Abstract

Previously, we discussed an optical delay device consisting of a directional coupler of two different photonic crystal (PC) waveguides. It generates wideband and low dispersion slow light. However, it is easily degraded by a large reflection loss for a small imperfection of the coupling condition. In this paper, we propose and theoretically discuss a PC coupled waveguide, which allows more robust slow light with lower loss. For this device, unique photonic bands with a zero or negative group velocity at the inflection point can be designed by the structural tuning. Finite difference time domain simulation demonstrates the stopping and/or back and forth motion of an ultrashort optical pulse in the device combined with the chirped structure. For a signal bandwidth of 40 GHz, the average group index of the slow light will be 450, which gives a 1 ns delay for a device length of 670 μm. The theoretical total insertion loss at the device and input/output structures is as low as 0.11 dB.

© 2005 Optical Society of America

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References

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  1. C. Li, Z. Dutton, C. H. Behroozi, and L. V. Hau, �??Observation of coherent optical information storage in an atomic medium using halted light pulses,�?? Nature 409, 490-493 (2001).
    [CrossRef]
  2. R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, �??Novel applications of photonic band gap materials: Low-loss bends and high Q cavities,�?? Appl. Phys. Lett. 75, 4753-4755 (1994).
  3. A. Mekis, J. C. Chen, I. Kurland, 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).
    [CrossRef] [PubMed]
  4. J. Yonekura, M. Ikeda, and T. Baba, �??Analysis of finite 2-D photonic crystals of columns and lightwave devices using the scattering matrix method,�?? J. Lightwave Technol. 17, 1500-1508 (1999).
    [CrossRef]
  5. T. Baba, N. Fukaya, and J. Yonekura, �??Observation of light propagation in photonic crystal optical waveguides with bends,�?? Electron. Lett. 35, 654-655 (1999); T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, �??Light propagation characteristics of straight single line defect optical waveguides in a photonic crystal slab fabricated into a silicon-on-insulator substrate,�?? IEEE J. Quantum Electron. 38, 743-752 (2002).
    [CrossRef]
  6. M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, �??Lightwave propagation through a 120 sharply bent single-line-defect photonic crystal waveguide,�?? Appl. Phys. Lett. 76, 952-954 (2000).
    [CrossRef]
  7. M. Lon�?ar, D. Nedeljkovi�?, T. Doll, J. Vu�?kovi�?, and A. Scherer, �??Waveguiding in planar photonic crystals,�?? Appl. Phys. Lett. 77, 1937-1939 (2000).
    [CrossRef]
  8. S. Noda, A. Chutinan, and M. Imada, �??Trapping and emission of photons by a single defect in a photonic bandgap structure,�?? Nature 407, 608-610 (2000).
    [CrossRef] [PubMed]
  9. C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, �??Low-loss channel waveguides with two-dimensional photonic crystal boundaries,�?? Appl. Phys. Lett. 77, 2813-2815 (2000).
    [CrossRef]
  10. M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, �??Singlemode transmission within photonic bandgap of width-varied single-line-defect photonic crystal waveguides on SOI substrates,�?? Electron. Lett. 37, 293-294 (2001); M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. -Y. Ryu, �??Waveguides, resonators and their coupled elements in photonic crystal slabs,�?? Opt. Express. 12, 1551-1561 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1551">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1551</a>
    [CrossRef]
  11. W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, and R. Baets, �??Fabrication of photonic crystals in silicon-on-insulator using 248-nm deep UV lithography,�?? IEEE J. Sel. Top. Quantum Electron. 8, 928-934 (2002).
