Abstract

We present an evolutionary design process of a photonic crystal notch filter using a particle swarm optimization (PSO) algorithm in conjunction with finite-difference time domain (FDTD). The notch-filter parameter is optimized by PSO, and a fitness function is evaluated by FDTD simulations to represent the performance of each candidate design. Using these methods, a filter with desired resonant wavelength is obtained by the optimization process. Then this optimized filter is analyzed and simulated by FDTD to validate the robustness of the algorithm.

© 2009 Optical Society of America

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
    [Crossref] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
    [Crossref] [PubMed]
  3. P. R. Villeneuve and M. Piche, “Photonic band gaps in two-dimensional square and hexagonal lattices,” Phys. Rev. B 46, 4969-4972 (1992).
    [Crossref]
  4. Y. Xu, H. B. Sun, J. Y. Ye, S. Matsuo, and H. Misawa, “Fabrication and direct transmission measurement of high-aspect-ratio two-dimensional silicon-based photonic crystal chips,” J. Opt. Soc. Am. B 18, 1084-1091 (2001).
    [Crossref]
  5. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, (Princeton U. Press, 1995).
  6. O. Painter, J. Vuc'kovic, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275-285 (1999).
    [Crossref]
  7. V. Kuzmiak and A. A. Maradudin, “Localized defect modes in a two-dimensional triangular photonic crystal,” Phys. Rev. B 57, 15242-15250 (1998).
    [Crossref]
  8. P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837-7842 (1996).
    [Crossref]
  9. R. K. Lee, O. Painter, B. Kitzke, A. Scherer, and A. Yariv, “Emission properties of a defect cavity in a two dimensional photonic bandgap crystal slab,” J. Opt. Soc. Am. B 17, 629-633 (2000).
    [Crossref]
  10. W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. W. Berg, P. C. Yu, and S. W. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153-1160 (2001).
    [Crossref]
  11. A. Taflove, Computational Electrodynamics: The Finite--Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  12. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
    [Crossref]
  13. J. D. Brown and E. G. Johnson, “Micro-cavity resonator optimization using particle swarm optimization,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ITuF6.
  14. R. C. Eberhart, P. K. Simpson, and R. W. Dobbins, Computational Intelligence PC Tools, 1st ed. (Academic, 1996).
  15. R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (IEEE, 1995), pp. 39-43.
    [Crossref]
  16. J. Kennedy and R. C. Eberhart “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks Vol. IV (IEEE, 1995), pp. 1942-1948.
    [Crossref]
  17. J. Kennedy, “The particle swarm: social adaptation of knowledge,” Proceedings of IEEE International Conference on Evolutionary Computation (IEEE, 1997), pp. 303-308.

2007 (1)

J. D. Brown and E. G. Johnson, “Micro-cavity resonator optimization using particle swarm optimization,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ITuF6.

2005 (1)

A. Taflove, Computational Electrodynamics: The Finite--Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

2001 (2)

W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. W. Berg, P. C. Yu, and S. W. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153-1160 (2001).
[Crossref]

Y. Xu, H. B. Sun, J. Y. Ye, S. Matsuo, and H. Misawa, “Fabrication and direct transmission measurement of high-aspect-ratio two-dimensional silicon-based photonic crystal chips,” J. Opt. Soc. Am. B 18, 1084-1091 (2001).
[Crossref]

2000 (1)

1999 (1)

1998 (1)

V. Kuzmiak and A. A. Maradudin, “Localized defect modes in a two-dimensional triangular photonic crystal,” Phys. Rev. B 57, 15242-15250 (1998).
[Crossref]

1997 (1)

J. Kennedy, “The particle swarm: social adaptation of knowledge,” Proceedings of IEEE International Conference on Evolutionary Computation (IEEE, 1997), pp. 303-308.

1996 (2)

R. C. Eberhart, P. K. Simpson, and R. W. Dobbins, Computational Intelligence PC Tools, 1st ed. (Academic, 1996).

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837-7842 (1996).
[Crossref]

1995 (3)

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

R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (IEEE, 1995), pp. 39-43.
[Crossref]

J. Kennedy and R. C. Eberhart “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks Vol. IV (IEEE, 1995), pp. 1942-1948.
[Crossref]

1994 (1)

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

1992 (1)

P. R. Villeneuve and M. Piche, “Photonic band gaps in two-dimensional square and hexagonal lattices,” Phys. Rev. B 46, 4969-4972 (1992).
[Crossref]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
[Crossref] [PubMed]

Berenger, J. P.

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

Berg, E. W.

W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. W. Berg, P. C. Yu, and S. W. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153-1160 (2001).
[Crossref]

Bhattacharya, P.

W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. W. Berg, P. C. Yu, and S. W. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153-1160 (2001).
[Crossref]

Brown, J. D.

J. D. Brown and E. G. Johnson, “Micro-cavity resonator optimization using particle swarm optimization,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ITuF6.

Dobbins, R. W.

R. C. Eberhart, P. K. Simpson, and R. W. Dobbins, Computational Intelligence PC Tools, 1st ed. (Academic, 1996).

Eberhart, R. C.

R. C. Eberhart, P. K. Simpson, and R. W. Dobbins, Computational Intelligence PC Tools, 1st ed. (Academic, 1996).

J. Kennedy and R. C. Eberhart “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks Vol. IV (IEEE, 1995), pp. 1942-1948.
[Crossref]

R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (IEEE, 1995), pp. 39-43.
[Crossref]

Fan, S.

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837-7842 (1996).
[Crossref]

Joannopoulos, J. D.

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837-7842 (1996).
[Crossref]

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

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
[Crossref] [PubMed]

Johnson, E. G.

