Abstract

This paper reports a new designed square lattice GaAs structure of two-dimensional photonic crystals with absolute band gap approach to 0.1623 (2πc/a), where a is the period of the square lattice. The optimal structure is obtained by combining the Geometry Projection Method and Finite Element Method. Both gradient information and symmetric control points are introduced to reduce the calculation cost. For benefit to the fabrication in reality, the structure is simplified by the combination of triangle and rectangular geometry. Through parameter optimization, the absolute band gap of the new structure is improved to 0.1735 (2πc/a), which is much larger than those reported before. The new PC structure is convenient and stab for fabrication, and may be found applications in the future optical devices.

© 2011 OSA

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  1. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
    [CrossRef] [PubMed]
  2. L. F. Shen, S. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66(16), 165315 (2002).
    [CrossRef]
  3. H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282(14), 3012–3017 (2009).
    [CrossRef]
  4. S. Zarei, M. Shahabadi, and S. Mohajerzadeh, “Symmetry reduction for maximization of higher-order stop-bands in two-dimensional photonic crystals,” J. Mod. Opt. 55(18), 2971–2980 (2008).
    [CrossRef]
  5. L. F. Shen, Z. Ye, and S. L. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
    [CrossRef]
  6. M. Qiu and S. He, “Optimal design of a two-dimensional photonic crystal of square lattice with a large complete two-dimensional band gap,” J. Opt. Soc. Am. B 17(6), 1027–1030 (2000).
    [CrossRef]
  7. W. L. Liu and T. J. Yang, “Engineering the band-gap of a two-dimensional photonic crystal with slender dielectric veins,” Phys. Lett. A 369(5-6), 518–523 (2007).
    [CrossRef]
  8. F. Wen, S. David, X. Checoury, M. El Kurdi, and P. Boucaud, “Two-dimensional photonic crystals with large complete photonic band gaps in both TE and TM polarizations,” Opt. Express 16(16), 12278–12289 (2008).
    [CrossRef] [PubMed]
  9. O. Sigmund and K. Hougaard, “Geometric properties of optimal photonic crystals,” Phys. Rev. Lett. 100(15), 153904 (2008).
    [CrossRef] [PubMed]
  10. H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined band gaps,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046703 (2011).
    [CrossRef] [PubMed]
  11. J. Norato, R. Haber, D. Tortorelli, and M. P. Bendsoe, “A geometry projection method for shape optimization,” Int. J. Numer. Methods Eng. 60(14), 2289–2312 (2004).
    [CrossRef]
  12. W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
    [CrossRef]
  13. S. Preble, M. Lipson, and H. Lipson, “Two-dimensional photonic crystals designed by evolutionary algorithms,” Appl. Phys. Lett. 86(6), 061111 (2005).
    [CrossRef]
  14. O. Sigmund and J. Petersson, “Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima,” Struct. Optim. 16(1), 68–75 (1998).
    [CrossRef]
  15. W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Geometry projection method for optimizing photonic nanostructures,” Opt. Lett. 32(1), 77–79 (2007).
    [CrossRef] [PubMed]
  16. G. Turk and J. F. O’Brien, “Modeling with Implicit Surfaces that Interpolate,” ACM Trans. Graph. 21(4), 855–873 (2002).
    [CrossRef]
  17. H. Tian, Z. Yu, L. Han, and Y. Liu, “Birefringence and confinement loss properties in photonic crystal fibers under lateral stress,” IEEE Photon. Technol. Lett. 20(22), 1830–1832 (2008).
    [CrossRef]
  18. T. Hong-Da, Y. Zhong-Yuan, H. Li-Hong, and L. Yu-Min, “Lateral stress-induced propagation characteristics in photonic crystal fibres,” Chin. Phys. B 18(3), 1109–1115 (2009).
    [CrossRef]
  19. J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: low-loss waveguide bends,” Appl. Phys. Lett. 84(12), 2022–2024 (2004).
    [CrossRef]
  20. E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B 61(20), 13458–13464 (2000).
    [CrossRef]

2011

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined band gaps,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046703 (2011).
[CrossRef] [PubMed]

2009

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282(14), 3012–3017 (2009).
[CrossRef]

