Abstract

Various bending waveguides with different bending angles in photonic crystal are proposed and studied. Analyses show that the bending waveguides can provide a high transmission for the whole frequencies within the photonic band gap. Numerical simulations confirm that high transmissions over 98.5% can be achieved for the proposed waveguides.

© 2006 Optical Society of America

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References

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  1. S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
    [CrossRef] [PubMed]
  2. T. Baba, N. Fukaya, and J. Yonekura, "Observation of light propagation in photonic crystal optical waveguides with bends," Electron. Lett. 35, 654-655 (1999).
    [CrossRef]
  3. S. Yamada, T. Koyama, Y. Katayama, N. Ikeda, Y. Sugimoto, K, Asakawa, N. Kawai, and K. Inoue, "Observation of light propagation in two-dimensional photonic crystal-based bent optical waveguides," J. Appl. Phys. 89, 855-858 (2001).
    [CrossRef]
  4. A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs," Phys. Rev. B 62, 4488-4492 (2000).
    [CrossRef]
  5. M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides," Phys. Rev. B 63, 0811071-4 (2001).
    [CrossRef]
  6. M. Lončar, T. Doll, J. Vučković, and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave. Technol. 18, 1402-1411 (2000).
    [CrossRef]
  7. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
  8. A. Talneau, P. Lalanne, M. Agio, and C. M. Soukoulis, "Low-reflection photonic-crystal taper for efficient coupling," Opt. Lett. 27, 1522-1524 (2002).
    [CrossRef]
  9. A. Talneau, L. L. Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).
  10. J. Smajic, C. Hafner, and D. Erni, "Design and optimization of an achromatic photonic crystal bend," Opt. Express. 11, 1378-1384 (2003).
    [CrossRef] [PubMed]
  11. M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, "Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide," Appl. Phys. Lett. 76, 952-954 (2000).
    [CrossRef]
  12. N. Malkova and C. Z. Ning, "Photonic crystal waveguides with acute bending angles," Appl. Phys. Lett. 87, 1611131-3 (2005).
    [CrossRef]
  13. P. G. Luan and K. D. Chang, "Transmission characteristics of finite periodic dielectric waveguides," Opt. Express 14, 3263-3272 (2006).
    [CrossRef] [PubMed]
  14. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
    [CrossRef] [PubMed]

2006 (1)

2005 (1)

N. Malkova and C. Z. Ning, "Photonic crystal waveguides with acute bending angles," Appl. Phys. Lett. 87, 1611131-3 (2005).
[CrossRef]

2003 (1)

J. Smajic, C. Hafner, and D. Erni, "Design and optimization of an achromatic photonic crystal bend," Opt. Express. 11, 1378-1384 (2003).
[CrossRef] [PubMed]

2002 (2)

A. Talneau, L. L. Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).

A. Talneau, P. Lalanne, M. Agio, and C. M. Soukoulis, "Low-reflection photonic-crystal taper for efficient coupling," Opt. Lett. 27, 1522-1524 (2002).
[CrossRef]

2001 (3)

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides," Phys. Rev. B 63, 0811071-4 (2001).
[CrossRef]

S. Yamada, T. Koyama, Y. Katayama, N. Ikeda, Y. Sugimoto, K, Asakawa, N. Kawai, and K. Inoue, "Observation of light propagation in two-dimensional photonic crystal-based bent optical waveguides," J. Appl. Phys. 89, 855-858 (2001).
[CrossRef]

2000 (3)

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

M. Lončar, T. Doll, J. Vučković, and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave. Technol. 18, 1402-1411 (2000).
[CrossRef]

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, "Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide," Appl. Phys. Lett. 76, 952-954 (2000).
[CrossRef]

1999 (1)

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

1998 (1)

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

1996 (1)

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

Agio, M.

A. Talneau, L. L. Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).

A. Talneau, P. Lalanne, M. Agio, and C. M. Soukoulis, "Low-reflection photonic-crystal taper for efficient coupling," Opt. Lett. 27, 1522-1524 (2002).
[CrossRef]

Baba, T.

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

Bayindir, M.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides," Phys. Rev. B 63, 0811071-4 (2001).
[CrossRef]

Biswas, R.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides," Phys. Rev. B 63, 0811071-4 (2001).
[CrossRef]

Bouadma, N.

A. Talneau, L. L. Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).

Chang, K. D.

Chen, J. C.

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

Chow, E.

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Chutinan, A.

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

Doll, T.

