Abstract

The performance of the perfectly matched layer absorption boundary condition is fully exploited when it is applied to the planewave based transfer-scattering matrix method in photonic crystal device simulation. The mode profile of one dimensional dielectric waveguide and the optical properties of sub-wavelength aluminum grating with semi-infinite substrate are studied to illustrate the accuracy and power of this approach.

© 2008 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 (1987).
    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  3. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, 1995).
  4. S. P. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227 (2004).
  5. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819 (1999).
    [CrossRef] [PubMed]
  6. E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
    [PubMed]
  7. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech Houses, 2000).
  8. J. Jin, The Finite Element Method in Electromagnetics (Wiley and Sons, 2002).
  9. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys Rev. Lett. 65, 3125 (1990).
    [CrossRef] [PubMed]
  10. J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 41, 209 (1994).
    [CrossRef]
  11. Z. Y. Li and K. M. Ho, “Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides,” Phys. Rev. B 68, 245117 (2003).
  12. Z. Y. Li and K. M. Ho, “Bloch mode reflection and lasing threshold in semiconductor nanowire laser arrays,” Phys. Rev. B 71, 045315 (2005).
  13. M. Li, Z. Y. Li, K. M. Ho, J. R. Cao, and M. Miyawaki, “High-efficiency calculations for three-dimensional photonic crystal cavities,” Opt. Lett. 31, 262 (2006).
    [PubMed]
  14. M. Li, X. Hu, Z. Ye, K. M. Ho, J. R. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. 31, 3498 (2006).
    [CrossRef] [PubMed]
  15. Z. Ye, X. Hu, M. Li, and K. M. Ho, “Propagation of guided modes in curved nanoribbon waveguides,” Appl. Phys. Lett. 89, 241108 (2006).
    [CrossRef]
  16. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Computational Physics, 114, 185 (1994).
    [CrossRef]
  17. J.P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Computational Physics, 127, 363, (1996)
    [CrossRef]
  18. Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas and Propagation 43, 1460 (1995).
    [CrossRef]
  19. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas and Propagation 44, 1630 (1996).
    [CrossRef]
  20. A. Yariv and P. Yeh, Optical Waves in Crystal, (Wiley, 1984).
  21. X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, “Diamagnetic response of metallic photonic crystals at infrared and visible Frequencies,” Phys. Rev. Lett. 96, 223901 (2006).
    [CrossRef] [PubMed]
  22. S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).

2006 (5)

M. Li, Z. Y. Li, K. M. Ho, J. R. Cao, and M. Miyawaki, “High-efficiency calculations for three-dimensional photonic crystal cavities,” Opt. Lett. 31, 262 (2006).
[PubMed]

M. Li, X. Hu, Z. Ye, K. M. Ho, J. R. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. 31, 3498 (2006).
[CrossRef] [PubMed]

Z. Ye, X. Hu, M. Li, and K. M. Ho, “Propagation of guided modes in curved nanoribbon waveguides,” Appl. Phys. Lett. 89, 241108 (2006).
[CrossRef]

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, “Diamagnetic response of metallic photonic crystals at infrared and visible Frequencies,” Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).

2005 (1)

Z. Y. Li and K. M. Ho, “Bloch mode reflection and lasing threshold in semiconductor nanowire laser arrays,” Phys. Rev. B 71, 045315 (2005).

2004 (1)

S. P. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227 (2004).

2003 (1)

Z. Y. Li and K. M. Ho, “Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides,” Phys. Rev. B 68, 245117 (2003).

2002 (1)

J. Jin, The Finite Element Method in Electromagnetics (Wiley and Sons, 2002).

2000 (1)

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
[PubMed]

1999 (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819 (1999).
[CrossRef] [PubMed]

1996 (2)

J.P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Computational Physics, 127, 363, (1996)
[CrossRef]

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas and Propagation 44, 1630 (1996).
[CrossRef]

1995 (1)

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

1994 (2)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Computational Physics, 114, 185 (1994).
[CrossRef]

J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 41, 209 (1994).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys Rev. Lett. 65, 3125 (1990).
[CrossRef] [PubMed]

1987 (2)

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

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

Alleman, A.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
[PubMed]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Computational Physics, 114, 185 (1994).
[CrossRef]

Berenger, J.P.

J.P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Computational Physics, 127, 363, (1996)
[CrossRef]

Cao, J. R.

M. Li, Z. Y. Li, K. M. Ho, J. R. Cao, and M. Miyawaki, “High-efficiency calculations for three-dimensional photonic crystal cavities,” Opt. Lett. 31, 262 (2006).
[PubMed]

M. Li, X. Hu, Z. Ye, K. M. Ho, J. R. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. 31, 3498 (2006).
[CrossRef] [PubMed]

Chan, C. T.

