Abstract

In this paper, a modified and easy finite-difference time-domain (FDTD) method based on a regular Cartesian Yee's lattice is developed for calculating the dispersion diagram of triangular lattice photonic crystals (PCs). Our method uses the standard central-difference equation, which is very easy to implement in any computing environment. The Bloch periodic boundary conditions are applied on the sides of the unit cell by translating the periodic boundary conditions to match with the directions of periodicity in the triangular lattice. Complete and accurate bandgap information is obtained by using this FDTD approach. Convergence, accuracy, and stability analysis were carried out, which ensures the reliability of this method. Numerical results for 2-D TE/TM modes in triangular lattice PC are in good agreement with results from 2-D plane wave expansion method. To ease the practical application of this method, clear explanations on the computer implementation are also provided.

© 2009 IEEE

PDF Article

References

  • View by:
  • |
  • |

  1. E. Yablonovitch, "Inhibited spontaneous emission in solidstate physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
  3. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).
  4. A. Taflove, S. C. Hagness, Computational Electromagnetics—The Finite-Difference Time-Domain Method (Artech House, 2005).
  5. W. Kuang, W. J. Kim, J. D. O'Brien, "Finite-difference time-domain method for nonorthogonal unit-cell two-dimensional photonic crystals," J. Lightw. Technol. 25, 2612-2617 (2007).
  6. S. G. Johnson, J. D. Joannopoulos, Photonic Crystals: The Road From Theory to Practice (Kluwer, 2002).
  7. J. F. Lee, R. Palendech, R. Mitta, "Modeling threedimensional discontinuities in waveguides using nonorthogonal FDTD algorithm," IEEE Trans. Microw. Theory Tech. 40, 346-352 (1992).
  8. A. Chutinan, S. Noda, "Waveguides and Waveguide bends in two-dimensional Photonic crystal slabs," Phys. Rev. B, Condens. Matter 62, 4488-4492 (2000).
  9. A. Taflove, S. C. Hagness, Computational Electromagnetics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  10. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).
  11. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B, Condens. Matter 54, 11245-11251 (1996).
  12. R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, "Accurate theoretical analysis of photonic bandgap materials," Phys. Rev. B, Condens. Matter 48, 8434-8437 (1993).
  13. M. Plihal, A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B, Condens. Matter 44, 8565-8571 (1991).
  14. P. R. Villeneuve, M. Piche, "Photonic band gaps in two-dimensional square and hexagonal lattices," Phys. Rev. B, Condens. Matter 46, 4969-4972 (1992).
  15. S. G. Johnson, J. D. Joannopoulos, "Block-iterative frequency-domain methods for maxwell's equations in a planewave basis," Opt. Exp. 8, 173-190 (2001).
  16. R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc.-Optoelectron. 145, 391-397 (1998).
  17. M. Boroditsky, R. Coccioli, E. Yablonovitch, "Analysis of photonic crystals for light emitting diodes using the finite-difference time-domain technique," presented at the Photon. West 1998 San JoseCA ().
  18. A. J. Ward, J. B. Pendry, "Calculating photonic green's functions using a nonorthogonal finite-difference time-domain method," Phys. Rev. B 58, 7252-7259 (1998).
  19. S. Guo, S. Albin, "Simple plane wave implementation for photonic crystal calculations," Opt. Exp. 11, 167-175 (2003).
  20. F. J. Haris, "On the use of windows for harmonic analysis with the discrete Fourier transform," IEEE Proc. 66, 51-83 (1978).
  21. M. R. Wall, D. Neuhauser, "Extraction, through filter-diagonalization, of general quantum eigenvalues or classical normal-mode frequencies from a small number of residues or a short-time segment of a signal," J. Chem. Phys. 102, 8011-8022 (1995).
  22. S. G. Johnson, S. Fan, A. Mekis, J. D. Joannopoulos, "Multipole-cancellation mechanism for high-q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78, 3388-3390 (2001).

2007 (1)

W. Kuang, W. J. Kim, J. D. O'Brien, "Finite-difference time-domain method for nonorthogonal unit-cell two-dimensional photonic crystals," J. Lightw. Technol. 25, 2612-2617 (2007).

2003 (1)

S. Guo, S. Albin, "Simple plane wave implementation for photonic crystal calculations," Opt. Exp. 11, 167-175 (2003).

2001 (2)

S. G. Johnson, J. D. Joannopoulos, "Block-iterative frequency-domain methods for maxwell's equations in a planewave basis," Opt. Exp. 8, 173-190 (2001).

S. G. Johnson, S. Fan, A. Mekis, J. D. Joannopoulos, "Multipole-cancellation mechanism for high-q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78, 3388-3390 (2001).

2000 (1)

A. Chutinan, S. Noda, "Waveguides and Waveguide bends in two-dimensional Photonic crystal slabs," Phys. Rev. B, Condens. Matter 62, 4488-4492 (2000).

1998 (2)

R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc.-Optoelectron. 145, 391-397 (1998).

