Abstract

The finite-element method including simulated annealing algorithm is adopted for the analysis and optimization of photonic-crystal waveguiding structures. The dispersion relations of the photonic-crystal waveguides are found by solution of an eigenvalue equation. The waveguide structures including bends and branches are analyzed by use of a scattering formulation. The symmetry of the structure is exploited to classify the modes as well as to reduce the computations. Based on the transmission spectra of a waveguide’s bends and branches, a branch is optimized by use of the simulated annealing algorithm.

© 2004 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. O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic crystal defect laser,” Science 284, 1819–1821 (1999).
    [CrossRef] [PubMed]
  4. T. Baba, N. Fukaya, and Y. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
    [CrossRef]
  5. M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991).
    [CrossRef]
  6. S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
    [CrossRef]
  7. H. Y. D. Yang, “Finite difference analysis of 2-D photonic crystals,” IEEE Trans. Microwave Theory Tech. 44, 2688–2695 (1996).
    [CrossRef]
  8. A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
    [CrossRef]
  9. G. Tayeb and D. Maystre, “Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities,” J. Opt. Soc. Am. A 14, 3323–3332 (1997).
    [CrossRef]
  10. W. Zhang, C. T. Chan, and P. Sheng, “Multiple scattering theory and its application to photonic band gap systems consisting of coated spheres,” Opt. Express 8, 203–208 (2001), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  11. P. Lalanne, “Effective medium theory applied to photonic crystals composed of cubic or square cylinders,” Appl. Opt. 35, 5369–5380 (1996).
    [CrossRef] [PubMed]
  12. E. Popov and B. Bozhkov, “Differential method applied for photonic crystals,” Appl. Opt. 39, 4926–4932 (2000).
    [CrossRef]
  13. C. Mias, J. P. Webb, and R. I. Ferrari, “Finite element eigenvalue analysis of periodic structures,” in IEE Colloquium on Semiconductor Optical Microcavity Devices and Photonic Bandgaps, digest 1996/267 (Institute of Electrical Engineers, London, 1996).
  14. J.-K. Hwang, S.-B. Hyun, H. Y. Ryu, and Y.-H. Lee, “Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition,” J. Opt. Soc. Am. B 15, 2316–2324 (1998).
    [CrossRef]
  15. W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials,” J. Comput. Phys. 150, 468–481 (1999).
    [CrossRef]
  16. M. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” IEEE J. Quantum Electron. 18, 102–110 (2000).
  17. G. Pelosi, A. Cocchi, and A. Monorchio, “A hybrid FEM-based procedure for the scattering from photonic crystals illuminated by a Gaussian beam,” IEEE Trans. Antennas Propag. 48, 973–980 (2000).
    [CrossRef]
  18. D. C. Dobson, J. Gopalakrishnan, and J. E. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161, 668–679 (2000).
    [CrossRef]
  19. K. Sakoda, “Optical transmittance of a two-dimensional triangular photonic lattice,” Phys. Rev. B 51, 4672–4675 (1995).
    [CrossRef]
  20. N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
    [CrossRef]
  21. D. Hermann, M. Frank, K. Busch, and P. Wölfle, “Photonic band structure computations,” Opt. Express 8, 167–190 (2001), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  22. M. A. Haider, S. P. Shipman, and S. Venakides, “Boundary-integral calculations of two-dimensional electromagnetic scattering in infinite photonic crystal slabs: channel defects and resonances,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 62, 2129–2148 (2002).
    [CrossRef]
  23. S. P. Peet and R. L. Ferrari, Finite Elements for Electrical Engineers, 3rd ed. (Cambridge U. Press, Cambridge, 1996), Chap. 8.
  24. http://www.netlib.org/linalg/spooles/spooles.2.2.html.
  25. http://www.ime.unicamp.br/chico/arpack++/.
  26. J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  27. Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
    [CrossRef]
  28. S. Boscolo, C. Conti, M. Midrio, and C. G. Someda, “Numerical analysis of propagation and impedance matching in 2D photonic crystal waveguides with finite length,” J. Lightwave Technol. 20, 304–310 (2002).
    [CrossRef]
  29. S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).
    [CrossRef]
  30. S. Boscolo, M. Midrio, and T. F. Krauss, “Y junctions in photonic crystal channel waveguides: high transmission and impedance matching,” Opt. Lett. 27, 1001–1003 (2002).
    [CrossRef]
  31. A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 80, 1698–1700 (2002).
    [CrossRef]
  32. A. Sharkawy, S. Shi, and D. W. Prather, “Heterostructure photonic crystals: theory and applications,” Appl. Opt. 41, 7245–7253 (2002).
    [CrossRef] [PubMed]

