Abstract

We present an adiabatic taper design in three dimensions for coupling light into photonic crystal defect waveguides in a square lattice of circular dielectric rods. The taper is a two-stage structure in which the first stage makes the transition from a dielectric waveguide to a coupled-cavity waveguide. The second stage subsequently transforms the waveguide mode from an index-guided mode to a band-gap-guided mode. We discuss differences between the two-dimensional device and its three-dimensional slab version.

© 2003 Optical Society of America

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References

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  1. E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173–194 (1994).
    [CrossRef]
  2. C. M. Soukoulis, ed., Photonic Bandgap Materials (Kluwer, Dordrecht, The Netherlands, 1996).
  3. J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, Princeton, N.J., 1995).
  4. S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
    [CrossRef]
  5. A. Mekis and J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Technol. 19, 861–865 (2001).
    [CrossRef]
  6. A. Talneau, P. Lalanne, M. Agio, and C. M. Soukoulis, “Low-reflection photonic-crystal taper for efficient coupling between guide sections of arbitrary widths,” Opt. Lett. 27, 1522–1524 (2002).
    [CrossRef]
  7. T. D. Happ, M. Kamp, and A. Forchel, “Photonic crystal tapers for ultracompact mode conversion,” Opt. Lett. 26, 1102–1104 (2001).
    [CrossRef]
  8. S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Likoridis, and J. D. Joannopoulos, “The adiabatic theorem and a continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
    [CrossRef]
  9. P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron. 33, 327–341 (2001).
    [CrossRef]
  10. http://camfr.sourceforge.net.
  11. Y. Xu, R. K. Lee, and A. Yariv, “Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387–400 (2000).
    [CrossRef]

2002

A. Talneau, P. Lalanne, M. Agio, and C. M. Soukoulis, “Low-reflection photonic-crystal taper for efficient coupling between guide sections of arbitrary widths,” Opt. Lett. 27, 1522–1524 (2002).
[CrossRef]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Likoridis, and J. D. Joannopoulos, “The adiabatic theorem and a continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

2001

2000

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

Y. Xu, R. K. Lee, and A. Yariv, “Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387–400 (2000).
[CrossRef]

1994

E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173–194 (1994).
[CrossRef]

Agio, M.

Baets, R.

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron. 33, 327–341 (2001).
[CrossRef]

Bienstman, P.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Likoridis, and J. D. Joannopoulos, “The adiabatic theorem and a continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron. 33, 327–341 (2001).
[CrossRef]

Fan, S. H.

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

Forchel, A.

Happ, T. D.

Ibanescu, M.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Likoridis, and J. D. Joannopoulos, “The adiabatic theorem and a continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Likoridis, and J. D. Joannopoulos, “The adiabatic theorem and a continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

A. Mekis and J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Technol. 19, 861–865 (2001).
[CrossRef]

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

Johnson, S. G.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Likoridis, and J. D. Joannopoulos, “The adiabatic theorem and a continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

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

Kamp, M.

Lalanne, P.

Lee, R. K.

Likoridis, E.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Likoridis, and J. D. Joannopoulos, “The adiabatic theorem and a continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Mekis, A.

Skorobogatiy, M. A.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Likoridis, and J. D. Joannopoulos, “The adiabatic theorem and a continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Soukoulis, C. M.

Talneau, A.

Villeneuve, P. R.

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

Xu, Y.

Yablonovitch, E.

E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173–194 (1994).
[CrossRef]

Yariv, A.

J. Lightwave Technol.

J. Mod. Opt.

E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173–194 (1994).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Opt. Quantum Electron.

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron. 33, 327–341 (2001).
[CrossRef]

Phys. Rev. B

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

Phys. Rev. E

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Likoridis, and J. D. Joannopoulos, “The adiabatic theorem and a continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Other

http://camfr.sourceforge.net.

C. M. Soukoulis, ed., Photonic Bandgap Materials (Kluwer, Dordrecht, The Netherlands, 1996).

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, Princeton, N.J., 1995).

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Figures (10)

Fig. 1
Fig. 1

Photonic crystal slab based on a square lattice of dielectric rods in air.

Fig. 2
Fig. 2

Band diagram of defect modes in photonic crystal slab structure of Fig. 1 for different defect radii.

Fig. 3
Fig. 3

Experimental prototype of photonic crystal slab structure.

Fig. 4
Fig. 4

Transmission through bulk crystal and two untapered waveguides of different lengths.

Fig. 5
Fig. 5

Transmission through a stage I input coupler (geometry shown in the inset), a 20-period coupled-cavity waveguide (not shown in inset), and a stage I output coupler (mirror image of the inset).

Fig. 6
Fig. 6

Transmission through a “bad” taper structure in which the cladding rods are varied in diameter in stage II.

Fig. 7
Fig. 7

Transmission through the two-stage input coupler, a waveguide of 8 or 10 periods length, and the output coupler.

Fig. 8
Fig. 8

Time snapshot of the electric field in the taper structure. Only the top half of the structure is shown.

Fig. 9
Fig. 9

3D transmission through bulk crystal, untapered waveguide (both 8 periods long), stage I taper (with the same length as the full taper, but with the bulk crystal cladding removed), and full taper.

Fig. 10
Fig. 10

Same as Fig. 9, but this time with a stage I taper having a defect radius of 0.23a instead of 0.25a.

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