J. D. Brown and E. G. Johnson, “Micro-cavity resonator optimization using particle swarm optimization,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ITuF6.

Kennedy, J.

J. Kennedy, “The particle swarm: social adaptation of knowledge,” Proceedings of IEEE International Conference on Evolutionary Computation (IEEE, 1997), pp. 303-308.

R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (IEEE, 1995), pp. 39-43.
[Crossref]

J. Kennedy and R. C. Eberhart “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks Vol. IV (IEEE, 1995), pp. 1942-1948.
[Crossref]

Kitzke, B.

Kochman, B.

W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. W. Berg, P. C. Yu, and S. W. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153-1160 (2001).
[Crossref]

Kuzmiak, V.

V. Kuzmiak and A. A. Maradudin, “Localized defect modes in a two-dimensional triangular photonic crystal,” Phys. Rev. B 57, 15242-15250 (1998).
[Crossref]

Lee, R. K.

Maradudin, A. A.

V. Kuzmiak and A. A. Maradudin, “Localized defect modes in a two-dimensional triangular photonic crystal,” Phys. Rev. B 57, 15242-15250 (1998).
[Crossref]

Matsuo, S.

Meade, R. D.

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

Misawa, H.

Painter, O.

Pang, S. W.

W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. W. Berg, P. C. Yu, and S. W. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153-1160 (2001).
[Crossref]

Piche, M.

P. R. Villeneuve and M. Piche, “Photonic band gaps in two-dimensional square and hexagonal lattices,” Phys. Rev. B 46, 4969-4972 (1992).
[Crossref]

Sabarinathan, J.

W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. W. Berg, P. C. Yu, and S. W. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153-1160 (2001).
[Crossref]

Scherer, A.

Simpson, P. K.

R. C. Eberhart, P. K. Simpson, and R. W. Dobbins, Computational Intelligence PC Tools, 1st ed. (Academic, 1996).

Sun, H. B.

Taflove, A.

A. Taflove, Computational Electrodynamics: The Finite--Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Villeneuve, P. R.

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837-7842 (1996).
[Crossref]

P. R. Villeneuve and M. Piche, “Photonic band gaps in two-dimensional square and hexagonal lattices,” Phys. Rev. B 46, 4969-4972 (1992).
[Crossref]

Vuc'kovic, J.

Winn, J. N.

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

Xu, Y.

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[Crossref] [PubMed]

Yariv, A.

Ye, J. Y.

Yu, P. C.

W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. W. Berg, P. C. Yu, and S. W. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153-1160 (2001).
[Crossref]

Zhou, W. D.

W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. W. Berg, P. C. Yu, and S. W. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153-1160 (2001).
[Crossref]

IEEE J. Quantum Electron. (1)

W. D. Zhou, J. Sabarinathan, P. Bhattacharya, B. Kochman, E. W. Berg, P. C. Yu, and S. W. Pang, “Characteristics of a photonic bandgap single defect microcavity electroluminescent device,” IEEE J. Quantum Electron. 37, 1153-1160 (2001).
[Crossref]

J. Comput. Phys. (1)

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

J. Opt. Soc. Am. B (3)

Phys. Rev. B (3)

P. R. Villeneuve and M. Piche, “Photonic band gaps in two-dimensional square and hexagonal lattices,” Phys. Rev. B 46, 4969-4972 (1992).
[Crossref]

V. Kuzmiak and A. A. Maradudin, “Localized defect modes in a two-dimensional triangular photonic crystal,” Phys. Rev. B 57, 15242-15250 (1998).
[Crossref]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837-7842 (1996).
[Crossref]

Phys. Rev. Lett. (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
[Crossref] [PubMed]

Other (7)

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

J. D. Brown and E. G. Johnson, “Micro-cavity resonator optimization using particle swarm optimization,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2007), paper ITuF6.

R. C. Eberhart, P. K. Simpson, and R. W. Dobbins, Computational Intelligence PC Tools, 1st ed. (Academic, 1996).

R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (IEEE, 1995), pp. 39-43.
[Crossref]

J. Kennedy and R. C. Eberhart “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks Vol. IV (IEEE, 1995), pp. 1942-1948.
[Crossref]

J. Kennedy, “The particle swarm: social adaptation of knowledge,” Proceedings of IEEE International Conference on Evolutionary Computation (IEEE, 1997), pp. 303-308.

A. Taflove, Computational Electrodynamics: The Finite--Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Supplementary Material (2)

» Media 1: AVI (3547 KB)     
» Media 2: AVI (3238 KB)     

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Figures (3)

Fig. 1
Fig. 1

Convergence results of notch-filter designs. The filter is optimized (a) using fitness function of wavelength, (b) using fitness function of normalized transmission; (c) convergence results of dielectric constant corresponding to desired resonant wavelength, and (d) convergence results of dielectric constant and resonant wavelength simultaneously during 20 iterations.

Fig. 2
Fig. 2

(a) Our designed notch filter based on microcavity. (b) Optical power transmission characteristic of this filter.

Fig. 3
Fig. 3

Single-frame excerpts from video recordings of electric field intensity of the notch filter, achieved by FDTD at (a) λ 1 = 1500 nm (Media 1) and (b) λ 2 = 1578 nm (Media 2).

Tables (1)

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Table 1 The Pseudocode of the Algorithm Used in Our Design

Equations (2)

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Δ ɛ r = Δ ɛ r + C 1 * rand ( ) * ( ɛ r ( pbest ) ɛ r ) + C 2 * rand ( ) * ( ɛ r ( gbest ) * ɛ r ) ,
ɛ r = ɛ r + Δ ɛ r ,

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