IEICE Trans. Electron. E85-C, 1025–1032 (2002).

Lalanne, P.

Lee, J.

Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

Lee, R.

Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

Lee, Y. H.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

H. Y. Ryu, H. G. Park, Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: Computational design, fabrication, and characterization,” IEEE J. Sel. Top. Quantum Electron. 8, 891–908 (2002).
[CrossRef]

Li, Z. Y.

Z. Y. Li, J. Wang, B. Y. Gu, “Creation of partial band gaps in anisotropic photonic-bandgap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

Loncar, M.

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, T. Yoshie, “Photonic crystals for confining, guiding, and emitting light,” IEEE Trans. Nanotech. 1, 4–11 (2002).
[CrossRef]

M. Loncar, T. Doll, J. Vuckovic, A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
[CrossRef]

Meade, R. D.

R. D. Meade, A. M. Rappe, K. M. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic bandgap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Mekis, A.

S. G. Johnson, A. Mekis, J. Fan, J. D. Joannopoulos, “Molding the flow of light,” Comput. Sci. Eng. 3, 38–47 (2001).
[CrossRef]

Moreno, L. M.

P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Motegi, A.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

Noda, S.

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

Notomi, M.

M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, S. Kawakami, “Si-based photonic crystals and photonic-bandgap waveguides,” IEICE Trans. Electron. E85-C, 1025–1032 (2002).

Olyslager, F.

H. Derudder, F. Olyslager, D. D. Zutter, S. V. D. Berghe, “Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers,” IEEE Trans. Antennas Propag. 49, 185–195 (2001).
[CrossRef]

Painter, O.

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, T. Yoshie, “Photonic crystals for confining, guiding, and emitting light,” IEEE Trans. Nanotech. 1, 4–11 (2002).
[CrossRef]

Park, H. G.

H. Y. Ryu, H. G. Park, Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: Computational design, fabrication, and characterization,” IEEE J. Sel. Top. Quantum Electron. 8, 891–908 (2002).
[CrossRef]

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Pasciak, J.

D. C. Dobson, J. Gopalakrishnan, J. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161, 668–679 (2000).
[CrossRef]

Pendry, J. B.

P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Qiu, M.

M. Qiu, S. L. He, “FDTD algorithm for computing the off-plane band structure in a two-dimensional photonic crystal with dielectric or metallic inclusions,” Phys. Lett. A 278, 348–354 (2001).
[CrossRef]

M. Qiu, S. L. He, “A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,” J. Appl. Phys. 87, 8268–8275 (2000).
[CrossRef]

Rappe, A. M.

R. D. Meade, A. M. Rappe, K. M. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic bandgap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Rogier, H.

H. Rogier, D. D. Zutter, “Berenger and leaky modes in microstrip substrates terminated by a perfectly matched layer,” IEEE Trans. Microwave Theory Tech. 49, 712–715 (2001).
[CrossRef]

Ryu, H. Y.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

H. Y. Ryu, H. G. Park, Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: Computational design, fabrication, and characterization,” IEEE J. Sel. Top. Quantum Electron. 8, 891–908 (2002).
[CrossRef]

Sacks, Z. S.

Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

Sakai, A.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

Scherer, A.

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, T. Yoshie, “Photonic crystals for confining, guiding, and emitting light,” IEEE Trans. Nanotech. 1, 4–11 (2002).
[CrossRef]

M. Loncar, T. Doll, J. Vuckovic, A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
[CrossRef]

Shen, L. F.

S. S. Xiao, L. F. Shen, S. L. He, “A plane-wave expansion method based on the effective medium theory for calculating the band structure of a two-dimensional photonic crystal,” Phys. Lett. A 313, 132–138 (2003).
[CrossRef]

L. F. Shen, S. L. He, L. Wu, “The application of effective-medium theory in the plane-wave expansion method for analyzing photonic crystals,” Acta Phys. Sin. 51, 1133–1138 (2002).

Shimada, R.

R. Shimada, A. L. Yablonskii, S. G. Tikhodeev, T. Ishihara, “Transmission properties of a two-dimensional photonic crystal slab with an excitonic resonance,” IEEE J. Quantum Electron. 38, 872–879 (2002).
[CrossRef]

Shinya, A.

