Abstract

We propose a new power-splitting scheme in two-dimensional photonic crystals that can be applicable to photonic integrated circuits. The proposed power-splitting mechanism is analogous to that of conventional three-waveguide directional couplers, utilizing coupling between guided modes supported by line-defect waveguides. Through the analysis of dispersion curve and field patterns of modes, the position in propagation direction, where an input field is split into a two-folded image, is determined by simple mode analysis. Based on the calculated position, a photonic crystal power-splitter is designed and verified by finite-difference time-domain computation

© 2004 Optical Society of America

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References

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  1. Thomas F. Krauss, �??Planar photonic crystal waveguide devices for integrated optics,�?? Phys. Stat. Sol. (a) 197, 688-702 (2003).
    [CrossRef]
  2. Sharee J. McNab, Nikolaj Moll, and Yurii A. Vlasov, �??Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,�?? Opt. Express 11, 2927-2939 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2927">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2927</a>
    [CrossRef] [PubMed]
  3. Mehmet Bayindir, B. Temelkuran, and E. Ozbay, �??Photonic-crystal-based beam splitters,�?? Appl. Phys. Lett. 77, 3902-3904 (2000).
    [CrossRef]
  4. 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]
  5. Fan SH, Johnson SG, Joannopoulos JD, Manolatou C, "Waveguide branches in photonic crystals." J. Opt. Soc. Am. B 18, 162-165 (2001).
    [CrossRef]
  6. David M. Pustai, Ahmed S. Sharkawy, Shouyuan Shi, Ge Jin, Janusz A. Murakowski, Dennis W. Prather, �??Characterization and Analysis of Photonic Crystal Coupled Waveguides,�?? JM3, 2, 292-299, (2003).
  7. F. S. -. Chien, Y. -. Hsu, W. -. Hsieh, and S. -. Cheng, "Dual wavelength demultiplexing by coupling and decoupling of photonic crystal waveguides," Opt. Express 12, 1119-1125 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1119">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1119</a>
    [CrossRef] [PubMed]
  8. Koshiba M, �??Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,�?? J. Lightwave Technol. 19, 1970-1975 (2001).
    [CrossRef]
  9. A. S. Sharkawy, S. Shi, D. W. Prather, and R. A. Soref, "Electro-optical switching using coupled photonic crystal waveguides," Opt. Express 10, 1048-1059 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-20-1048">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-20-1048</a>
    [CrossRef] [PubMed]
  10. M. Bayindir and E. Ozbay, "Band-dropping via coupled photonic crystal waveguides," Opt. Express 10, 1279-1284 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1279">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1279</a>
    [CrossRef] [PubMed]
  11. 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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>
    [CrossRef] [PubMed]
  12. Morten Thorhauge, Lars H. Frandsen, and Peter I. Borel, �??Efficient photonic crystal directional couplers,�?? Opt. Lett. 28, 1525-1527 (2003).
    [CrossRef] [PubMed]
  13. Boscolo, S., Midrio, M., Someda, and C.G., �??Coupling and decoupling of electromagnetic waves in parallel 2D photonic crystal waveguides,�?? IEEE J. Quantum Electron. 38, 47-53 (2002).
    [CrossRef]
  14. A. Yariv, P. Yeh, Optical Waves in Crystals, (Wiley, NewYork, 1984).
  15. A. Taflove, S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, second ed., (Artech House, Boston, 2000).
  16. Olivier, M. Rattier, H. Benisty, C. Weisbuch, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle and R. Houdré, �??Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,�?? Phys. Rev. B 63, 113311 1-4 (2001).
    [CrossRef]
  17. S. Olivier, H.Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, and R. Houdre, �??Coupled-mode theory and propagation losses in photonic crystal waveguides,�?? Opt. Express 11, 1490-1496 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490</a>
    [CrossRef] [PubMed]

Appl. Phys. Lett.

Mehmet Bayindir, B. Temelkuran, and E. Ozbay, �??Photonic-crystal-based beam splitters,�?? Appl. Phys. Lett. 77, 3902-3904 (2000).
[CrossRef]

IEEE J. Quantum Electron.

