Abstract

we experimentally investigate the effects of slow light modes within a one dimensional photonic crystal resonator. We show that the slow light mode leads to significant increase in the quality factor of the resonator. We provide a theoretical analysis explaining our experimental results. We also include the effect of disorder to simulate the fabrication imperfection. Further results regarding the properties of the one dimensional photonic crystal are discussed.

© 2008 Optical Society of America

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References

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  1. Y. Okawachi, M. A. Foster, J. E. Sharping, A. L. Gaeta, Q. Xu, and M. Lipson, "All-optical slow-light on a photonic chip," Opt. Express 14, 2318-2322 (2006).
    [CrossRef]
  2. J. E. Heebner and R. W. Boyd, "‘Slow’ and ‘fast’ light in resonator-coupled waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
    [CrossRef]
  3. M. Notomi, K. Yamada, A. Shinaya, J. Takahashi, C. Takahashi, and J. Yokohama, "Single mode transmission within photonic bandgap of width-varied single-line-defect photonic crystal waveguides on SOI substrates," Electron. Lett. 37, 293-295 (2001)
    [CrossRef]
  4. S. McNab, N. Moll, and Y. Vlasov, "Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides," Opt. Express 11, 2928-2939 (2003).
    [CrossRef]
  5. W. Bogaerts, D. tailaret, B. Luyssaert, P. Dumon, J. Van-Campenhount, P. Bienstman, D. Van-Thourhout, R. Baets, Wiaux, and S. Beckx, "Basic structures for photonic integrated circuits in silicon-on-insulator," Opt. Express 12, 1583-1591 (2004).
    [CrossRef] [PubMed]
  6. N. Wu, M. Javanmard, B. Momeni, M. Soltani, and A. Adibi, "General methods for designing single mode planar photonic crystal waveguides in hexagonal lattice structures," Opt. Express 11, 1371-1377 (2003).
    [CrossRef] [PubMed]
  7. M. Notomi, K. Yamada, A. Shinaya, J. Takahashi, C. Takahashi, and J. Yokohama, "Structural Tuning of Guiding Modes of Line-Defect Waveguides of Silicon-on-Insulator Photonic Crystal Slabs," IEEE J. of Quantum Electron. 38, 736-742 (2002).
    [CrossRef]
  8. M. Notomi, K. Yamada, A. Shinaya, J. Takahashi, C. Takahashi, and J. Yokohama, "Extremely large group velocity dispersion of line defect waveguides in photonic crystals slabs," Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef] [PubMed]
  9. Yu. A. Vlasov, S. J. McNab, "Coupling into the slow light mode in slab-type photonic crystal waveguides," Opt. Lett. 31, 50-52 (2006).
    [CrossRef] [PubMed]
  10. M. Povinelli, S. Johnson, and J. Joannopoulos, "Slow-light, band-edge waveguides for tunable time delays," Opt. Express 13, 7145-7159 (2005).
    [CrossRef] [PubMed]
  11. M. Soljacic, E. Lidorikis, L. Vestergaard Hau, and J. D. Joannopoulus, "Enhancement of microcavities lifetime using highly dispersive materials," Phys. Rev. E. 71, 026602 (2005).
    [CrossRef]
  12. D. Goldring, U. Levy, and D. Mendlovic, "Highly dispersive micro-ring resonator based on one dimensional photonic crystal waveguide - Design and analysis," Opt. Express 15, 3156-3168 (2007).
    [CrossRef] [PubMed]
  13. C. Sauvan, G. Lecamp, P. Lalanne, and J.P. Hugonin, "Modal-reflectivity enhancement by geometry tuning in Photonic Crystal microcavities," Opt. Express 13, 245-255 (2005).
    [CrossRef] [PubMed]
  14. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystal: modeling the flow of light (Princeton University Press., Princeton, NJ, 1995).
  15. The 3D problem was reduced to a 2D problem using effective index method. The core’s index is chosen so that the effective index of the strip waveguide’s modes in 3D will be the same as or very close to the one in 2D.
  16. B. E. A. Saleh and M. C. Teich, Fundamentals of photonics (John Wiley &Sons, New York, 1991)
    [CrossRef]

2007

2006

Yu. A. Vlasov, S. J. McNab, "Coupling into the slow light mode in slab-type photonic crystal waveguides," Opt. Lett. 31, 50-52 (2006).
[CrossRef] [PubMed]

Y. Okawachi, M. A. Foster, J. E. Sharping, A. L. Gaeta, Q. Xu, and M. Lipson, "All-optical slow-light on a photonic chip," Opt. Express 14, 2318-2322 (2006).
[CrossRef]

2005

2004

2003

N. Wu, M. Javanmard, B. Momeni, M. Soltani, and A. Adibi, "General methods for designing single mode planar photonic crystal waveguides in hexagonal lattice structures," Opt. Express 11, 1371-1377 (2003).
[CrossRef] [PubMed]

S. McNab, N. Moll, and Y. Vlasov, "Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides," Opt. Express 11, 2928-2939 (2003).
[CrossRef]