T. Hong-Da, Y. Zhong-Yuan, H. Li-Hong, and L. Yu-Min, “Lateral stress-induced propagation characteristics in photonic crystal fibres,” Chin. Phys. B 18(3), 1109–1115 (2009).
[CrossRef]

2008

S. Zarei, M. Shahabadi, and S. Mohajerzadeh, “Symmetry reduction for maximization of higher-order stop-bands in two-dimensional photonic crystals,” J. Mod. Opt. 55(18), 2971–2980 (2008).
[CrossRef]

F. Wen, S. David, X. Checoury, M. El Kurdi, and P. Boucaud, “Two-dimensional photonic crystals with large complete photonic band gaps in both TE and TM polarizations,” Opt. Express 16(16), 12278–12289 (2008).
[CrossRef] [PubMed]

O. Sigmund and K. Hougaard, “Geometric properties of optimal photonic crystals,” Phys. Rev. Lett. 100(15), 153904 (2008).
[CrossRef] [PubMed]

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[CrossRef]

H. Tian, Z. Yu, L. Han, and Y. Liu, “Birefringence and confinement loss properties in photonic crystal fibers under lateral stress,” IEEE Photon. Technol. Lett. 20(22), 1830–1832 (2008).
[CrossRef]

2007

W. L. Liu and T. J. Yang, “Engineering the band-gap of a two-dimensional photonic crystal with slender dielectric veins,” Phys. Lett. A 369(5-6), 518–523 (2007).
[CrossRef]

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Geometry projection method for optimizing photonic nanostructures,” Opt. Lett. 32(1), 77–79 (2007).
[CrossRef] [PubMed]

2005

S. Preble, M. Lipson, and H. Lipson, “Two-dimensional photonic crystals designed by evolutionary algorithms,” Appl. Phys. Lett. 86(6), 061111 (2005).
[CrossRef]

2004

J. Norato, R. Haber, D. Tortorelli, and M. P. Bendsoe, “A geometry projection method for shape optimization,” Int. J. Numer. Methods Eng. 60(14), 2289–2312 (2004).
[CrossRef]

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: low-loss waveguide bends,” Appl. Phys. Lett. 84(12), 2022–2024 (2004).
[CrossRef]

2003

L. F. Shen, Z. Ye, and S. L. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[CrossRef]

2002

L. F. Shen, S. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66(16), 165315 (2002).
[CrossRef]

G. Turk and J. F. O’Brien, “Modeling with Implicit Surfaces that Interpolate,” ACM Trans. Graph. 21(4), 855–873 (2002).
[CrossRef]

2000

M. Qiu and S. He, “Optimal design of a two-dimensional photonic crystal of square lattice with a large complete two-dimensional band gap,” J. Opt. Soc. Am. B 17(6), 1027–1030 (2000).
[CrossRef]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B 61(20), 13458–13464 (2000).
[CrossRef]

1998

O. Sigmund and J. Petersson, “Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima,” Struct. Optim. 16(1), 68–75 (1998).
[CrossRef]

1987

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

Bendsoe, M. P.

J. Norato, R. Haber, D. Tortorelli, and M. P. Bendsoe, “A geometry projection method for shape optimization,” Int. J. Numer. Methods Eng. 60(14), 2289–2312 (2004).
[CrossRef]

Boucaud, P.

Checoury, X.

Choquette, K. D.

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[CrossRef]

David, S.

Economou, E. N.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B 61(20), 13458–13464 (2000).
[CrossRef]

El Kurdi, M.

Frei, W. R.

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[CrossRef]

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Geometry projection method for optimizing photonic nanostructures,” Opt. Lett. 32(1), 77–79 (2007).
[CrossRef] [PubMed]

Freund, R. M.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined band gaps,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046703 (2011).
[CrossRef] [PubMed]

Haber, R.

J. Norato, R. Haber, D. Tortorelli, and M. P. Bendsoe, “A geometry projection method for shape optimization,” Int. J. Numer. Methods Eng. 60(14), 2289–2312 (2004).
[CrossRef]

Han, L.

H. Tian, Z. Yu, L. Han, and Y. Liu, “Birefringence and confinement loss properties in photonic crystal fibers under lateral stress,” IEEE Photon. Technol. Lett. 20(22), 1830–1832 (2008).
[CrossRef]

He, S.