Boscolo, S., Midrio, M., Someda, and C.G., �??Coupling and decoupling of electromagnetic waves in parallel 2D photonic crystal waveguides,�?? IEEE J. Quantum Electron. 38, 47-53 (2002).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

JM3

David M. Pustai, Ahmed S. Sharkawy, Shouyuan Shi, Ge Jin, Janusz A. Murakowski, Dennis W. Prather, �??Characterization and Analysis of Photonic Crystal Coupled Waveguides,�?? JM3, 2, 292-299, (2003).

Opt. Express

F. S. -. Chien, Y. -. Hsu, W. -. Hsieh, and S. -. Cheng, "Dual wavelength demultiplexing by coupling and decoupling of photonic crystal waveguides," Opt. Express 12, 1119-1125 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1119">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1119</a>
[CrossRef] [PubMed]

S. Olivier, H.Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, and R. Houdre, �??Coupled-mode theory and propagation losses in photonic crystal waveguides,�?? Opt. Express 11, 1490-1496 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1490</a>
[CrossRef] [PubMed]

A. S. Sharkawy, S. Shi, D. W. Prather, and R. A. Soref, "Electro-optical switching using coupled photonic crystal waveguides," Opt. Express 10, 1048-1059 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-20-1048">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-20-1048</a>
[CrossRef] [PubMed]

M. Bayindir and E. Ozbay, "Band-dropping via coupled photonic crystal waveguides," Opt. Express 10, 1279-1284 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1279">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1279</a>
[CrossRef] [PubMed]

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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>
[CrossRef] [PubMed]

Sharee J. McNab, Nikolaj Moll, and Yurii A. Vlasov, �??Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,�?? Opt. Express 11, 2927-2939 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2927">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2927</a>
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. B

Olivier, M. Rattier, H. Benisty, C. Weisbuch, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle and R. Houdré, �??Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,�?? Phys. Rev. B 63, 113311 1-4 (2001).
[CrossRef]

Phys. Stat. Sol.`

Thomas F. Krauss, �??Planar photonic crystal waveguide devices for integrated optics,�?? Phys. Stat. Sol. (a) 197, 688-702 (2003).
[CrossRef]

Other

A. Yariv, P. Yeh, Optical Waves in Crystals, (Wiley, NewYork, 1984).

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

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Figures (5)

Fig. 1.
Fig. 1.

Geometry of photonic crystal power-splitter and setup for the finite-difference time-domain computation. The device can be divided into two regions, as labeled on top. Black boxed areas indicate super-cells for the PWE calculation. White holes represent air-holes perforated in GaAs (n=3).

Fig. 2.
Fig. 2.

(a) The dispersion relation and the computational super-cell (inset) for coupling region. (b) The dispersion relation and the computational super-cell (inset) for output region. Gray areas in (a) and (b) indicate the designed frequency range. Red lines in (a) designate the possible frequency range with a spectrally constant coupling length and the excitable modes. Boxed area in (b) indicates the region of anti-crossing between modes of different order. The two modes labeled ‘even’ and ‘odd’ in (b) have the corresponding symmetry.

Fig. 3.
Fig. 3.

PWE calculated patterns of magnetic field for the modes of interest. (a) Hy field profile of the 0th mode. (b) Hy field profile of the 1st mode. (c) Hy field profile of the 2nd mode. PWE calculation points are marked on dispersion curves in Fig. 2(a).

Fig. 4.
Fig. 4.

Normalized output power after FDTD computation. Grayed area indicates spectrally flat coupling range.

Fig. 5.
Fig. 5.

Amplitude of Hy field calculated by the FDTD at a/λ=0.258. The coupling and output regions are separated by black vertical lines.

Equations (4)

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Ψ ( x , z ) = c 0 ψ 0 ( x , y ) e j β 0 z + c 2 ψ 2 ( x , z ) e j β 2 z ,
Ψ ( x , L ) = c 0 ψ 0 ( x , L ) e j β 0 L + c 2 ψ 2 ( x , L ) e j β 2 L
= [ c 0 ψ 0 ( x , L ) c 2 ψ 2 ( x , L ) ] e j β 0 L .
L = π β 2 β 0 .

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