Abstract

In this paper, an improved complex-envelope alternating-direction-implicit finite-difference time-domain (CE-ADI-FDTD) method has been presented for the analysis of photonic-bandgap cavities. The improvement relies on a different approach of the perfectly matched-layer absorbing-boundary condition in order to avoid the formation of instability, as reported in the literature. The high numerical precision and efficiency obtained are clearly demonstrated through the agreement of the results obtained using CE-ADI-FDTD and their counterparts obtained using other rigorous approaches reported in the literature.

© 2007 IEEE

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  1. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).
  2. P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, S. Beckx, "Bandwidth engineering of photonic crystal waveguide bends," Electron. Lett. 40, 1263-1264 (2004).
  3. R. Costa, A. Melloni, M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).
  4. E. Pistono, P. Ferrari, L. Duvillaret, J. L. Coutaz, A. Jrad, "Tunable bandpass microwave filters based on defect commandable photonic bandgap waveguides ," Electron. Lett. 39, 1131-1133 (2003).
  5. P. R. Villeneuve, S. Fan, J. D. Joannopoulos, "Microcavities in photonic crystals: Mode symmetry, tunability, and coupling efficiency ," Phys. Rev. B, Condens. Matter 54, 7837-7842 (1996).
  6. H. M. H. Chong, R. M. De La Rue, "Tuning of photonic crystal waveguide microcavity by thermooptic effect," IEEE Photon. Technol. Lett. 16, 1528-1530 (2004).
  7. A. Mekis, M. Meier, A. DodaBalapur, R. E. Slusher, J. D. Joannopulos, "Lasing mechanism in two dimensional photonic crystal lasers," Appl. Phys., A Mater. Sci. Process. 69, 111-114 (1999).
  8. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
  9. B. M. Nyman, P. R. Prucnal, "The modified beam propagation method," J. Lightw. Technol. 7, 931-936 (1989).
  10. W. Huang, C. Xu, S. T. Chu, S. K. Chaudhuri, "The finite-difference vector beam propagation method: Analysis and assessment," J. Lightw. Technol. 10, 295-305 (1992).
  11. S. S. A. Obayya, B. M. A. Rahman, H. A. El-Mikati, "New full-vectorial numerically efficient propagation algorithm based on the finite element method ," J. Lightw. Technol. 18, 409-415 (2000).
  12. W. P. Huang, S. T. Chu, S. K. Chaudhuri, "A semivectorial finite-difference time-domain method," IEEE Photon. Technol. Lett. 3, 803-806 (1991).
  13. W. Xue, G. Zhou, Y. Xiao, R. Yang, "Analysis of dispersion properties in hexagonal hollow fiber," J. Lightw. Technol. 22, 1909-1914 (2004).
  14. S. S. A. Obayya, "Efficient finite-element-based time-domain beam propagation analysis of optical integrated circuits," IEEE J. Quantum Electron. 40, 591-595 (2004).
  15. H. Rao, R. Scarmozzino, R. M. Osgood, "An improved ADI-FDTD method and its application to photonic simulations," IEEE Photon. Technol. Lett. 14, 477-479 (2002).
  16. S. Wang, F. L. Teixeira, "An efficient PML implementation for the ADI-FDTD method," IEEE Microw. Wireless Compon. Lett. 13, 72-74 (2003).
  17. V. F. Rodriguez-Esquerre, M. Koshiba, H. Figueroa, "Finite-element analysis of photonic crystal cavities: Time and frequency domain," J. Lightw. Technol. 23, 1514-1521 (2005).
  18. A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  19. V. F. Rodriguez-Esquerre, M. Koshiba, H. Figueroa, "Finite-element time-domain analysis of 2-D photonic crystal resonant cavities," IEEE Photon. Technol. Lett. 16, 816-818 (2004).
  20. S. S. A. Obayya, "Finite element time domain solution of resonant modes in photonic bandgap cavities," J. Opt. Quantum Electron. 37, 865-873 (2005).
  21. M. R. Watts, S. G. Johnson, H. A. Haus, J. D. Joannopoulos, "Electromagnetic cavity with arbitrary Q and small modal volume without a complete photonic bandgap," Opt. Lett. 27, 1785-1787 (2002).
  22. J. K. Hwang, S. B. Hyun, H. Y. Ryu, Y. H. Lee, "Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition," J. Opt. Soc. Amer. B, Opt. Phys. 15, 2316-2324 (1998).