    [CrossRef]
  12. S. J. McNab, N. Moll, and Y. 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]
  13. 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] [PubMed]
  14. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, �??Extremely large group-velocity dispersion of line defect waveguides in photonic crystal slabs,�?? Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef] [PubMed]
  15. K. Inoue, N. Kawai, Y. Sugimoto, N. Carlsson, N. Ikeda, and K. Asakawa, �??Observation of small group velocity in two-dimensional AlGaAs-based photonic crystal slabs,�?? Phys. Rev. B 65, 121308 (2002).
    [CrossRef]
  16. T. Asano, K. Kiyota, D. Kumamoto, B-S. Song, and S. Noda, �??Time-domain measurement of picosecond light-pulse propagation in a two-dimensional photonic crystal-slab waveguide,�?? Appl. Phys. Lett. 84, 4690-4692 (2004).
    [CrossRef]
  17. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, �??Real-space observation of ultraslow light in photonic crystal waveguides,�?? Phys. Rev. Lett. 94, 073903 (2005).
    [CrossRef] [PubMed]
  18. M. D. Lukin, S. F. Yelin, and M. Fleischhauer, �??Entanglement of atomic ensembles by trapping correlated photon states,�?? Phys. Rev. Lett. 84, 004232 (2000).
    [CrossRef]
  19. M. F. Yanik, W. Suh, Z. Wang, and S. Fan, �??Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,�?? Phys. Rev. Lett. 93, 233903 (2004).
    [CrossRef] [PubMed]
  20. T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, �??Light localization in line defect photonic crystal waveguides,�?? IEEE J. Sel. Top. Quantum Electron. 10, 484-491 (2004).
    [CrossRef]
  21. D. Mori and T. Baba, �??Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,�?? Appl. Phys. Lett. 85, 1101-1103 (2004).
    [CrossRef]
  22. M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos �??Slow-light, band-edge waveguides for tunable time delays,�?? Opt. Express. 13, 7145-7159 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-7145">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-7145</a>
    [CrossRef] [PubMed]
  23. A. Sakai, I. Katoh, D. Mori, T. Baba, and Y. Takiguchi, �??Anomalous low group velocity and low dispersion in simple line defect photonic crystal waveguides,�?? Proc. IEEE/LEOS Annual Meet., ThQ5 (2004).
  24. A. Yu. Petrov and M. Eich, �??Zero dispersion at small group velocities in photonic crystal waveguides,�?? Appl. Phys. Lett. 85, 4866-4868 (2004).
    [CrossRef]
  25. T. Ogawa, N. Yamamoto, Y. Watanabe, K. Komori, M. Itoh, and T. Yatagai, �??Photonic crystal directional coupler switch with short switching length and wide band width,�?? Proc. Fall Meet. of JSAP, 3p-ZC-14 (2004).
  26. A. Sakai, G. Hara, and T. Baba, �??Propagation characteristics of ultra-high �? optical waveguide on silicon-oninsulator substrate,�?? Jpn. J. Appl. Phys. 40, L383-L385 (2001).
    [CrossRef]
  27. A. Sakai, T. Fukazawa, and T. Baba, �??Low loss ultra-small branches in Si photonic wire waveguides,�?? IEICE Trans. Electron. E85-C, 1033-1038 (2002).
  28. D. Gerace and L. C. Andreani, �??Disorder-induced losses in photonic crystal waveguides with line defects,�?? Opt. Lett. 29, 1897-1899 (2004).
    [CrossRef] [PubMed]
  29. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, �??Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,�?? Phys. Rev. Lett. 94, 033903 (2005).
    [CrossRef] [PubMed]
  30. S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, �??Roughness losses and volume-current methods in photonic-crystal waveguides,�?? Appl. Phys. B 81, 283-293 (2005).
    [CrossRef]
  31. E. Mizuta, T. Ide, J. Hashimoto, K. Nozaki, T. Baba, T. Kise, K. Kiyota, and N. Yokouchi, �??Characterization of photonic crystal waveguide for SOA operation,�?? Proc. Pacific Rim Conf. Laser and Electro-Optics, CThE1-4 (2005).

