Abstract

The dispersion and transmission characteristics of transverse electric modes of a flexible photonic crystal waveguide are investigated by numerical simulation. Calculated results indicate that for arbitrary-angle bends of this waveguide with very small curved radii no more than two wavelengths, a very high transmission (>98.5%) is observed for a broad enough bandwidth. Owing to its unique advantage of compactness and flexibility, this waveguide is expected to be applied to highly dense photonic integrated circuits after further research.

© 2009 Optical Society of America

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References

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  1. 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).
    [PubMed]
  2. S. 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).
    [PubMed]
  3. 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).
  4. P. Borel, A. Harpøth, L. Frandsen, M. Kristensen, P. Shi, J. Jensen, and O. Sigmund, "Topology optimization and fabrication of photonic crystal structures," Opt. Express 12, 1996-2001 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-9-1996.
    [PubMed]
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    [PubMed]
  6. B. Chen, T. Tang, Z. Wang, H. Chen, and Z. Liu, "Flexible optical waveguides based on the omnidirectional reflection of one-dimensional photonic crystals," Appl. Phys. Lett. 93, 181107 1-3 (2008).
  7. J. D. Joannopoulos, S. G. Johnson, J. N. Winn and R. D. Meade, Photonic Crystals-Molding the Flow of Light, 2nd ed. (Princeton University Press, New Jersey, 2008).
  8. J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).
  9. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Refector, " Science 282, 1679-1682 (1998).
    [PubMed]
  10. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-3-173.
    [PubMed]
  11. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method, 2nd ed. (Artech House, Boston, 2000).

2006 (1)

2004 (1)

2002 (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).

2001 (1)

1998 (3)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Refector, " Science 282, 1679-1682 (1998).
[PubMed]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).

S. 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).
[PubMed]

1996 (1)

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).
[PubMed]

Borel, P.

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Refector, " Science 282, 1679-1682 (1998).
[PubMed]

Chow, E.

S. 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).
[PubMed]

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).

Fan, S.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Refector, " Science 282, 1679-1682 (1998).
[PubMed]

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).
[PubMed]

Fink, Y.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Refector, " Science 282, 1679-1682 (1998).
[PubMed]

Frandsen, L.

Harpøth, A.

Hietala, V.

S. 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).
[PubMed]

Jensen, J.

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-3-173.
[PubMed]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).

S. 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).
[PubMed]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Refector, " Science 282, 1679-1682 (1998).
[PubMed]

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).
[PubMed]

Johnson, S. G.

Kristensen, M.

Li, B.

Lin, S.

S. 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).
[PubMed]

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Refector, " Science 282, 1679-1682 (1998).
[PubMed]

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).

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).

Shi, P.

Sigmund, O.

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Refector, " Science 282, 1679-1682 (1998).
[PubMed]

Villeneuve, P. R.

S. 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).
[PubMed]

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).
[PubMed]

Winn, J. N.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Refector, " Science 282, 1679-1682 (1998).
[PubMed]

Zhang, Y.

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).

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

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).
[PubMed]

Science (2)

S. 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).
[PubMed]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A Dielectric Omnidirectional Refector, " Science 282, 1679-1682 (1998).
[PubMed]

Other (3)

B. Chen, T. Tang, Z. Wang, H. Chen, and Z. Liu, "Flexible optical waveguides based on the omnidirectional reflection of one-dimensional photonic crystals," Appl. Phys. Lett. 93, 181107 1-3 (2008).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn and R. D. Meade, Photonic Crystals-Molding the Flow of Light, 2nd ed. (Princeton University Press, New Jersey, 2008).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method, 2nd ed. (Artech House, Boston, 2000).

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Figures (7)

Fig. 1.
Fig. 1.

The dispersion curves of TE mode flexible waveguides for different widths of defect layers (h0 ). The solid lines are that of even modes and the dotted line is that for the odd mode. The abscissa is of the normalized wavevector (unit: /a), and the ordinate is of the normalized frequency (unit: c/a). A schematic drawing of the flexible waveguide is shown in the inset; a denotes the lattice constant of the 1D PC. n1 =1.6, n2 =4.6, n0 =1, h1 =0.75a, and h2 =0.25a.

Fig. 2.
Fig. 2.

(a), (b), (c) and (d). Ey field distributions for operation points A, B, C and D in four dispersion curves in Fig. 1, respectively.

Fig. 3.
Fig. 3.

The transmission spectrum of 180° arc waveguide bend for the case of h0 =2.75a. A schematic drawing of this waveguide bend is shown in the inset; R=7a, W=4a, and other parameters are the same as those in Fig. 1.

Fig. 4.
Fig. 4.

The transmission spectrum of 180° arc waveguide bend for the case of h0 =3.75a. R=7a, W=4a; other parameters are the same as those in Fig. 1. Ey field profile in this waveguide bend at 0.21 [c/a] is shown in the inset.

Fig. 5.
Fig. 5.

The transmission spectrum of the Z-type waveguide bend combination composed of two 151.05° bends with R=7a. A schematic drawing of this waveguide combination is shown in the inset; other parameters are the same as those in Fig. 4.

Fig. 6.
Fig. 6.

The transmission spectrum of the 7-type waveguide bend combination composed of a 27.82° bend and a 117.82° bend with R=7a. A schematic drawing of this waveguide structure is shown in the inset; other parameters are the same as those in Fig. 4.

Fig. 7.
Fig. 7.

The Ey field profiles at normalized frequency 0.21 [c/a] (a) in the Z-type waveguide bend combination and (b) in the 7-type waveguide bend combination.

Tables (1)

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Table 1. A Comparison with TM-mode and TE-mode flexible waveguides

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