M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, S. Kawakami, “Si-based photonic crystals and photonic-bandgap waveguides,” IEICE Trans. Electron. E85-C, 1025–1032 (2002).

Sigalas, M. M.

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58, 6791–6794 (1998).
[CrossRef]

Soukoulis, C. M.

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58, 6791–6794 (1998).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

Takahashi, C.

M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, S. Kawakami, “Si-based photonic crystals and photonic-bandgap waveguides,” IEICE Trans. Electron. E85-C, 1025–1032 (2002).

Takahashi, J.

M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, S. Kawakami, “Si-based photonic crystals and photonic-bandgap waveguides,” IEICE Trans. Electron. E85-C, 1025–1032 (2002).

Tikhodeev, S. G.

R. Shimada, A. L. Yablonskii, S. G. Tikhodeev, T. Ishihara, “Transmission properties of a two-dimensional photonic crystal slab with an excitonic resonance,” IEEE J. Quantum Electron. 38, 872–879 (2002).
[CrossRef]

Tischler, T.

T. Tischler, W. Heinrich, “The perfectly matched layer as lateral boundary in finite-difference transmission-line analysis,” IEEE Trans. Microwave Theory Tech. 48, 2249–2253 (2000).
[CrossRef]

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Vuckovic, J.

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, T. Yoshie, “Photonic crystals for confining, guiding, and emitting light,” IEEE Trans. Nanotech. 1, 4–11 (2002).
[CrossRef]

M. Loncar, T. Doll, J. Vuckovic, A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
[CrossRef]

Wang, J.

Z. Y. Li, J. Wang, B. Y. Gu, “Creation of partial band gaps in anisotropic photonic-bandgap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

Ward, A. J.

P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Watanabe, Y.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

Wu, L.

L. F. Shen, S. L. He, L. Wu, “The application of effective-medium theory in the plane-wave expansion method for analyzing photonic crystals,” Acta Phys. Sin. 51, 1133–1138 (2002).

L. Wu, S. L. He, “Revised finite-difference time-domain algorithm in a nonorthogonal coordinate system and its application to the computation of the band structure of a photonic crystal,” J. Appl. Phys. 91, 6499–6506 (2002).
[CrossRef]

Xiao, S. S.

S. S. Xiao, L. F. Shen, S. L. He, “A plane-wave expansion method based on the effective medium theory for calculating the band structure of a two-dimensional photonic crystal,” Phys. Lett. A 313, 132–138 (2003).
[CrossRef]

Yablonskii, A. L.

R. Shimada, A. L. Yablonskii, S. G. Tikhodeev, T. Ishihara, “Transmission properties of a two-dimensional photonic crystal slab with an excitonic resonance,” IEEE J. Quantum Electron. 38, 872–879 (2002).
[CrossRef]

Yamada, K.

M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, S. Kawakami, “Si-based photonic crystals and photonic-bandgap waveguides,” IEICE Trans. Electron. E85-C, 1025–1032 (2002).

Yokohama, I.

M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, S. Kawakami, “Si-based photonic crystals and photonic-bandgap waveguides,” IEICE Trans. Electron. E85-C, 1025–1032 (2002).

Yoshie, T.

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, T. Yoshie, “Photonic crystals for confining, guiding, and emitting light,” IEEE Trans. Nanotech. 1, 4–11 (2002).
[CrossRef]

Yu, Q. L.

C. T. Chan, Q. L. Yu, K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995).
[CrossRef]

Zutter, D. D.

H. Rogier, D. D. Zutter, “Berenger and leaky modes in microstrip substrates terminated by a perfectly matched layer,” IEEE Trans. Microwave Theory Tech. 49, 712–715 (2001).
[CrossRef]

H. Derudder, F. Olyslager, D. D. Zutter, S. V. D. Berghe, “Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers,” IEEE Trans. Antennas Propag. 49, 185–195 (2001).
[CrossRef]

Acta Phys. Sin. (1)

L. F. Shen, S. L. He, L. Wu, “The application of effective-medium theory in the plane-wave expansion method for analyzing photonic crystals,” Acta Phys. Sin. 51, 1133–1138 (2002).