Appl. Phys. B (1)

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, �??Roughness losses and volume-current methods in photonic-crystal waveguides,�?? Appl. Phys. B 81, 283-293 (2005).
[CrossRef]

Appl. Phys. Lett. (7)

A. Yu. Petrov and M. Eich, �??Zero dispersion at small group velocities in photonic crystal waveguides,�?? Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, �??Low-loss channel waveguides with two-dimensional photonic crystal boundaries,�?? Appl. Phys. Lett. 77, 2813-2815 (2000).
[CrossRef]

M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, �??Lightwave propagation through a 120 sharply bent single-line-defect photonic crystal waveguide,�?? Appl. Phys. Lett. 76, 952-954 (2000).
[CrossRef]

M. Lon�?ar, D. Nedeljkovi�?, T. Doll, J. Vu�?kovi�?, and A. Scherer, �??Waveguiding in planar photonic crystals,�?? Appl. Phys. Lett. 77, 1937-1939 (2000).
[CrossRef]

T. Asano, K. Kiyota, D. Kumamoto, B-S. Song, and S. Noda, �??Time-domain measurement of picosecond light-pulse propagation in a two-dimensional photonic crystal-slab waveguide,�?? Appl. Phys. Lett. 84, 4690-4692 (2004).
[CrossRef]

D. Mori and T. Baba, �??Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,�?? Appl. Phys. Lett. 85, 1101-1103 (2004).
[CrossRef]

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, �??Novel applications of photonic band gap materials: Low-loss bends and high Q cavities,�?? Appl. Phys. Lett. 75, 4753-4755 (1994).

Electron. Lett. (2)

T. Baba, N. Fukaya, and J. Yonekura, �??Observation of light propagation in photonic crystal optical waveguides with bends,�?? Electron. Lett. 35, 654-655 (1999); T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, �??Light propagation characteristics of straight single line defect optical waveguides in a photonic crystal slab fabricated into a silicon-on-insulator substrate,�?? IEEE J. Quantum Electron. 38, 743-752 (2002).
[CrossRef]

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, �??Singlemode transmission within photonic bandgap of width-varied single-line-defect photonic crystal waveguides on SOI substrates,�?? Electron. Lett. 37, 293-294 (2001); M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. -Y. Ryu, �??Waveguides, resonators and their coupled elements in photonic crystal slabs,�?? Opt. Express. 12, 1551-1561 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1551">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1551</a>
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, and R. Baets, �??Fabrication of photonic crystals in silicon-on-insulator using 248-nm deep UV lithography,�?? IEEE J. Sel. Top. Quantum Electron. 8, 928-934 (2002).
[CrossRef]

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, �??Light localization in line defect photonic crystal waveguides,�?? IEEE J. Sel. Top. Quantum Electron. 10, 484-491 (2004).
[CrossRef]

IEICE Trans. Electron. (1)

A. Sakai, T. Fukazawa, and T. Baba, �??Low loss ultra-small branches in Si photonic wire waveguides,�?? IEICE Trans. Electron. E85-C, 1033-1038 (2002).

J. Lightwave Technol. (1)

Jpn. J. Appl. Phys. (1)

A. Sakai, G. Hara, and T. Baba, �??Propagation characteristics of ultra-high �? optical waveguide on silicon-oninsulator substrate,�?? Jpn. J. Appl. Phys. 40, L383-L385 (2001).
[CrossRef]

Nature (2)

S. Noda, A. Chutinan, and M. Imada, �??Trapping and emission of photons by a single defect in a photonic bandgap structure,�?? Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

C. Li, Z. Dutton, C. H. Behroozi, and L. V. Hau, �??Observation of coherent optical information storage in an atomic medium using halted light pulses,�?? Nature 409, 490-493 (2001).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (1)

K. Inoue, N. Kawai, Y. Sugimoto, N. Carlsson, N. Ikeda, and K. Asakawa, �??Observation of small group velocity in two-dimensional AlGaAs-based photonic crystal slabs,�?? Phys. Rev. B 65, 121308 (2002).
[CrossRef]

Phys. Rev. Lett. (6)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, �??Extremely large group-velocity dispersion of line defect waveguides in photonic crystal slabs,�?? Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, 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).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, �??Real-space observation of ultraslow light in photonic crystal waveguides,�?? Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