2002 (5)

M. A. Haider, S. P. Shipman, and S. Venakides, “Boundary-integral calculations of two-dimensional electromagnetic scattering in infinite photonic crystal slabs: channel defects and resonances,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 62, 2129–2148 (2002).
[CrossRef]

S. Boscolo, C. Conti, M. Midrio, and C. G. Someda, “Numerical analysis of propagation and impedance matching in 2D photonic crystal waveguides with finite length,” J. Lightwave Technol. 20, 304–310 (2002).
[CrossRef]

S. Boscolo, M. Midrio, and T. F. Krauss, “Y junctions in photonic crystal channel waveguides: high transmission and impedance matching,” Opt. Lett. 27, 1001–1003 (2002).
[CrossRef]

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 80, 1698–1700 (2002).
[CrossRef]

A. Sharkawy, S. Shi, and D. W. Prather, “Heterostructure photonic crystals: theory and applications,” Appl. Opt. 41, 7245–7253 (2002).
[CrossRef] [PubMed]

2001 (3)

2000 (6)

E. Popov and B. Bozhkov, “Differential method applied for photonic crystals,” Appl. Opt. 39, 4926–4932 (2000).
[CrossRef]

M. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” IEEE J. Quantum Electron. 18, 102–110 (2000).

G. Pelosi, A. Cocchi, and A. Monorchio, “A hybrid FEM-based procedure for the scattering from photonic crystals illuminated by a Gaussian beam,” IEEE Trans. Antennas Propag. 48, 973–980 (2000).
[CrossRef]

D. C. Dobson, J. Gopalakrishnan, and J. E. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161, 668–679 (2000).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

1999 (3)

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic crystal defect laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

T. Baba, N. Fukaya, and Y. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
[CrossRef]

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials,” J. Comput. Phys. 150, 468–481 (1999).
[CrossRef]

1998 (2)

1997 (1)

1996 (2)

H. Y. D. Yang, “Finite difference analysis of 2-D photonic crystals,” IEEE Trans. Microwave Theory Tech. 44, 2688–2695 (1996).
[CrossRef]

P. Lalanne, “Effective medium theory applied to photonic crystals composed of cubic or square cylinders,” Appl. Opt. 35, 5369–5380 (1996).
[CrossRef] [PubMed]

1995 (2)

K. Sakoda, “Optical transmittance of a two-dimensional triangular photonic lattice,” Phys. Rev. B 51, 4672–4675 (1995).
[CrossRef]

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

1994 (1)

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

1991 (1)

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991).
[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]

Axmann, W.

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials,” J. Comput. Phys. 150, 468–481 (1999).
[CrossRef]

Baba, T.

T. Baba, N. Fukaya, and Y. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
[CrossRef]

Berenger, J.-P.

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

Boscolo, S.

Bozhkov, B.

Busch, K.

Chan, C. T.

Chutinan, A.

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 80, 1698–1700 (2002).
[CrossRef]

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

Cocchi, A.

G. Pelosi, A. Cocchi, and A. Monorchio, “A hybrid FEM-based procedure for the scattering from photonic crystals illuminated by a Gaussian beam,” IEEE Trans. Antennas Propag. 48, 973–980 (2000).
[CrossRef]

Conti, C.

Dapkus, P. D.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic crystal defect laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Dobson, D. C.

D. C. Dobson, J. Gopalakrishnan, and J. E. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161, 668–679 (2000).
[CrossRef]

Fan, S.

S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

Frank, M.

Fukaya, N.

T. Baba, N. Fukaya, and Y. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
[CrossRef]

Gopalakrishnan, J.