2005

V. F. Rodriguez-Esquerre, M. Koshiba, H. Figueroa, "Finite-element analysis of photonic crystal cavities: Time and frequency domain," J. Lightw. Technol. 23, 1514-1521 (2005).

S. S. A. Obayya, "Finite element time domain solution of resonant modes in photonic bandgap cavities," J. Opt. Quantum Electron. 37, 865-873 (2005).

2004

V. F. Rodriguez-Esquerre, M. Koshiba, H. Figueroa, "Finite-element time-domain analysis of 2-D photonic crystal resonant cavities," IEEE Photon. Technol. Lett. 16, 816-818 (2004).

W. Xue, G. Zhou, Y. Xiao, R. Yang, "Analysis of dispersion properties in hexagonal hollow fiber," J. Lightw. Technol. 22, 1909-1914 (2004).

S. S. A. Obayya, "Efficient finite-element-based time-domain beam propagation analysis of optical integrated circuits," IEEE J. Quantum Electron. 40, 591-595 (2004).

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, S. Beckx, "Bandwidth engineering of photonic crystal waveguide bends," Electron. Lett. 40, 1263-1264 (2004).

H. M. H. Chong, R. M. De La Rue, "Tuning of photonic crystal waveguide microcavity by thermooptic effect," IEEE Photon. Technol. Lett. 16, 1528-1530 (2004).

2003

R. Costa, A. Melloni, M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).

E. Pistono, P. Ferrari, L. Duvillaret, J. L. Coutaz, A. Jrad, "Tunable bandpass microwave filters based on defect commandable photonic bandgap waveguides ," Electron. Lett. 39, 1131-1133 (2003).

S. Wang, F. L. Teixeira, "An efficient PML implementation for the ADI-FDTD method," IEEE Microw. Wireless Compon. Lett. 13, 72-74 (2003).

2002

H. Rao, R. Scarmozzino, R. M. Osgood, "An improved ADI-FDTD method and its application to photonic simulations," IEEE Photon. Technol. Lett. 14, 477-479 (2002).

M. R. Watts, S. G. Johnson, H. A. Haus, J. D. Joannopoulos, "Electromagnetic cavity with arbitrary Q and small modal volume without a complete photonic bandgap," Opt. Lett. 27, 1785-1787 (2002).

2000

S. S. A. Obayya, B. M. A. Rahman, H. A. El-Mikati, "New full-vectorial numerically efficient propagation algorithm based on the finite element method ," J. Lightw. Technol. 18, 409-415 (2000).

1999

A. Mekis, M. Meier, A. DodaBalapur, R. E. Slusher, J. D. Joannopulos, "Lasing mechanism in two dimensional photonic crystal lasers," Appl. Phys., A Mater. Sci. Process. 69, 111-114 (1999).

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).

1998

J. K. Hwang, S. B. Hyun, H. Y. Ryu, Y. H. Lee, "Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition," J. Opt. Soc. Amer. B, Opt. Phys. 15, 2316-2324 (1998).

1996

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

1992

W. Huang, C. Xu, S. T. Chu, S. K. Chaudhuri, "The finite-difference vector beam propagation method: Analysis and assessment," J. Lightw. Technol. 10, 295-305 (1992).

1991

W. P. Huang, S. T. Chu, S. K. Chaudhuri, "A semivectorial finite-difference time-domain method," IEEE Photon. Technol. Lett. 3, 803-806 (1991).