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, “Diamagnetic response of metallic photonic crystals at infrared and visible Frequencies,” Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys Rev. Lett. 65, 3125 (1990).
[CrossRef] [PubMed]

Chow, E.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
[PubMed]

Cummer, S. A.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819 (1999).
[CrossRef] [PubMed]

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas and Propagation 44, 1630 (1996).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech Houses, 2000).

Ho, K. M.

M. Li, Z. Y. Li, K. M. Ho, J. R. Cao, and M. Miyawaki, “High-efficiency calculations for three-dimensional photonic crystal cavities,” Opt. Lett. 31, 262 (2006).
[PubMed]

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, “Diamagnetic response of metallic photonic crystals at infrared and visible Frequencies,” Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

Z. Ye, X. Hu, M. Li, and K. M. Ho, “Propagation of guided modes in curved nanoribbon waveguides,” Appl. Phys. Lett. 89, 241108 (2006).
[CrossRef]

M. Li, X. Hu, Z. Ye, K. M. Ho, J. R. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. 31, 3498 (2006).
[CrossRef] [PubMed]

Z. Y. Li and K. M. Ho, “Bloch mode reflection and lasing threshold in semiconductor nanowire laser arrays,” Phys. Rev. B 71, 045315 (2005).

Z. Y. Li and K. M. Ho, “Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides,” Phys. Rev. B 68, 245117 (2003).

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys Rev. Lett. 65, 3125 (1990).
[CrossRef] [PubMed]

Hou, H.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
[PubMed]

Hu, X.

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, “Diamagnetic response of metallic photonic crystals at infrared and visible Frequencies,” Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

M. Li, X. Hu, Z. Ye, K. M. Ho, J. R. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. 31, 3498 (2006).
[CrossRef] [PubMed]

Z. Ye, X. Hu, M. Li, and K. M. Ho, “Propagation of guided modes in curved nanoribbon waveguides,” Appl. Phys. Lett. 89, 241108 (2006).
[CrossRef]

Imada, M.

S. P. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227 (2004).

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics (Wiley and Sons, 2002).

Joannopoulos, J. D.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
[PubMed]

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

John, S.

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

Johnson, S. G.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
[PubMed]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819 (1999).
[CrossRef] [PubMed]

Kingsland, D. M.

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

Lee, J. F.

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

Lee, R.

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

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819 (1999).
[CrossRef] [PubMed]

Li, M.

M. Li, Z. Y. Li, K. M. Ho, J. R. Cao, and M. Miyawaki, “High-efficiency calculations for three-dimensional photonic crystal cavities,” Opt. Lett. 31, 262 (2006).
[PubMed]

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, “Diamagnetic response of metallic photonic crystals at infrared and visible Frequencies,” Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

Z. Ye, X. Hu, M. Li, and K. M. Ho, “Propagation of guided modes in curved nanoribbon waveguides,” Appl. Phys. Lett. 89, 241108 (2006).
[CrossRef]

M. Li, X. Hu, Z. Ye, K. M. Ho, J. R. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. 31, 3498 (2006).
[CrossRef] [PubMed]

Li, Z. Y.

M. Li, Z. Y. Li, K. M. Ho, J. R. Cao, and M. Miyawaki, “High-efficiency calculations for three-dimensional photonic crystal cavities,” Opt. Lett. 31, 262 (2006).
[PubMed]

Z. Y. Li and K. M. Ho, “Bloch mode reflection and lasing threshold in semiconductor nanowire laser arrays,” Phys. Rev. B 71, 045315 (2005).

Z. Y. Li and K. M. Ho, “Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides,” Phys. Rev. B 68, 245117 (2003).

Lin, S. Y.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
[PubMed]

Meade, R. D.

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

Miyawaki, M.

M. Li, Z. Y. Li, K. M. Ho, J. R. Cao, and M. Miyawaki, “High-efficiency calculations for three-dimensional photonic crystal cavities,” Opt. Lett. 31, 262 (2006).
[PubMed]

M. Li, X. Hu, Z. Ye, K. M. Ho, J. R. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. 31, 3498 (2006).
[CrossRef] [PubMed]

Noda, S.

S. P. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227 (2004).

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819 (1999).
[CrossRef] [PubMed]

Ogawa, S. P.

S. P. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227 (2004).

Okano, M.

S. P. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227 (2004).

Painter, O.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819 (1999).
[CrossRef] [PubMed]

Pendry, J.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).

Pendry, J. B.

J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 41, 209 (1994).
[CrossRef]

Popa, B. I.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).

Sacks, Z. S.

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

Scherer, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819 (1999).
[CrossRef] [PubMed]

Schurig, D.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).

Smith, D. R.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys Rev. Lett. 65, 3125 (1990).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech Houses, 2000).

Vawter, G. A.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
[PubMed]

Villeneuve, P. R.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
[PubMed]

Wendt, J. R.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
[PubMed]

Winn, J. N.

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

Yablonovitch, E.

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

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819 (1999).
[CrossRef] [PubMed]

A. Yariv and P. Yeh, Optical Waves in Crystal, (Wiley, 1984).

Ye, Z.