D. C. Dobson, J. Gopalakrishnan, and J. E. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161, 668–679 (2000).
[CrossRef]

Haider, M. A.

M. A. Haider, S. P. Shipman, and S. Venakides, “Boundary-integral calculations of two-dimensional electromagnetic scattering in infinite photonic crystal slabs: channel defects and resonances,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 62, 2129–2148 (2002).
[CrossRef]

Haus, H. A.

Hermann, D.

Hikari, M.

M. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” IEEE J. Quantum Electron. 18, 102–110 (2000).

Hwang, J.-K.

Hyun, S.-B.

Joannopoulos, J. D.

S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

John, S.

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

Johnson, S. G.

S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

Kim, I.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic crystal defect laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Kingsland, D. M.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

Koshiba, M.

M. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” IEEE J. Quantum Electron. 18, 102–110 (2000).

Krauss, T. F.

Kuchment, P.

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials,” J. Comput. Phys. 150, 468–481 (1999).
[CrossRef]

Lalanne, P.

Lee, J.-F.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

Lee, R.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

Lee, R. K.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic crystal defect laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Lee, Y.-H.

Manolatou, C.

Maradudin, A. A.

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991).
[CrossRef]

Maystre, D.

Midrio, M.

Modinos, A.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[CrossRef]

Monorchio, A.

G. Pelosi, A. Cocchi, and A. Monorchio, “A hybrid FEM-based procedure for the scattering from photonic crystals illuminated by a Gaussian beam,” IEEE Trans. Antennas Propag. 48, 973–980 (2000).
[CrossRef]

Noda, S.

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 80, 1698–1700 (2002).
[CrossRef]

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

O’Brien, J. D.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic crystal defect laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Okano, M.

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 80, 1698–1700 (2002).
[CrossRef]

Painter, O.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic crystal defect laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Pasciak, J. E.

D. C. Dobson, J. Gopalakrishnan, and J. E. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161, 668–679 (2000).
[CrossRef]

Pelosi, G.

G. Pelosi, A. Cocchi, and A. Monorchio, “A hybrid FEM-based procedure for the scattering from photonic crystals illuminated by a Gaussian beam,” IEEE Trans. Antennas Propag. 48, 973–980 (2000).
[CrossRef]

Plihal, M.

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991).
[CrossRef]

Popov, E.

Prather, D. W.

Ryu, H. Y.

Sacks, Z. S.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

Sakoda, K.

K. Sakoda, “Optical transmittance of a two-dimensional triangular photonic lattice,” Phys. Rev. B 51, 4672–4675 (1995).
[CrossRef]

Scherer, A.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic crystal defect laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Sharkawy, A.

Sheng, P.

Shi, S.

Shipman, S. P.

M. A. Haider, S. P. Shipman, and S. Venakides, “Boundary-integral calculations of two-dimensional electromagnetic scattering in infinite photonic crystal slabs: channel defects and resonances,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 62, 2129–2148 (2002).
[CrossRef]

Someda, C. G.

Stefanou, N.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[CrossRef]

Tayeb, G.

Tsuji, Y.

M. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” IEEE J. Quantum Electron. 18, 102–110 (2000).

Venakides, S.

M. A. Haider, S. P. Shipman, and S. Venakides, “Boundary-integral calculations of two-dimensional electromagnetic scattering in infinite photonic crystal slabs: channel defects and resonances,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 62, 2129–2148 (2002).
[CrossRef]

Villeneuve, P. R.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

Wölfle, P.

Yablonovitch, E.

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

Yang, H. Y. D.

H. Y. D. Yang, “Finite difference analysis of 2-D photonic crystals,” IEEE Trans. Microwave Theory Tech. 44, 2688–2695 (1996).
[CrossRef]

Yannopapas, V.

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[CrossRef]

Yariv, A.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic crystal defect laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Yonekura, Y.

T. Baba, N. Fukaya, and Y. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
[CrossRef]

Zhang, W.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 80, 1698–1700 (2002).
[CrossRef]

Comput. Phys. Commun. (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[CrossRef]

Electron. Lett. (1)

T. Baba, N. Fukaya, and Y. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” IEEE J. Quantum Electron. 18, 102–110 (2000).