A. J. Ward, J. B. Pendry, "Calculating photonic green's functions using a nonorthogonal finite-difference time-domain method," Phys. Rev. B 58, 7252-7259 (1998).

1996 (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B, Condens. Matter 54, 11245-11251 (1996).

1995 (1)

M. R. Wall, D. Neuhauser, "Extraction, through filter-diagonalization, of general quantum eigenvalues or classical normal-mode frequencies from a small number of residues or a short-time segment of a signal," J. Chem. Phys. 102, 8011-8022 (1995).

1993 (1)

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, "Accurate theoretical analysis of photonic bandgap materials," Phys. Rev. B, Condens. Matter 48, 8434-8437 (1993).

1992 (2)

J. F. Lee, R. Palendech, R. Mitta, "Modeling threedimensional discontinuities in waveguides using nonorthogonal FDTD algorithm," IEEE Trans. Microw. Theory Tech. 40, 346-352 (1992).

P. R. Villeneuve, M. Piche, "Photonic band gaps in two-dimensional square and hexagonal lattices," Phys. Rev. B, Condens. Matter 46, 4969-4972 (1992).

1991 (1)

M. Plihal, A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B, Condens. Matter 44, 8565-8571 (1991).

1987 (2)

E. Yablonovitch, "Inhibited spontaneous emission in solidstate physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).

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

1978 (1)

F. J. Haris, "On the use of windows for harmonic analysis with the discrete Fourier transform," IEEE Proc. 66, 51-83 (1978).

1966 (1)

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

Appl. Phys. Lett. (1)

S. G. Johnson, S. Fan, A. Mekis, J. D. Joannopoulos, "Multipole-cancellation mechanism for high-q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78, 3388-3390 (2001).

IEE Proc.-Optoelectron. (1)

R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, E. Yablonovitch, "Smallest possible electromagnetic mode volume in a dielectric cavity," IEE Proc.-Optoelectron. 145, 391-397 (1998).

IEEE Proc. (1)

F. J. Haris, "On the use of windows for harmonic analysis with the discrete Fourier transform," IEEE Proc. 66, 51-83 (1978).

IEEE Trans. Antennas Propag. (1)

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

IEEE Trans. Microw. Theory Tech. (1)

J. F. Lee, R. Palendech, R. Mitta, "Modeling threedimensional discontinuities in waveguides using nonorthogonal FDTD algorithm," IEEE Trans. Microw. Theory Tech. 40, 346-352 (1992).

J. Chem. Phys. (1)

M. R. Wall, D. Neuhauser, "Extraction, through filter-diagonalization, of general quantum eigenvalues or classical normal-mode frequencies from a small number of residues or a short-time segment of a signal," J. Chem. Phys. 102, 8011-8022 (1995).

J. Lightw. Technol. (1)

W. Kuang, W. J. Kim, J. D. O'Brien, "Finite-difference time-domain method for nonorthogonal unit-cell two-dimensional photonic crystals," J. Lightw. Technol. 25, 2612-2617 (2007).

Opt. Exp. (2)

S. G. Johnson, J. D. Joannopoulos, "Block-iterative frequency-domain methods for maxwell's equations in a planewave basis," Opt. Exp. 8, 173-190 (2001).

S. Guo, S. Albin, "Simple plane wave implementation for photonic crystal calculations," Opt. Exp. 11, 167-175 (2003).

Phys. Rev. B (1)

A. J. Ward, J. B. Pendry, "Calculating photonic green's functions using a nonorthogonal finite-difference time-domain method," Phys. Rev. B 58, 7252-7259 (1998).

Phys. Rev. B, Condens. Matter (5)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B, Condens. Matter 54, 11245-11251 (1996).

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, "Accurate theoretical analysis of photonic bandgap materials," Phys. Rev. B, Condens. Matter 48, 8434-8437 (1993).

M. Plihal, A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B, Condens. Matter 44, 8565-8571 (1991).

P. R. Villeneuve, M. Piche, "Photonic band gaps in two-dimensional square and hexagonal lattices," Phys. Rev. B, Condens. Matter 46, 4969-4972 (1992).

A. Chutinan, S. Noda, "Waveguides and Waveguide bends in two-dimensional Photonic crystal slabs," Phys. Rev. B, Condens. Matter 62, 4488-4492 (2000).

Phys. Rev. Lett. (2)

E. Yablonovitch, "Inhibited spontaneous emission in solidstate physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).

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

Other (5)

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 Electromagnetics—The Finite-Difference Time-Domain Method (Artech House, 2005).

A. Taflove, S. C. Hagness, Computational Electromagnetics: The Finite-Difference Time-Domain Method (Artech House, 2000).

S. G. Johnson, J. D. Joannopoulos, Photonic Crystals: The Road From Theory to Practice (Kluwer, 2002).

M. Boroditsky, R. Coccioli, E. Yablonovitch, "Analysis of photonic crystals for light emitting diodes using the finite-difference time-domain technique," presented at the Photon. West 1998 San JoseCA ().

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.