Abstract

An accurate and efficient numerical method is developed for computing leaky modes of two-dimensional photonic crystal (PhC) waveguides corresponding to line defects surrounded by finite PhCs. The method reformulates the eigenvalue problem on a single edge of the defect cell and uses exact boundary conditions at the edges of the surrounding PhC. Unlike previous works for leaky modes, perfectly matched layers or other absorbing boundary conditions are avoided.

© 2010 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. A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
  3. 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).
  4. D. C. Dobson, "An efficient method for band structure calculations in 2-D photonic crystals," J. Comput. Phys. 149, 363-379 (1999).
  5. W. Axmann, P. Kuchment, "An efficient finite element method for computing spectra of photonic and acoustic bandgap materials: I. Scalar case," J. Comput. Phys. 150, 468-481 (1999).
  6. 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).
  7. M. Marrone, V. F. Rodriguez-Esquerre, H. E. Hernández-Figueroa, "Novel numerical method for the analysis of 2-D photonic crystals: The cell method," Opt. Exp. 10, 1299-1304 (2002).
  8. E. Moreno, D. Erni, C. Hafner, "Band structure computations of metallic photonic crystals with the multiple multipole method," Phys. Rev. B 65, 155120 (2002).
  9. C. P. Yu, H. C. Chang, "Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals," Opt. Exp. 12, 1397-1408 (2004).
  10. P. J. Chiang, C. P. Yu, H. C. Chang, "Analysis of two-dimensional photonic crystals using a multidomain pseudospectral method," Phys. Rev. E 75, 026703 (2007).
  11. L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. De Sterke, A. A. Asatryan, "Photonic band structure calculations using scattering matrices," Phys. Rev. E 64, 046603 (2001).
  12. K. Yasumoto, H. Jia, K. Sun, "Rigorous modal analysis of two-dimensional photonic crystal waveguides," Radio Sci. 40, RS6S02 (2005).
  13. J. Yuan, Y. Y. Lu, "Photonic bandgap calculations using Dirichlet-to-Neumann maps," J. Opt. Soc. Amer. A 23, 3217-3222 (2006).
  14. J. Yuan, Y. Y. Lu, "Computing photonic band structures by Dirichlet-to-Neumann maps: The triangular lattice," Opt. Commun. 273, 114-120 (2007).
  15. Y. Huang, Y. Y. Lu, S. Li, "Analyzing photonic crystal waveguides by Dirichlet-to-Neumann maps," J. Opt. Soc. Amer. B 24, 2860-2867 (2008).
  16. D. Zhang, H. Jia, "Numerical analysis of leaky modes in two-dimensional photonic crystal waveguides using Fourier series expansion method with perfectly matched layer," IEICE Trans. Electron. E90-C, 613-622 (2007).
  17. J. Tausch, J. Butler, "Efficient analysis of periodic dielectric waveguides using Dirichlet-to-Neumann maps," J. Opt. Soc. Amer. A 19, 1120-1128 (2002).
  18. S. Li, Y. Y. Lu, "Computing photonic crystal defect modes by Dirichlet-to-Neumann maps," Opt. Exp. 15, 14454-14466 (2007).
  19. Y. Huang, Y. Y. Lu, "Scattering from periodic arrays of cylinders by Dirichlet-to-Neumann maps," J. Lightw. Technol. 24, 3448-3453 (2006).
  20. Y. Wu, Y. Y. Lu, "Dirichlet-to-Neumann map method for analyzing interpenetrating cylinder arrays in a triangular lattice," J. Opt. Soc. Amer. B 25, 1466-1473 (2008).
  21. Z. Hu, Y. Y. Lu, "Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps," Opt. Exp. 16, 17383-17399 (2008).
  22. G. Bao, D. C. Dobson, J. A. Cox, "Mathematical studies in rigorous grating theory," J. Opt. Soc. Amer. A 12, 1029-1042 (1995).

2008 (3)

Y. Huang, Y. Y. Lu, S. Li, "Analyzing photonic crystal waveguides by Dirichlet-to-Neumann maps," J. Opt. Soc. Amer. B 24, 2860-2867 (2008).

Y. Wu, Y. Y. Lu, "Dirichlet-to-Neumann map method for analyzing interpenetrating cylinder arrays in a triangular lattice," J. Opt. Soc. Amer. B 25, 1466-1473 (2008).

Z. Hu, Y. Y. Lu, "Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps," Opt. Exp. 16, 17383-17399 (2008).

2007 (4)

J. Yuan, Y. Y. Lu, "Computing photonic band structures by Dirichlet-to-Neumann maps: The triangular lattice," Opt. Commun. 273, 114-120 (2007).

D. Zhang, H. Jia, "Numerical analysis of leaky modes in two-dimensional photonic crystal waveguides using Fourier series expansion method with perfectly matched layer," IEICE Trans. Electron. E90-C, 613-622 (2007).

S. Li, Y. Y. Lu, "Computing photonic crystal defect modes by Dirichlet-to-Neumann maps," Opt. Exp. 15, 14454-14466 (2007).

P. J. Chiang, C. P. Yu, H. C. Chang, "Analysis of two-dimensional photonic crystals using a multidomain pseudospectral method," Phys. Rev. E 75, 026703 (2007).

2006 (2)

J. Yuan, Y. Y. Lu, "Photonic bandgap calculations using Dirichlet-to-Neumann maps," J. Opt. Soc. Amer. A 23, 3217-3222 (2006).