Am. J. Phys. (1)

D. E. Aspnes, “Effective medium theory,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

Comput. Phys. Commun. (1)

P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Comput. Sci. Eng. (1)

S. G. Johnson, A. Mekis, J. Fan, J. D. Joannopoulos, “Molding the flow of light,” Comput. Sci. Eng. 3, 38–47 (2001).
[CrossRef]

IEEE J. Quantum Electron. (3)

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

R. Shimada, A. L. Yablonskii, S. G. Tikhodeev, T. Ishihara, “Transmission properties of a two-dimensional photonic crystal slab with an excitonic resonance,” IEEE J. Quantum Electron. 38, 872–879 (2002).
[CrossRef]

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. Y. Ryu, H. G. Park, Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: Computational design, fabrication, and characterization,” IEEE J. Sel. Top. Quantum Electron. 8, 891–908 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

H. Derudder, F. Olyslager, D. D. Zutter, S. V. D. Berghe, “Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers,” IEEE Trans. Antennas Propag. 49, 185–195 (2001).
[CrossRef]

Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

T. Tischler, W. Heinrich, “The perfectly matched layer as lateral boundary in finite-difference transmission-line analysis,” IEEE Trans. Microwave Theory Tech. 48, 2249–2253 (2000).
[CrossRef]

H. Rogier, D. D. Zutter, “Berenger and leaky modes in microstrip substrates terminated by a perfectly matched layer,” IEEE Trans. Microwave Theory Tech. 49, 712–715 (2001).
[CrossRef]

IEEE Trans. Nanotech. (1)

A. Scherer, O. Painter, J. Vuckovic, M. Loncar, T. Yoshie, “Photonic crystals for confining, guiding, and emitting light,” IEEE Trans. Nanotech. 1, 4–11 (2002).
[CrossRef]

IEICE Trans. Electron. (1)

M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, S. Kawakami, “Si-based photonic crystals and photonic-bandgap waveguides,” IEICE Trans. Electron. E85-C, 1025–1032 (2002).

J. Appl. Phys. (2)

M. Qiu, S. L. He, “A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,” J. Appl. Phys. 87, 8268–8275 (2000).
[CrossRef]

L. Wu, S. L. He, “Revised finite-difference time-domain algorithm in a nonorthogonal coordinate system and its application to the computation of the band structure of a photonic crystal,” J. Appl. Phys. 91, 6499–6506 (2002).
[CrossRef]

J. Comput. Phys. (4)

W. Axmann, P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic bandgap materials,” J. Comput. Phys. 150, 467–481 (1999).
[CrossRef]

D. C. Dobson, “An efficient method for band structure calculations in 2D photonic crystals,” J. Comput. Phys. 149, 363–376 (1999).
[CrossRef]

D. C. Dobson, J. Gopalakrishnan, J. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161, 668–679 (2000).
[CrossRef]

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

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Phys. Lett. A (2)

M. Qiu, S. L. He, “FDTD algorithm for computing the off-plane band structure in a two-dimensional photonic crystal with dielectric or metallic inclusions,” Phys. Lett. A 278, 348–354 (2001).
[CrossRef]

S. S. Xiao, L. F. Shen, S. L. He, “A plane-wave expansion method based on the effective medium theory for calculating the band structure of a two-dimensional photonic crystal,” Phys. Lett. A 313, 132–138 (2003).
[CrossRef]

Phys. Rev. B (6)

Z. Y. Li, J. Wang, B. Y. Gu, “Creation of partial band gaps in anisotropic photonic-bandgap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, “Theoretical investigation of off-plane propagation of electromagnetic waves in two-dimensional photonic crystals,” Phys. Rev. B 58, 6791–6794 (1998).
[CrossRef]

C. T. Chan, Q. L. Yu, K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995).
[CrossRef]

R. D. Meade, A. M. Rappe, K. M. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic bandgap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

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

Phys. Rev. Lett. (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

Other (1)

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

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