Z. Ye, X. Hu, M. Li, and K. M. Ho, “Propagation of guided modes in curved nanoribbon waveguides,” Appl. Phys. Lett. 89, 241108 (2006).
[CrossRef]

M. Li, X. Hu, Z. Ye, K. M. Ho, J. R. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. 31, 3498 (2006).
[CrossRef] [PubMed]

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystal, (Wiley, 1984).

Yoshimoto, S.

S. P. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227 (2004).

Zi, J.

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, “Diamagnetic response of metallic photonic crystals at infrared and visible Frequencies,” Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

Zubrzycki, W.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
[PubMed]

Appl. Phys. Lett. (1)

Z. Ye, X. Hu, M. Li, and K. M. Ho, “Propagation of guided modes in curved nanoribbon waveguides,” Appl. Phys. Lett. 89, 241108 (2006).
[CrossRef]

IEEE Trans. Antennas and Propagation (2)

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

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas and Propagation 44, 1630 (1996).
[CrossRef]

J. Computational Physics, (2)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Computational Physics, 114, 185 (1994).
[CrossRef]

J.P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Computational Physics, 127, 363, (1996)
[CrossRef]

J. Mod. Opt. (1)

J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 41, 209 (1994).
[CrossRef]

Nature (1)

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Nature 407, 6807 (2000)
[PubMed]

Opt. Lett. (2)

M. Li, Z. Y. Li, K. M. Ho, J. R. Cao, and M. Miyawaki, “High-efficiency calculations for three-dimensional photonic crystal cavities,” Opt. Lett. 31, 262 (2006).
[PubMed]

M. Li, X. Hu, Z. Ye, K. M. Ho, J. R. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. 31, 3498 (2006).
[CrossRef] [PubMed]

Phys Rev. Lett. (1)

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Figures (6)

Fig. 1.
Fig. 1.

(a). s wave oblique incidence upon Z-axis PML, (b) p wave oblique incidence upon Z-axis PML: E for electric field and H for magnetic field. (c) 3D illustration of side and corner PMLs. (d) 3×3 supercell illustration at XY plane of PC structure with a defect located at the center with s and p wave shown for normal incidence; three PML regions are labeled: 1 for X-axi' side PML, 2 for Y-axis side PML, and 3 for XY-corner PML.

Fig. 2.
Fig. 2.

(a). Transmission and reflection amplitudes for a normal incident planewave upon the Z-axis PML: reflectance amplitudes are below 10-10 for all normalized frequency and transmittance amplitudes are attenuated exponentially as normalized frequency increases, (b) Transmittance and reflectance amplitudes for a planewave upon Z-axis PML as functions of incident angle at normalized frequency a0 /λ=0.4: reflectance amplitudes are below 10-10 at all angles and transmittance amplitudes increase and approaches 100% when incidence angle approaches 90 degree. Only s wave results are shown, p wave presents the same behavior.

Fig. 3.
Fig. 3.

Two approaches to improve the performance of Z-axis PML -- double the thickness of PML and double the imaginary part of sz : (a) transmittance amplitudes are attenuated more compared to Fig. 2(b) for every incidence angle but still approaches to 100% as incidence angle approaches 90 degree, (b) reflectance amplitudes are still perfectly matched for all incidence angles. Only s wave results are shown, p wave presents the same behavior.

Fig. 4.
Fig. 4.

Planewave incidence upon one-dimensional dielectric waveguide (periodic along Y-axis): (a) Electric field profile of finite length periodic waveguide without any PMLs. (b) Electric field profile of infinite long periodic waveguide with Z-axis PML. (c) Electric field profile of infinite long single waveguide with Z-axis, Y-side and YZ-corner PMLs. (d) Y-axis cross section of electric field magnitude at Z-axis position 0.1μm before the Z-axis PML for both (b) (blue curve) and (c) (red curve), and the analytical solution of electric field magnitude for infinite long single dielectric waveguide (black curve), with the shadow area indicating the location of the waveguide.

Fig. 5.
Fig. 5.

Reflectance of sub-wavelength grating for both s and p planewave with incident angle θ=70 at visible frequencies: (a) with finite SiO2 substrate, and (b) with infinite SiO2 substrate by applying Z-axis PML at the end of substrate.

Fig. 6.
Fig. 6.

Electric field mode profiles of sub-wavelength grating for the infinite substrate case at wavelength 0.45μm: (a) s wave incidence, Ey is dominant and electromagnetic energy is highly reflected, (b) p wave incidence, Ex is dominant and electromagnetic energy is almost 100% transmitted.

Equations (4)

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ε ˜ 2 = ε 1 s ˜ ; , μ ˜ 2 = μ 1 s ˜
s ˜ = [ s 2 0 0 0 s 2 0 0 0 1 / s 2 ]
s ˜ = [ 1 / s x 0 0 0 s x 0 0 0 s x ]
s ˜ = [ s y 0 0 0 1 / s y 0 0 0 s y ]

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