M. Lončar, T. Doll, J. Vučković, and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave. Technol. 18, 1402-1411 (2000).
[CrossRef]

Erni, D.

J. Smajic, C. Hafner, and D. Erni, "Design and optimization of an achromatic photonic crystal bend," Opt. Express. 11, 1378-1384 (2003).
[CrossRef] [PubMed]

Fan, S.

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

Fukaya, N.

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

Gouezigou, L. L.

A. Talneau, L. L. Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).

Hafner, C.

J. Smajic, C. Hafner, and D. Erni, "Design and optimization of an achromatic photonic crystal bend," Opt. Express. 11, 1378-1384 (2003).
[CrossRef] [PubMed]

Hietala, V.

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Ho, K. M.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides," Phys. Rev. B 63, 0811071-4 (2001).
[CrossRef]

Ikeda, N.

S. Yamada, T. Koyama, Y. Katayama, N. Ikeda, Y. Sugimoto, K, Asakawa, N. Kawai, and K. Inoue, "Observation of light propagation in two-dimensional photonic crystal-based bent optical waveguides," J. Appl. Phys. 89, 855-858 (2001).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

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

Johnson, S. G.

Kafesaki, M.

A. Talneau, L. L. Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).

Katayama, Y.

S. Yamada, T. Koyama, Y. Katayama, N. Ikeda, Y. Sugimoto, K, Asakawa, N. Kawai, and K. Inoue, "Observation of light propagation in two-dimensional photonic crystal-based bent optical waveguides," J. Appl. Phys. 89, 855-858 (2001).
[CrossRef]

Kosaka, H.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, "Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide," Appl. Phys. Lett. 76, 952-954 (2000).
[CrossRef]

Koyama, T.

S. Yamada, T. Koyama, Y. Katayama, N. Ikeda, Y. Sugimoto, K, Asakawa, N. Kawai, and K. Inoue, "Observation of light propagation in two-dimensional photonic crystal-based bent optical waveguides," J. Appl. Phys. 89, 855-858 (2001).
[CrossRef]

Kurland, I.

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

Lalanne, P.

Lin, S. Y.

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Loncar, M.

M. Lončar, T. Doll, J. Vučković, and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave. Technol. 18, 1402-1411 (2000).
[CrossRef]

Luan, P. G.

Malkova, N.

N. Malkova and C. Z. Ning, "Photonic crystal waveguides with acute bending angles," Appl. Phys. Lett. 87, 1611131-3 (2005).
[CrossRef]

Mekis, A.

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

Ning, C. Z.

N. Malkova and C. Z. Ning, "Photonic crystal waveguides with acute bending angles," Appl. Phys. Lett. 87, 1611131-3 (2005).
[CrossRef]

Noda, S.

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

Ozbay, E.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides," Phys. Rev. B 63, 0811071-4 (2001).
[CrossRef]

Scherer, A.

M. Lončar, T. Doll, J. Vučković, and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave. Technol. 18, 1402-1411 (2000).
[CrossRef]

Sigalas, M. M.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides," Phys. Rev. B 63, 0811071-4 (2001).
[CrossRef]

Smajic, J.

J. Smajic, C. Hafner, and D. Erni, "Design and optimization of an achromatic photonic crystal bend," Opt. Express. 11, 1378-1384 (2003).
[CrossRef] [PubMed]

Soukoulis, C. M.

A. Talneau, L. L. Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).

A. Talneau, P. Lalanne, M. Agio, and C. M. Soukoulis, "Low-reflection photonic-crystal taper for efficient coupling," Opt. Lett. 27, 1522-1524 (2002).
[CrossRef]

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides," Phys. Rev. B 63, 0811071-4 (2001).
[CrossRef]

Sugimoto, Y.

S. Yamada, T. Koyama, Y. Katayama, N. Ikeda, Y. Sugimoto, K, Asakawa, N. Kawai, and K. Inoue, "Observation of light propagation in two-dimensional photonic crystal-based bent optical waveguides," J. Appl. Phys. 89, 855-858 (2001).
[CrossRef]

Talneau, A.

A. Talneau, L. L. Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).

A. Talneau, P. Lalanne, M. Agio, and C. M. Soukoulis, "Low-reflection photonic-crystal taper for efficient coupling," Opt. Lett. 27, 1522-1524 (2002).
[CrossRef]

Temelkuran, B.

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides," Phys. Rev. B 63, 0811071-4 (2001).
[CrossRef]

Tokushima, M.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, "Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide," Appl. Phys. Lett. 76, 952-954 (2000).
[CrossRef]

Tomita, A.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, "Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide," Appl. Phys. Lett. 76, 952-954 (2000).
[CrossRef]

Villeneuve, P. R.

