Abstract

We show that the self-imaging principle still holds true in multimode photonic crystal (PhC) line-defect waveguides just as it does in conventional multi-mode waveguides. To observe the images reproduced by this self-imaging phenomenon, the finite-difference time-domain computation is performed on a multi-mode PhC line-defect waveguide that supports five guided modes. From the computed result, the reproduced images are identified and their positions along the propagation axis are theoretically described by self-imaging conditions which are derived from guided mode propagation analysis. We report a good agreement between the computational simulation and the theoretical description. As a possible application of our work, a photonic crystal 1-to-2 wavelength demultiplexer is designed and its performance is numerically verified. This approach can be extended to novel designs of PhC devices.

© 2004 Optical Society of America

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  1. Eli Yablonovitch, �??Inhibited Spontaneous Emission in Solid-State Physics and Electronics,�?? Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef]
  2. Sajeev John, �??Strong localization of photons in certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486�??2489 (1987).
    [CrossRef]
  3. K. Busch (Editor), S. Lölkes (Editor), R. B. Wehrspohn (Editor), H. Föll (Editor), Photonic Crystals: Advances in Design, Fabrication, and Characterization ( Wiley-VCH, Verlag GmbH & Co. KGaA, 2004).
  4. Y. Sugimoto, Y. Tanaka, N. Ikeda, Y. Nakamura, K. Asakawa, and K. Inoue, "Low propagation loss of 0.76 dB/mm in GaAs-based single-line-defect two-dimensional photonic crystal slab waveguides up to 1 cm in length," Opt. Express 12, 1090-1096 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1090">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1090<a/>
    [CrossRef]
  5. 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>
  6. P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund, "Topology optimization and fabrication of photonic crystal structures," Opt. Express 12, 1996-2001 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996</a>
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    [CrossRef]
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  9. K. Srinivasan, P. E. Barclay, and O. Painter, "Fabrication-tolerant high quality factor photonic crystal microcavities," Opt. Express 12, 1458-1463 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1458">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1458</a>
    [CrossRef]
  10. 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]
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    [CrossRef]
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    [CrossRef]
  14. 8S. 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>
  15. Attila Mekis, J. C. Chen, I. Kurland, Shanhui Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, �??High Transmission through Sharp Bends in Photonic Crystal Waveguides,�?? Phys. Rev. Lett. 77, 3787�??3790 (1996)
    [CrossRef]
  16. Hyun-Jun Kim, In-Su Park, Dae-Seo Park, Seung-Gol Lee, Beom-Hoan O, Se-Geun Park, El-Hang Lee, �??Multi-Mode Interference-Based Photonic Crystal Waveguide Devices: Demultiplexer and Power Splitter,�?? presented at the Frontiers in Optics 2004/Laser Science XX, Rochester, New York, USA, 10-14 Oct. 2004.

Frontiers in Optics 2004

Hyun-Jun Kim, In-Su Park, Dae-Seo Park, Seung-Gol Lee, Beom-Hoan O, Se-Geun Park, El-Hang Lee, �??Multi-Mode Interference-Based Photonic Crystal Waveguide Devices: Demultiplexer and Power Splitter,�?? presented at the Frontiers in Optics 2004/Laser Science XX, Rochester, New York, USA, 10-14 Oct. 2004.

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.

L.B. Soldano and E.C.M. Pennings, �??Optical multi-mode interference devices based on self-imaging: principles and applications,�?? J. Lightwave Technol. 13, 615-627 (1995
[CrossRef]

Koshiba M, �??Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,�?? J. Lightwave Technol. 19, 1970-1975 (2001).
[CrossRef]

Opt. Express

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>

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>

Y. Sugimoto, Y. Tanaka, N. Ikeda, Y. Nakamura, K. Asakawa, and K. Inoue, "Low propagation loss of 0.76 dB/mm in GaAs-based single-line-defect two-dimensional photonic crystal slab waveguides up to 1 cm in length," Opt. Express 12, 1090-1096 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1090">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1090<a/>
[CrossRef]

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]

K. Srinivasan, P. E. Barclay, and O. Painter, "Fabrication-tolerant high quality factor photonic crystal microcavities," Opt. Express 12, 1458-1463 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1458">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1458</a>
[CrossRef]

P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund, "Topology optimization and fabrication of photonic crystal structures," Opt. Express 12, 1996-2001 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996</a>
[CrossRef]

8S. 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>

Phys. Rev. Lett.

Attila Mekis, J. C. Chen, I. Kurland, Shanhui Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, �??High Transmission through Sharp Bends in Photonic Crystal Waveguides,�?? Phys. Rev. Lett. 77, 3787�??3790 (1996)
[CrossRef]

Eli Yablonovitch, �??Inhibited Spontaneous Emission in Solid-State Physics and Electronics,�?? Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef]

Sajeev John, �??Strong localization of photons in certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486�??2489 (1987).
[CrossRef]

Other

K. Busch (Editor), S. Lölkes (Editor), R. B. Wehrspohn (Editor), H. Föll (Editor), Photonic Crystals: Advances in Design, Fabrication, and Characterization ( Wiley-VCH, Verlag GmbH & Co. KGaA, 2004).

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

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