Abstract

We propose and analyze a highly efficient method of coupling light from optical fibers to two-dimensional photonic crystal waveguides. Efficient coupling is achieved by positioning of a tapered fiber parallel to the linear defect, where the photonic crystal’s cladding functions as a grating coupler and provides field confinement as well. Numerical simulations indicate that better than 90% transmission is possible with a full width at half-magnitude bandwidth of 12 nm. It is shown that one can increase the bandwidth by increasing the field overlap between the two waveguides.

© 2002 Optical Society of America

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  1. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  2. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
    [CrossRef] [PubMed]
  3. A. Chutinan and S. Noda, Phys. Rev. B 62, 4488 (2000).
    [CrossRef]
  4. A. Mekis and J. D. Joannopoulos, J. Lightwave Technol. 19, 861 (2001).
    [CrossRef]
  5. A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, Phys. Rev. B 64, 041102(R) (2001).
    [CrossRef]
  6. M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
    [CrossRef]
  7. T. D. Happ, M. Kamp, and A. Forchel, Opt. Lett. 26, 1102 (2001).
    [CrossRef]
  8. K. S. Lee, IEEE Trans. Antennas Propag. AP-14, 302 (1966).
  9. A. Taflove, Computational Electrodynamics—The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 1995).
  10. J.-P. Berenger, J. Comput. Phys. 127, 363 (1996).
    [CrossRef]
  11. C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16,635 (1995).
    [CrossRef]
  12. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

2001 (4)

A. Mekis and J. D. Joannopoulos, J. Lightwave Technol. 19, 861 (2001).
[CrossRef]

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, Phys. Rev. B 64, 041102(R) (2001).
[CrossRef]

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

T. D. Happ, M. Kamp, and A. Forchel, Opt. Lett. 26, 1102 (2001).
[CrossRef]

2000 (1)

A. Chutinan and S. Noda, Phys. Rev. B 62, 4488 (2000).
[CrossRef]

1996 (2)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

J.-P. Berenger, J. Comput. Phys. 127, 363 (1996).
[CrossRef]

1995 (1)

C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16,635 (1995).
[CrossRef]

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

1966 (1)

K. S. Lee, IEEE Trans. Antennas Propag. AP-14, 302 (1966).

Adibi, A.

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, Phys. Rev. B 64, 041102(R) (2001).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, J. Comput. Phys. 127, 363 (1996).
[CrossRef]

Chan, C. T.

C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16,635 (1995).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Chutinan, A.

A. Chutinan and S. Noda, Phys. Rev. B 62, 4488 (2000).
[CrossRef]

Fan, S.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Forchel, A.

Happ, T. D.

Ho, K. M.

C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16,635 (1995).
[CrossRef]

Joannopoulos, J. D.

A. Mekis and J. D. Joannopoulos, J. Lightwave Technol. 19, 861 (2001).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Kamp, M.

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Lee, K. S.

K. S. Lee, IEEE Trans. Antennas Propag. AP-14, 302 (1966).

Lee, R. K.

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, Phys. Rev. B 64, 041102(R) (2001).
[CrossRef]

Loncar, M.

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, Phys. Rev. B 64, 041102(R) (2001).
[CrossRef]

Mekis, A.

A. Mekis and J. D. Joannopoulos, J. Lightwave Technol. 19, 861 (2001).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Noda, S.

A. Chutinan and S. Noda, Phys. Rev. B 62, 4488 (2000).
[CrossRef]

Notomi, M.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

Scherer, A.

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, Phys. Rev. B 64, 041102(R) (2001).
[CrossRef]

Shinya, A.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

Taflove, A.

A. Taflove, Computational Electrodynamics—The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 1995).

Takahashi, C.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

Takahashi, J.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Xu, Y.

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, Phys. Rev. B 64, 041102(R) (2001).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yamada, K.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

Yariv, A.

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, Phys. Rev. B 64, 041102(R) (2001).
[CrossRef]

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yokohama, I.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

Yu, Q. L.

C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16,635 (1995).
[CrossRef]

Electron. Lett. (1)

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Lee, IEEE Trans. Antennas Propag. AP-14, 302 (1966).

J. Comput. Phys. (1)

J.-P. Berenger, J. Comput. Phys. 127, 363 (1996).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Lett. (1)

Phys. Rev. B (3)

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, Phys. Rev. B 64, 041102(R) (2001).
[CrossRef]

C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16,635 (1995).
[CrossRef]

A. Chutinan and S. Noda, Phys. Rev. B 62, 4488 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Other (2)

A. Taflove, Computational Electrodynamics—The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 1995).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

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Figures (4)

Fig. 1
Fig. 1

Schematic showing the coupling scheme of a PCSW and a tapered fiber. We formed the PCSW by inserting a linear defect on a triangular lattice of air holes perforating a GaAs membrane. A tapered fiber is positioned parallel to the photonic crystal defect.

Fig. 2
Fig. 2

Magnetic-field magnitude profile, showing contradirectional coupling of energy from a tapered fiber to a PCSW, calculated by 3-D FDTD. The power flowing from left to right inside the tapered fiber gets significantly weaker by coupling energy to the photonic crystal waveguide. Meanwhile, the power flowing from right to left in the photonic crystal waveguide becomes stronger with the interaction.

Fig. 3
Fig. 3

Dispersion diagram for vertically even (TE-like) guided modes in a PCSW and the tapered fiber. The lighter shaded area shows the light cone region; modes above it are leaky in air cladding.

Fig. 4
Fig. 4

Spectra of coupling efficiency from a tapered fiber to a PCSW, calculated by 2-D FDTD. Points, calculated values; curves, interpolated curves. Solid and dotted curves, the power transmission coefficient for fiber–PCSW separation made from air from a high-index material, respectively. The FWHM bandwidth of the air-buffered fiber-PCSW coupling is approximately 12 nm, which increases with improved perturbation strength.

Equations (3)

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βfiber+βPCSW=2mπ/a.
Δω=2κβPCSWω-βfiberω,
κ=ω4-+HPCSW*μ0Δϵϵ¯Hfiberdx.

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