1989

B. M. Nyman, P. R. Prucnal, "The modified beam propagation method," J. Lightw. Technol. 7, 931-936 (1989).

Appl. Phys., A Mater. Sci. Process.

A. Mekis, M. Meier, A. DodaBalapur, R. E. Slusher, J. D. Joannopulos, "Lasing mechanism in two dimensional photonic crystal lasers," Appl. Phys., A Mater. Sci. Process. 69, 111-114 (1999).

Electron. Lett.

P. I. Borel, L. H. Frandsen, A. Harpøth, J. B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, S. Beckx, "Bandwidth engineering of photonic crystal waveguide bends," Electron. Lett. 40, 1263-1264 (2004).

E. Pistono, P. Ferrari, L. Duvillaret, J. L. Coutaz, A. Jrad, "Tunable bandpass microwave filters based on defect commandable photonic bandgap waveguides ," Electron. Lett. 39, 1131-1133 (2003).

IEEE J. Quantum Electron.

S. S. A. Obayya, "Efficient finite-element-based time-domain beam propagation analysis of optical integrated circuits," IEEE J. Quantum Electron. 40, 591-595 (2004).

IEEE Microw. Wireless Compon. Lett.

S. Wang, F. L. Teixeira, "An efficient PML implementation for the ADI-FDTD method," IEEE Microw. Wireless Compon. Lett. 13, 72-74 (2003).

IEEE Photon. Technol. Lett.

H. Rao, R. Scarmozzino, R. M. Osgood, "An improved ADI-FDTD method and its application to photonic simulations," IEEE Photon. Technol. Lett. 14, 477-479 (2002).

W. P. Huang, S. T. Chu, S. K. Chaudhuri, "A semivectorial finite-difference time-domain method," IEEE Photon. Technol. Lett. 3, 803-806 (1991).

R. Costa, A. Melloni, M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).

H. M. H. Chong, R. M. De La Rue, "Tuning of photonic crystal waveguide microcavity by thermooptic effect," IEEE Photon. Technol. Lett. 16, 1528-1530 (2004).

V. F. Rodriguez-Esquerre, M. Koshiba, H. Figueroa, "Finite-element time-domain analysis of 2-D photonic crystal resonant cavities," IEEE Photon. Technol. Lett. 16, 816-818 (2004).

J. Lightw. Technol.

W. Xue, G. Zhou, Y. Xiao, R. Yang, "Analysis of dispersion properties in hexagonal hollow fiber," J. Lightw. Technol. 22, 1909-1914 (2004).

B. M. Nyman, P. R. Prucnal, "The modified beam propagation method," J. Lightw. Technol. 7, 931-936 (1989).

W. Huang, C. Xu, S. T. Chu, S. K. Chaudhuri, "The finite-difference vector beam propagation method: Analysis and assessment," J. Lightw. Technol. 10, 295-305 (1992).

S. S. A. Obayya, B. M. A. Rahman, H. A. El-Mikati, "New full-vectorial numerically efficient propagation algorithm based on the finite element method ," J. Lightw. Technol. 18, 409-415 (2000).

V. F. Rodriguez-Esquerre, M. Koshiba, H. Figueroa, "Finite-element analysis of photonic crystal cavities: Time and frequency domain," J. Lightw. Technol. 23, 1514-1521 (2005).

J. Opt. Quantum Electron.

S. S. A. Obayya, "Finite element time domain solution of resonant modes in photonic bandgap cavities," J. Opt. Quantum Electron. 37, 865-873 (2005).

J. Opt. Soc. Amer. B, Opt. Phys.

J. K. Hwang, S. B. Hyun, H. Y. Ryu, Y. H. Lee, "Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition," J. Opt. Soc. Amer. B, Opt. Phys. 15, 2316-2324 (1998).

Opt. Lett.

Phys. Rev. B, Condens. Matter

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

Science

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).

Other

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

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