L. F. Shen, S. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66(16), 165315 (2002).
[CrossRef]

M. Qiu and S. He, “Optimal design of a two-dimensional photonic crystal of square lattice with a large complete two-dimensional band gap,” J. Opt. Soc. Am. B 17(6), 1027–1030 (2000).
[CrossRef]

He, S. L.

L. F. Shen, Z. Ye, and S. L. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[CrossRef]

Hong-Da, T.

T. Hong-Da, Y. Zhong-Yuan, H. Li-Hong, and L. Yu-Min, “Lateral stress-induced propagation characteristics in photonic crystal fibres,” Chin. Phys. B 18(3), 1109–1115 (2009).
[CrossRef]

Hougaard, K.

O. Sigmund and K. Hougaard, “Geometric properties of optimal photonic crystals,” Phys. Rev. Lett. 100(15), 153904 (2008).
[CrossRef] [PubMed]

Jensen, J. S.

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: low-loss waveguide bends,” Appl. Phys. Lett. 84(12), 2022–2024 (2004).
[CrossRef]

Jia, W.

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282(14), 3012–3017 (2009).
[CrossRef]

Jiang, L. Y.

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282(14), 3012–3017 (2009).
[CrossRef]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

Johnson, H. T.

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[CrossRef]

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Geometry projection method for optimizing photonic nanostructures,” Opt. Lett. 32(1), 77–79 (2007).
[CrossRef] [PubMed]

Li, H. P.

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282(14), 3012–3017 (2009).
[CrossRef]

Li, X. Y.

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282(14), 3012–3017 (2009).
[CrossRef]

Lidorikis, E.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B 61(20), 13458–13464 (2000).
[CrossRef]

Li-Hong, H.

T. Hong-Da, Y. Zhong-Yuan, H. Li-Hong, and L. Yu-Min, “Lateral stress-induced propagation characteristics in photonic crystal fibres,” Chin. Phys. B 18(3), 1109–1115 (2009).
[CrossRef]

Lim, K. M.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined band gaps,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046703 (2011).
[CrossRef] [PubMed]

Lipson, H.

S. Preble, M. Lipson, and H. Lipson, “Two-dimensional photonic crystals designed by evolutionary algorithms,” Appl. Phys. Lett. 86(6), 061111 (2005).
[CrossRef]

Lipson, M.

S. Preble, M. Lipson, and H. Lipson, “Two-dimensional photonic crystals designed by evolutionary algorithms,” Appl. Phys. Lett. 86(6), 061111 (2005).
[CrossRef]

Liu, W. L.

W. L. Liu and T. J. Yang, “Engineering the band-gap of a two-dimensional photonic crystal with slender dielectric veins,” Phys. Lett. A 369(5-6), 518–523 (2007).
[CrossRef]

Liu, Y.

H. Tian, Z. Yu, L. Han, and Y. Liu, “Birefringence and confinement loss properties in photonic crystal fibers under lateral stress,” IEEE Photon. Technol. Lett. 20(22), 1830–1832 (2008).
[CrossRef]

Men, H.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined band gaps,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046703 (2011).
[CrossRef] [PubMed]

Mohajerzadeh, S.

S. Zarei, M. Shahabadi, and S. Mohajerzadeh, “Symmetry reduction for maximization of higher-order stop-bands in two-dimensional photonic crystals,” J. Mod. Opt. 55(18), 2971–2980 (2008).
[CrossRef]

Nguyen, N. C.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined band gaps,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046703 (2011).
[CrossRef] [PubMed]

Norato, J.

J. Norato, R. Haber, D. Tortorelli, and M. P. Bendsoe, “A geometry projection method for shape optimization,” Int. J. Numer. Methods Eng. 60(14), 2289–2312 (2004).
[CrossRef]

O’Brien, J. F.

G. Turk and J. F. O’Brien, “Modeling with Implicit Surfaces that Interpolate,” ACM Trans. Graph. 21(4), 855–873 (2002).
[CrossRef]

Parrilo, P. A.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined band gaps,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046703 (2011).
[CrossRef] [PubMed]

Peraire, J.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined band gaps,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046703 (2011).
[CrossRef] [PubMed]

Petersson, J.

O. Sigmund and J. Petersson, “Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima,” Struct. Optim. 16(1), 68–75 (1998).
[CrossRef]

Preble, S.