IEEE Trans. Antennas Propag. (2)

G. Pelosi, A. Cocchi, and A. Monorchio, “A hybrid FEM-based procedure for the scattering from photonic crystals illuminated by a Gaussian beam,” IEEE Trans. Antennas Propag. 48, 973–980 (2000).
[CrossRef]

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

H. Y. D. Yang, “Finite difference analysis of 2-D photonic crystals,” IEEE Trans. Microwave Theory Tech. 44, 2688–2695 (1996).
[CrossRef]

J. Comput. Phys. (3)

D. C. Dobson, J. Gopalakrishnan, and J. E. Pasciak, “An efficient method for band structure calculations in 3D photonic crystals,” J. Comput. Phys. 161, 668–679 (2000).
[CrossRef]

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials,” J. Comput. Phys. 150, 468–481 (1999).
[CrossRef]

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

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

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

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (4)

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565–8571 (1991).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

K. Sakoda, “Optical transmittance of a two-dimensional triangular photonic lattice,” Phys. Rev. B 51, 4672–4675 (1995).
[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]

Science (1)

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic crystal defect laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. (1)

M. A. Haider, S. P. Shipman, and S. Venakides, “Boundary-integral calculations of two-dimensional electromagnetic scattering in infinite photonic crystal slabs: channel defects and resonances,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 62, 2129–2148 (2002).
[CrossRef]

Other (4)

S. P. Peet and R. L. Ferrari, Finite Elements for Electrical Engineers, 3rd ed. (Cambridge U. Press, Cambridge, 1996), Chap. 8.

http://www.netlib.org/linalg/spooles/spooles.2.2.html.

http://www.ime.unicamp.br/chico/arpack++/.

C. Mias, J. P. Webb, and R. I. Ferrari, “Finite element eigenvalue analysis of periodic structures,” in IEE Colloquium on Semiconductor Optical Microcavity Devices and Photonic Bandgaps, digest 1996/267 (Institute of Electrical Engineers, London, 1996).

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Figures (4)

Fig. 1
Fig. 1

(a) Unit cell of the 2D triangular lattice photonic-crystal waveguide. Only the half of the structure is shown for 2D simulation (top), and a quarter of the structure for 3D simulation (bottom). (b) Dispersion relations of the waveguides. The boundary condition for the line of symmetry (dashed line) is PEC for the odd mode and PMC for the even mode. The line from (0, 0) to (0.4, 0.4) denotes the air light line.

Fig. 2
Fig. 2

(a) Computational domain of the photonic-crystal waveguide transmittance calculation. The open boundary encompases a PML backed by a PEC boundary condition. The even and odd modes are excited by a dipole source with different orientations, defined by the line (-12, 0)–(-12, 0.3) for the odd mode and (-12.3, 0)–(-12, 0) for the even mode. The boundary condition for the line of symmetry (dashed line) is PEC for the odd mode and PMC for the even mode. (b) Transmission spectra of the waveguide. The frequency range of each mode is derived from the eigenmode calculation.

Fig. 3
Fig. 3

Computational domain of the calculation of waveguide bend and branch transmittance. The odd modes are excited by the dipole source, defined by the lines (-12, -1.432)–(-12, -2.032) for the bend and (-12, 0)–(-12, 0.3) for the branch. (b) Transmission spectra of waveguide bend and branch. The spectrum of the straight waveguide is also plotted for reference.

Fig. 4
Fig. 4

Picture of the junction. The numbered holes are those whose radii vary. Owing to symmetry, only half of the branch needs to be optimized. (a) Picture of optimized branch BR1 (Table 1). (b) Transmission spectra of the optimized waveguide branches.

Tables (1)

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Table 1 Optimized Branches

Equations (4)

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×[μr]-1×E-k02[r]E=f,
Ω×W·[μr]-1×EdΩ-k02ΩW·[r]EdΩ-ΩW·[μr]-1×E·dS=ΩW·fdΩ,
Ω×wm·[μr]-1×wn-k02wm[r]wndΩ=Ωwm·fdΩ,
Ω×wm·[μr]-1×wndΩ=k02Ωwm·[r]wndΩ,

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