2002

M. Notomi, K. Yamada, A. Shinaya, J. Takahashi, C. Takahashi, and J. Yokohama, "Structural Tuning of Guiding Modes of Line-Defect Waveguides of Silicon-on-Insulator Photonic Crystal Slabs," IEEE J. of Quantum Electron. 38, 736-742 (2002).
[CrossRef]

J. E. Heebner and R. W. Boyd, "‘Slow’ and ‘fast’ light in resonator-coupled waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
[CrossRef]

2001

M. Notomi, K. Yamada, A. Shinaya, J. Takahashi, C. Takahashi, and J. Yokohama, "Single mode transmission within photonic bandgap of width-varied single-line-defect photonic crystal waveguides on SOI substrates," Electron. Lett. 37, 293-295 (2001)
[CrossRef]

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

Electron. Lett.

M. Notomi, K. Yamada, A. Shinaya, J. Takahashi, C. Takahashi, and J. Yokohama, "Single mode transmission within photonic bandgap of width-varied single-line-defect photonic crystal waveguides on SOI substrates," Electron. Lett. 37, 293-295 (2001)
[CrossRef]

IEEE J. of Quantum Electron.

M. Notomi, K. Yamada, A. Shinaya, J. Takahashi, C. Takahashi, and J. Yokohama, "Structural Tuning of Guiding Modes of Line-Defect Waveguides of Silicon-on-Insulator Photonic Crystal Slabs," IEEE J. of Quantum Electron. 38, 736-742 (2002).
[CrossRef]

J. Mod. Opt.

J. E. Heebner and R. W. Boyd, "‘Slow’ and ‘fast’ light in resonator-coupled waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E.

M. Soljacic, E. Lidorikis, L. Vestergaard Hau, and J. D. Joannopoulus, "Enhancement of microcavities lifetime using highly dispersive materials," Phys. Rev. E. 71, 026602 (2005).
[CrossRef]

Phys. Rev. Lett

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

Other

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystal: modeling the flow of light (Princeton University Press., Princeton, NJ, 1995).

The 3D problem was reduced to a 2D problem using effective index method. The core’s index is chosen so that the effective index of the strip waveguide’s modes in 3D will be the same as or very close to the one in 2D.

B. E. A. Saleh and M. C. Teich, Fundamentals of photonics (John Wiley &Sons, New York, 1991)
[CrossRef]

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Figures (11)

Fig. 1.
Fig. 1.

Illustration of the investigated device - a 1D PhC waveguide.

Fig. 2.
Fig. 2.

Band diagram of a 1D PhC waveguide of the type presented in Fig. 1.

Fig. 3.
Fig. 3.

FDTD simulation of transmission through a 60 periods long PhC waveguide (360nm period).

Fig. 4.
Fig. 4.

(a) Reflection and (b) group index of the 1D PhC waveguide as extracted from the simulation results presented in Fig. 3.

Fig. 5.
Fig. 5.

The quality factor analysis of disorder free, simulated PhC waveguide’s transmission spectra. (a) absolute value of quality factors. (b) quality factor ratio.

Fig. 6.
Fig. 6.

Index of refraction distribution. a - distribution of the “perfect” structure. b - distribution of the disordered structure. The color-bar represents the refraction index.

Fig. 7.
Fig. 7.

FDTD simulation of transmission spectrum through a 60 periods long PhC waveguide (360nm period) where disorder effects were added.

Fig. 8.
Fig. 8.

(a) Reflection, (b) group index and c - quality factor enhancement extracted from the simulations of 14 disordered 1D PhC FP resonators’. Symbols represent the values extracted and the continuous line is the trend line calculated by a polynomial fit. Dashed line corresponds to the simulation results of the disorder-free device.

Fig. 9.
Fig. 9.

A scanning-electron-microscope (SEM) picture of the fabricated 1D PhC and the corresponding measured transmission spectrum.

Fig. 10.
Fig. 10.

(a) Reflection, (b) group index and (c) quality factor enhancement extracted from the experiment results of four SOI 1D PhC FP resonators’. Symbols represent the values extracted and the continuous line is the trend line calculated by a polynomial fit. Dashed line corresponds to the simulation results of the disorder free device. The x-axis shows wavelength difference with respect to the band-edge wavelength.

Fig. 11.
Fig. 11.

Quality factor of four 1D PhC FPs extracted from the transmission spectrum measurements. Each FP device is represented with different marker type and color in the graph.

Equations (9)

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V = I max I min I max + I min
R ( 1 1 V 2 ) V
n g λ 0 2 2 L · Δ λ
Q = λ 0 δ λ
T ( υ ) = T max 1 + ( 2 F π ) 2 sin 2 ( π υ υ F )
υ 1 2 = υ res ± 2 υ F · sin 1 [ π ( 2 F ) ] π
δ λ = λ res 2 · sin 1 [ π ( 2 F ) ] π L · n eff
G ( u ) = h ( z ) · h ( z + u ) d z
G ( D ) = σ rough 2 e

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