S. Preble, M. Lipson, and H. Lipson, “Two-dimensional photonic crystals designed by evolutionary algorithms,” Appl. Phys. Lett. 86(6), 061111 (2005).
[CrossRef]

Qiang, H. X.

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282(14), 3012–3017 (2009).
[CrossRef]

Qiu, M.

Shahabadi, M.

S. Zarei, M. Shahabadi, and S. Mohajerzadeh, “Symmetry reduction for maximization of higher-order stop-bands in two-dimensional photonic crystals,” J. Mod. Opt. 55(18), 2971–2980 (2008).
[CrossRef]

Shen, L. F.

L. F. Shen, Z. Ye, and S. L. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[CrossRef]

L. F. Shen, S. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66(16), 165315 (2002).
[CrossRef]

Sigalas, M. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B 61(20), 13458–13464 (2000).
[CrossRef]

Sigmund, O.

O. Sigmund and K. Hougaard, “Geometric properties of optimal photonic crystals,” Phys. Rev. Lett. 100(15), 153904 (2008).
[CrossRef] [PubMed]

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: low-loss waveguide bends,” Appl. Phys. Lett. 84(12), 2022–2024 (2004).
[CrossRef]

O. Sigmund and J. Petersson, “Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima,” Struct. Optim. 16(1), 68–75 (1998).
[CrossRef]

Soukoulis, C. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B 61(20), 13458–13464 (2000).
[CrossRef]

Tian, H.

H. Tian, Z. Yu, L. Han, and Y. Liu, “Birefringence and confinement loss properties in photonic crystal fibers under lateral stress,” IEEE Photon. Technol. Lett. 20(22), 1830–1832 (2008).
[CrossRef]

Tortorelli, D.

J. Norato, R. Haber, D. Tortorelli, and M. P. Bendsoe, “A geometry projection method for shape optimization,” Int. J. Numer. Methods Eng. 60(14), 2289–2312 (2004).
[CrossRef]

Tortorelli, D. A.

Turk, G.

G. Turk and J. F. O’Brien, “Modeling with Implicit Surfaces that Interpolate,” ACM Trans. Graph. 21(4), 855–873 (2002).
[CrossRef]

Wen, F.

Xiao, S. S.

L. F. Shen, S. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66(16), 165315 (2002).
[CrossRef]

Yang, T. J.

W. L. Liu and T. J. Yang, “Engineering the band-gap of a two-dimensional photonic crystal with slender dielectric veins,” Phys. Lett. A 369(5-6), 518–523 (2007).
[CrossRef]

Ye, Z.

L. F. Shen, Z. Ye, and S. L. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[CrossRef]

Yu, Z.

H. Tian, Z. Yu, L. Han, and Y. Liu, “Birefringence and confinement loss properties in photonic crystal fibers under lateral stress,” IEEE Photon. Technol. Lett. 20(22), 1830–1832 (2008).
[CrossRef]

Yu-Min, L.

T. Hong-Da, Y. Zhong-Yuan, H. Li-Hong, and L. Yu-Min, “Lateral stress-induced propagation characteristics in photonic crystal fibres,” Chin. Phys. B 18(3), 1109–1115 (2009).
[CrossRef]

Zarei, S.

S. Zarei, M. Shahabadi, and S. Mohajerzadeh, “Symmetry reduction for maximization of higher-order stop-bands in two-dimensional photonic crystals,” J. Mod. Opt. 55(18), 2971–2980 (2008).
[CrossRef]

Zhong-Yuan, Y.

T. Hong-Da, Y. Zhong-Yuan, H. Li-Hong, and L. Yu-Min, “Lateral stress-induced propagation characteristics in photonic crystal fibres,” Chin. Phys. B 18(3), 1109–1115 (2009).
[CrossRef]

ACM Trans. Graph.

G. Turk and J. F. O’Brien, “Modeling with Implicit Surfaces that Interpolate,” ACM Trans. Graph. 21(4), 855–873 (2002).
[CrossRef]

Appl. Phys. Lett.

