Abstract

A finite-difference time-domain (FDTD) method based on a regular Cartesian Yee's lattice is developed for calculating the dispersion band diagram of a 2-D photonic crystal. Unlike methods that require auxiliary difference equations or nonorthogonal grid schemes, our method uses the standard central-difference equations and can be easily implemented in a parallel computing environment. The application of the periodic boundary condition on an angled boundary involves a split-field formulation of Maxwell's equations. We show that the method can be applied for photonic crystals of both orthogonal and nonorthogonal unit cells. Complete and accurate bandgap information is obtained by using this FDTD approach. Numerical results for 2-D TE/TM modes in triangular lattice photonic crystals are in excellent agreement with the results from 2-D plane wave expansion method. For a triangular lattice photonic crystal slab, the dispersion relation is calculated by a 3-D FDTD method similarly formulated. The result agrees well with the 3-D finite-element method solution. The calculations also show that the 2-D simulation using an effective index approximation can result in considerable error for higher bands.

© 2007 IEEE

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  1. E. Yablonovitch, "Inhibited spontaneous emission in solid-state 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. W. Kuang, J. R. Cao, S.-J. Choi, J. D. O'Brien, P. D. Dapkus, "Classification of modes in suspended membrane 19-missing-hole photonic crystal microcavities ," J. Opt. Soc. Amer. B, Opt. Phys. 22, 1092-1099 (2005).
  5. C. Oubre, P. Nordlander, "Finite-difference time-domain studies of the optical properties of nanoshell dimers ," J. Phys. Chem. B 109, 10 042-10 051 (2005).
  6. W. J. Kim, Full vectorial finite element analysis of photonic crystal devices: Application to low-loss modulator Ph.D. dissertation Univ. Southern CaliforniaLos AngelesCA (2004).
  7. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B, Condens. Matter 54, 11 245-11 251 (1996).
  8. J.-F. Lee, R. Palendech, R. Mittra, "Modeling three-dimensional discontinuities in waveguides using nonorthogonal FDTD algorithm ," IEEE Trans. Microw. Theory Tech. 40, 346-352 (1992).
  9. 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).
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  17. A. Chutinan, S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs," Phys. Rev. B, Condens. Matter 62, 4488-4492 (2000).
  18. J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
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  22. W. Kuang, W. J. Kim, A. Mock, J. D. O'Brien, "Propagation loss of line-defect photonic crystal slab waveguides," IEEE J. Sel. Topics Quantum Electron. 12, 1183-1195 (2006).

2006 (1)

W. Kuang, W. J. Kim, A. Mock, J. D. O'Brien, "Propagation loss of line-defect photonic crystal slab waveguides," IEEE J. Sel. Topics Quantum Electron. 12, 1183-1195 (2006).

2005 (2)

W. Kuang, J. R. Cao, S.-J. Choi, J. D. O'Brien, P. D. Dapkus, "Classification of modes in suspended membrane 19-missing-hole photonic crystal microcavities ," J. Opt. Soc. Amer. B, Opt. Phys. 22, 1092-1099 (2005).

C. Oubre, P. Nordlander, "Finite-difference time-domain studies of the optical properties of nanoshell dimers ," J. Phys. Chem. B 109, 10 042-10 051 (2005).

2003 (1)

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).

1996 (3)

J.-P. Berenger, "Perfectly matched layer for the FDTD solution of wave–structure interaction problems ," IEEE Trans. Antennas Propag. 44, 110-117 (1996).

J.-P. Berenger, "Three-dimensional perfectly matched layer for the absorption of electromagnetic waves ," J. Comput. Phys. 127, 363-379 (1996).

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B, Condens. Matter 54, 11 245-11 251 (1996).

1995 (1)

C. Chan, Q. Yu, K. Ho, "Order-n spectral method for electromagnetic-waves," Phys. Rev. B, Condens. Matter 51, 16 635-16 642 (1995).

1994 (1)

J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).

1993 (1)

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

1992 (2)

J.-F. Lee, R. Palendech, R. Mittra, "Modeling three-dimensional 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 solid-state 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).

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).

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

W. Kuang, W. J. Kim, A. Mock, J. D. O'Brien, "Propagation loss of line-defect photonic crystal slab waveguides," IEEE J. Sel. Topics Quantum Electron. 12, 1183-1195 (2006).

IEEE Trans. Antennas Propag. (2)

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).

J.-P. Berenger, "Perfectly matched layer for the FDTD solution of wave–structure interaction problems ," IEEE Trans. Antennas Propag. 44, 110-117 (1996).

IEEE Trans. Microw. Theory Tech. (1)

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

J. Comput. Phys. (2)

J.-P. Berenger, "Three-dimensional perfectly matched layer for the absorption of electromagnetic waves ," J. Comput. Phys. 127, 363-379 (1996).

J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).

J. Opt. Soc. Amer. B, Opt. Phys. (1)

W. Kuang, J. R. Cao, S.-J. Choi, J. D. O'Brien, P. D. Dapkus, "Classification of modes in suspended membrane 19-missing-hole photonic crystal microcavities ," J. Opt. Soc. Amer. B, Opt. Phys. 22, 1092-1099 (2005).

J. Phys. Chem. B (1)

C. Oubre, P. Nordlander, "Finite-difference time-domain studies of the optical properties of nanoshell dimers ," J. Phys. Chem. B 109, 10 042-10 051 (2005).

Opt. Lett. (1)

Phys. Rev. B, Condens. Matter (6)

C. Chan, Q. Yu, K. Ho, "Order-n spectral method for electromagnetic-waves," Phys. Rev. B, Condens. Matter 51, 16 635-16 642 (1995).

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

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, "Accurate theoretical analysis of photonic band-gap 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).

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B, Condens. Matter 54, 11 245-11 251 (1996).

Phys. Rev. Lett. (2)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state 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).

W. J. Kim, Full vectorial finite element analysis of photonic crystal devices: Application to low-loss modulator Ph.D. dissertation Univ. Southern CaliforniaLos AngelesCA (2004).

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

W. Kuang, Photonic crystal waveguides Ph.D. dissertation Univ. Southern CaliforniaLos AngelesCA (2005).

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

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