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

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

Vuckovic, J.

M. Lončar, T. Doll, J. Vučković, and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave. Technol. 18, 1402-1411 (2000).
[CrossRef]

Yamada, H.

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, "Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide," Appl. Phys. Lett. 76, 952-954 (2000).
[CrossRef]

Yamada, S.

S. Yamada, T. Koyama, Y. Katayama, N. Ikeda, Y. Sugimoto, K, Asakawa, N. Kawai, and K. Inoue, "Observation of light propagation in two-dimensional photonic crystal-based bent optical waveguides," J. Appl. Phys. 89, 855-858 (2001).
[CrossRef]

Yonekura, J.

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

Appl. Phys. Lett. (3)

A. Talneau, L. L. Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, "Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm," Appl. Phys. Lett. 80, 547-549 (2002).

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, "Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide," Appl. Phys. Lett. 76, 952-954 (2000).
[CrossRef]

N. Malkova and C. Z. Ning, "Photonic crystal waveguides with acute bending angles," Appl. Phys. Lett. 87, 1611131-3 (2005).
[CrossRef]

Electron. Lett. (1)

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

J. Appl. Phys. (1)

S. Yamada, T. Koyama, Y. Katayama, N. Ikeda, Y. Sugimoto, K, Asakawa, N. Kawai, and K. Inoue, "Observation of light propagation in two-dimensional photonic crystal-based bent optical waveguides," J. Appl. Phys. 89, 855-858 (2001).
[CrossRef]

J. Lightwave. Technol. (1)

M. Lončar, T. Doll, J. Vučković, and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave. Technol. 18, 1402-1411 (2000).
[CrossRef]

Opt. Express (2)

Opt. Express. (1)

J. Smajic, C. Hafner, and D. Erni, "Design and optimization of an achromatic photonic crystal bend," Opt. Express. 11, 1378-1384 (2003).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. B (2)

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

M. Bayindir, E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides," Phys. Rev. B 63, 0811071-4 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

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

Science (1)

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

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Figures (12)

Fig. 1.
Fig. 1.

Schemes of the geometries of (a) the proposed 90° bending waveguide with an arc bend and (b) the compared bending waveguide with a beeline bend.

Fig. 2.
Fig. 2.

FDTD simulated distribution of steady-state electric field at ω 0=0.375(a/λ) of the proposed bending waveguide.

Fig. 3.
Fig. 3.

Reflection loss spectrum for the proposed bending waveguide and the compared bending waveguide.

Fig. 4.
Fig. 4.

Profiles of steady-state electric field at the frequency of 0.35(a/λ) for lightwaves in (a) the straight waveguide, (b) the arc bend of the proposed waveguide, and (c) the beeline bend of the compared waveguide.

Fig. 5.
Fig. 5.

Dispersion curves of k0, kb and k’b for the guided lightwaves in the straight waveguide, the beeline bend of the compared waveguide and the arc bend of the proposed waveguide, respectively.

Fig. 6.
Fig. 6.

(a) geometry of the arc bending corner in a 45° bending waveguide and (b) the FDTD simulated result at ω 0=0.375(a/λ).

Fig. 7.
Fig. 7.

(a) geometry of the arc bending corner in a 135° bending waveguide and (b) the FDTD simulated result at ω 0=0.375(a/λ).

Fig. 8.
Fig. 8.

(a) geometry of the arc bending corner in a 180° bending waveguide and (b) the FDTD simulated result at ω 0=0.375(a/λ).

Fig. 9.
Fig. 9.

Power transmittance spectrums of different bending waveguides with bending angles of (a) 45°, (b) 135°, and (c) 180°.

Fig. 10.
Fig. 10.

The FDTD simulated distributions of steady-state electric field at ω 0=0.375(a/λ) for “S-shape” waveguides formed by (a) cascading two 180° bends and (b) cascading a 180° bend with a 135° bend.

Fig. 11.
Fig. 11.

Power transmittance spectrums for “S-shape” waveguides formed by (a) cascading two 180° bends and (b) cascading a 180° bend with a 135° bend.

Fig. 12.
Fig. 12.

Power transmittance spectrums for 90° line-defect bending waveguides with the bending radius R b of 2a, 3a and 4a.

Equations (1)

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R = [ 1 + ( 2 k 0 k b [ k 0 2 k b 2 ] sin ( k b L ) ) 2 ] 1

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