S. Preble, M. Lipson, and H. Lipson, “Two-dimensional photonic crystals designed by evolutionary algorithms,” Appl. Phys. Lett. 86(6), 061111 (2005).
[CrossRef]

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: low-loss waveguide bends,” Appl. Phys. Lett. 84(12), 2022–2024 (2004).
[CrossRef]

Chin. Phys. B

T. Hong-Da, Y. Zhong-Yuan, H. Li-Hong, and L. Yu-Min, “Lateral stress-induced propagation characteristics in photonic crystal fibres,” Chin. Phys. B 18(3), 1109–1115 (2009).
[CrossRef]

IEEE Photon. Technol. Lett.

H. Tian, Z. Yu, L. Han, and Y. Liu, “Birefringence and confinement loss properties in photonic crystal fibers under lateral stress,” IEEE Photon. Technol. Lett. 20(22), 1830–1832 (2008).
[CrossRef]

Int. J. Numer. Methods Eng.

J. Norato, R. Haber, D. Tortorelli, and M. P. Bendsoe, “A geometry projection method for shape optimization,” Int. J. Numer. Methods Eng. 60(14), 2289–2312 (2004).
[CrossRef]

J. Appl. Phys.

W. R. Frei, H. T. Johnson, and K. D. Choquette, “Optimization of a single defect photonic crystal laser cavity,” J. Appl. Phys. 103(3), 033102 (2008).
[CrossRef]

J. Mod. Opt.

S. Zarei, M. Shahabadi, and S. Mohajerzadeh, “Symmetry reduction for maximization of higher-order stop-bands in two-dimensional photonic crystals,” J. Mod. Opt. 55(18), 2971–2980 (2008).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

H. P. Li, L. Y. Jiang, W. Jia, H. X. Qiang, and X. Y. Li, “Genetic optimization of two-dimensional photonic crystals for large absolute band-gap,” Opt. Commun. 282(14), 3012–3017 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

W. L. Liu and T. J. Yang, “Engineering the band-gap of a two-dimensional photonic crystal with slender dielectric veins,” Phys. Lett. A 369(5-6), 518–523 (2007).
[CrossRef]

Phys. Rev. B

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B 61(20), 13458–13464 (2000).
[CrossRef]

L. F. Shen, Z. Ye, and S. L. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68(3), 035109 (2003).
[CrossRef]

L. F. Shen, S. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66(16), 165315 (2002).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined band gaps,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046703 (2011).
[CrossRef] [PubMed]

Phys. Rev. Lett.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

O. Sigmund and K. Hougaard, “Geometric properties of optimal photonic crystals,” Phys. Rev. Lett. 100(15), 153904 (2008).
[CrossRef] [PubMed]

Struct. Optim.

O. Sigmund and J. Petersson, “Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima,” Struct. Optim. 16(1), 68–75 (1998).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

The primary symmetries of the unit cell of a square lattice 2D PC, one-eighth unit cell is selected to calculate.

Fig. 2
Fig. 2

The band structure of the initial structure, the solid lines are for the H polarization (TM) and the dashed lines for the E polarization (TE).

Fig. 3
Fig. 3

The schema of the GPM, the distribution of the dielectric can be controlled by control points.

Fig. 4
Fig. 4

The sensitivity information of the absolute band gap to the initial dielectric structure. Left is the initial dielectric distribution of the 2D PC. Right is the sensitivity distribution, red represents the positive value, blue is the negative value.

Fig. 5
Fig. 5

The new structure with an absolute band gap of 0.1623 (2πc/a) is found by our method. Blue is the dielectric material distribution, and white indicates air.

Fig. 6
Fig. 6

The band structure of the new PC structure.

Fig. 7
Fig. 7

The parameterized structure of the new PC structure, 12 geometric parameters are used to define the simplified structure.

Fig. 8
Fig. 8

The band structure of the optimal 2D PC structure with optimal parameters: r1 = 0.2918, w1 = 0.0284, h1 = 0.0501, k1 = 0.0656, b1 = 0.0203, θ1 = 48.6597°, r2 = 0.3125, w2 = 0.0228, h2 = 0.1203, k2 = 0.1164, b2 = 0.0447 and θ2 = 52.8430°.

Equations (4)

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S ( x ) = c 0 + c x + p λ p Φ ( | x x p | ) ,
Φ ( r ) = r 2 log r ,
ε r ( x ) = ε r , min + ( ε r , max ε r , min ) 2 ( tanh [ s i g n [ S ( x ) ] d ( x ) ξ ] + 1 ) ,
d ( x ) = min x | x x 0 | ,

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