M. D. Lukin, S. F. Yelin, and M. Fleischhauer, �??Entanglement of atomic ensembles by trapping correlated photon states,�?? Phys. Rev. Lett. 84, 004232 (2000).
[CrossRef]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, �??Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,�?? Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, �??Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,�?? Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef] [PubMed]

Proc. Fall Meet. of JSAP (1)

T. Ogawa, N. Yamamoto, Y. Watanabe, K. Komori, M. Itoh, and T. Yatagai, �??Photonic crystal directional coupler switch with short switching length and wide band width,�?? Proc. Fall Meet. of JSAP, 3p-ZC-14 (2004).

Proc. IEEE/LEOS Annual Meet (1)

A. Sakai, I. Katoh, D. Mori, T. Baba, and Y. Takiguchi, �??Anomalous low group velocity and low dispersion in simple line defect photonic crystal waveguides,�?? Proc. IEEE/LEOS Annual Meet., ThQ5 (2004).

Proc. Pacific Rim Conf. (1)

E. Mizuta, T. Ide, J. Hashimoto, K. Nozaki, T. Baba, T. Kise, K. Kiyota, and N. Yokouchi, �??Characterization of photonic crystal waveguide for SOA operation,�?? Proc. Pacific Rim Conf. Laser and Electro-Optics, CThE1-4 (2005).

Supplementary Material (2)

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of ideal band shifted by chirping against the frequency of incident light (dashed line).

Fig. 2.
Fig. 2.

Schematic of PC directional coupler with coupled mode profiles and corresponding bands.

Fig. 3.
Fig. 3.

Real structures of PC coupled waveguides and corresponding bands. Thick and thin lines indicate bands of the even mode and other modes, respectively. Light gray and dark gray regions show the light cone above the air light line and slab mode regions, respectively. For the band of (a), airhole shift d is set to be 0.25a.

Fig. 4.
Fig. 4.

Dependence of band for the structure of Fig. 3(a) on background index n, where d = 0.25a is assumed.

Fig. 5.
Fig. 5.

Dependence of band for the structure of Fig. 3(a) on airhole shift d, where n = 2.963 is assumed.

Fig. 6.
Fig. 6.

Light intensity profile for each time frame and pulse waveforms of light power toward the right side. (a) and (b) are those for structures of Fig. 3(a) with d = 0.25a and 0.10a, respectively. Line in each figure shows corresponding photonic band. Animations show the light propagation (Hz field) for each structure, where red, yellow, green, light blue and dark blue show intensities from plus to minus. [Media 1] [Media 2]

Fig. 7.
Fig. 7.

Schematic band diagram in the repeated zone scheme for the explanation of back and forth motion in Fig. 6(b).

Fig. 8.
Fig. 8.

Upper limit values of g and g ∆ωs/ω for bands of Fig. 5 calculated with ∆ωs/ω, where d is used as a parameter.

Fig. 9.
Fig. 9.

I/O structure for the structure of Fig. 3(a) with photonic wire waveguides. (a) Half elliptical taper used with bend waveguide type branch. (b) Half circular funnel taper as a confluence.

Fig. 10.
Fig. 10.

I/O structure for the structure of Fig. 3(a) with PC single line defect waveguides. (a) Branch. (b) Confluence.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

Δ T = 0 Δ L d x υ g ( x ) = 0 Δ L n g ( x ) c d x .
n ͂ g = c υ ͂ g = c Δ L Δ T = 0 Δ L n g ( x ) d x Δ L .
n ͂ g ω 0 ω 0 + Δ ω n g ( ω ) d ω / Δ ω = ω 0 ω 0 + Δ ω c d k d ω d ω / Δ ω = k 0 k 0 + Δ k c d k / Δ ω = c Δ k Δ ω
n ͂ g Δ ω s ω n ͂ g Δ ω 2 ω = Δ k 2 k .
n ͂ g Δ ω s ω n ͂ g Δ ω Δ ω p 2 ω = Δ k 2 k ( 1 Δ ω p Δ ω )

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