Y. Huang, Y. Y. Lu, "Scattering from periodic arrays of cylinders by Dirichlet-to-Neumann maps," J. Lightw. Technol. 24, 3448-3453 (2006).

2005 (1)

K. Yasumoto, H. Jia, K. Sun, "Rigorous modal analysis of two-dimensional photonic crystal waveguides," Radio Sci. 40, RS6S02 (2005).

2004 (1)

C. P. Yu, H. C. Chang, "Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals," Opt. Exp. 12, 1397-1408 (2004).

2002 (3)

M. Marrone, V. F. Rodriguez-Esquerre, H. E. Hernández-Figueroa, "Novel numerical method for the analysis of 2-D photonic crystals: The cell method," Opt. Exp. 10, 1299-1304 (2002).

E. Moreno, D. Erni, C. Hafner, "Band structure computations of metallic photonic crystals with the multiple multipole method," Phys. Rev. B 65, 155120 (2002).

J. Tausch, J. Butler, "Efficient analysis of periodic dielectric waveguides using Dirichlet-to-Neumann maps," J. Opt. Soc. Amer. A 19, 1120-1128 (2002).

2001 (2)

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. De Sterke, A. A. Asatryan, "Photonic band structure calculations using scattering matrices," Phys. Rev. E 64, 046603 (2001).

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).

1999 (2)

D. C. Dobson, "An efficient method for band structure calculations in 2-D photonic crystals," J. Comput. Phys. 149, 363-379 (1999).

W. Axmann, P. Kuchment, "An efficient finite element method for computing spectra of photonic and acoustic bandgap materials: I. Scalar case," J. Comput. Phys. 150, 468-481 (1999).

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).

1995 (1)

G. Bao, D. C. Dobson, J. A. Cox, "Mathematical studies in rigorous grating theory," J. Opt. Soc. Amer. A 12, 1029-1042 (1995).

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).

IEICE Trans. Electron. (1)

D. Zhang, H. Jia, "Numerical analysis of leaky modes in two-dimensional photonic crystal waveguides using Fourier series expansion method with perfectly matched layer," IEICE Trans. Electron. E90-C, 613-622 (2007).

J. Comput. Phys. (2)

D. C. Dobson, "An efficient method for band structure calculations in 2-D photonic crystals," J. Comput. Phys. 149, 363-379 (1999).

W. Axmann, P. Kuchment, "An efficient finite element method for computing spectra of photonic and acoustic bandgap materials: I. Scalar case," J. Comput. Phys. 150, 468-481 (1999).

J. Lightw. Technol. (1)

Y. Huang, Y. Y. Lu, "Scattering from periodic arrays of cylinders by Dirichlet-to-Neumann maps," J. Lightw. Technol. 24, 3448-3453 (2006).

J. Opt. Soc. Amer. A (3)

G. Bao, D. C. Dobson, J. A. Cox, "Mathematical studies in rigorous grating theory," J. Opt. Soc. Amer. A 12, 1029-1042 (1995).

J. Tausch, J. Butler, "Efficient analysis of periodic dielectric waveguides using Dirichlet-to-Neumann maps," J. Opt. Soc. Amer. A 19, 1120-1128 (2002).

J. Yuan, Y. Y. Lu, "Photonic bandgap calculations using Dirichlet-to-Neumann maps," J. Opt. Soc. Amer. A 23, 3217-3222 (2006).

J. Opt. Soc. Amer. B (2)

Y. Huang, Y. Y. Lu, S. Li, "Analyzing photonic crystal waveguides by Dirichlet-to-Neumann maps," J. Opt. Soc. Amer. B 24, 2860-2867 (2008).

Y. Wu, Y. Y. Lu, "Dirichlet-to-Neumann map method for analyzing interpenetrating cylinder arrays in a triangular lattice," J. Opt. Soc. Amer. B 25, 1466-1473 (2008).

Opt. Commun. (1)

J. Yuan, Y. Y. Lu, "Computing photonic band structures by Dirichlet-to-Neumann maps: The triangular lattice," Opt. Commun. 273, 114-120 (2007).

Opt. Exp. (5)

S. Li, Y. Y. Lu, "Computing photonic crystal defect modes by Dirichlet-to-Neumann maps," Opt. Exp. 15, 14454-14466 (2007).

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).

M. Marrone, V. F. Rodriguez-Esquerre, H. E. Hernández-Figueroa, "Novel numerical method for the analysis of 2-D photonic crystals: The cell method," Opt. Exp. 10, 1299-1304 (2002).

C. P. Yu, H. C. Chang, "Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals," Opt. Exp. 12, 1397-1408 (2004).

Z. Hu, Y. Y. Lu, "Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps," Opt. Exp. 16, 17383-17399 (2008).

Phys. Rev. B (1)

E. Moreno, D. Erni, C. Hafner, "Band structure computations of metallic photonic crystals with the multiple multipole method," Phys. Rev. B 65, 155120 (2002).

Phys. Rev. E (2)

P. J. Chiang, C. P. Yu, H. C. Chang, "Analysis of two-dimensional photonic crystals using a multidomain pseudospectral method," Phys. Rev. E 75, 026703 (2007).

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. De Sterke, A. A. Asatryan, "Photonic band structure calculations using scattering matrices," Phys. Rev. E 64, 046603 (2001).

Phys. Rev. Lett. (2)

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).

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).

Radio Sci. (1)

K. Yasumoto, H. Jia, K. Sun, "Rigorous modal analysis of two-dimensional photonic crystal waveguides," Radio Sci. 40, RS6S02 (2005).

Other (1)

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

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