Abstract

We report on time-of-flight experimental measurements and numerical calculations of the group-index dispersion in a photonic crystal waveguide realized in silicon-on-insulator material. Experimentally group indices higher than 230 has been observed. Numerical 2D and 3D time-domain simulations show excellent agreement with the measured data.

© 2005 Optical Society of America

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References

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  23. 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).
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Appl. Phys. B (1)

D. Coquilat, A. Ribayrol, R. M. De La Rue, M. Le Vassor D�??Yerville, D. Cassagne, and J. P. Albert, �??Observation of band structure and reduced group velocity in epitaxial GaN-sapphire 2D photonic crystals,�?? Appl. Phys. B 73, 591-593 (2001).
[CrossRef]

Appl. Phys. Lett. (5)

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]

A. Yu. Petrov, and M. Eich, �??Zero dispersion at small group velocities in photonic crystal waveguides,�?? Appl. Phys. Lett. 85, 4866-4868 (2002).
[CrossRef]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romero, P. Viktorovich, M. Le Vassor d�??Yerville, D. Cassagne and C. Jouanin, �??Group velocity and propagation losses measurements in a single-line photonic-crystal waveguide on InP membranes,�?? Appl. Phys. Lett. 79, 2312-2314 (2001).
[CrossRef]

J. N. Munday and W. M. Robertson, �??Slow electromagnetic pulse propagation through a narrow transmission band in a coaxial photonic crystal,�?? Appl. Phys. Lett. 83, 1053-1055 (2003).
[CrossRef]

M. C. Netti, C. F. Finlayson, J. J. Baumberg, M. D. B. Charlton, M. E. Zoorob, J. S. Wilkinson, and G. J. Parker, �??Separation of photonic crystal waveguides modes using femtosecond time-of-flight,�?? Appl. Phys. Lett. 81, 3927-3931 (2002).
[CrossRef]

J. Lumin. (1)

J. Nakagawa, H. Kitano, F. Minami, T. Sawada, S. Yamaguchi, and K. Ohtaka, �??Large pulse distortion in a 3D photonic crystal,�?? J. Lumin. 108, 255-258 (2004).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

V. Kimberg, F. Gel�??mukhanov, and H. Agren, �??Angular anisotropy of the delay time of short pulses in impurity band based photonic crystals,�?? J. Opt. A: Pure Appl. Opt. 7, 118-122 (2005).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature Materials (1)

M. Soljacic and J. D. Joannopoulos, �??Enhancement of nonlinear effects using photonic crystals,�?? Nature Materials 3, 211-219 (2004).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. B (4)

M. Galli, D. Bajoni, F. Marabelli, L. C. Andreani, L. Pavesi, and G. Pucker, �??Photonic bands and group-velocity dispersion in Si/SiO photonic crystals from white-light interferometry,�?? Phys. Rev. B 69, 115107 (2004).
[CrossRef]

J. Gomez Rivas, A. Farre Bent, J. Niehusmann, P. Haring Bolivar, and H. Kurz, �??Time-resolved broadband analysis of slow-light propagation and superluminal transmission of electromagnetic waves in three-dimensional photonic crystals,�?? Phys. Rev. B 71, 155110 (2005).
[CrossRef]

C. Sauvan, P. Lalanne, and J. P. Hugonin, �??Slow-wave effect and mode-profile matching in photonic crystal microcavities,�?? Phys. Rev. B 71, 1651118 (2005).
[CrossRef]

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. E (1)

Yu. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and Ch. Hirlimann, �??Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystals,�?? Phys. Rev. E 60, 1030-1035 (1999).
[CrossRef]

Phys. Rev. Lett. (4)

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. 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]

S. Inoue and Y. Aoyagi, �??Design and fabrication of two-dimensional photonic crystals with predetermined nonlinear optical properties,�?? Phys. Rev. Lett. 94, 103904 (2005).
[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]

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Figures (9)

Fig. 1.
Fig. 1.

Experimental setup. Continuous-wave laser light is small-signal modulated and transmitted through the PhCW sample. The envelope phase is measured by the network analyzer after detection at the photodiode. The computer controls the wavelength of the laser light and records the envelope phase detected by the network analyzer. Prior to the ToF experiments the polarization is set using the twister just before the sample by sending light through the polarizer and detecting it after propagation through the PhCW utilizing an optical spectrum analyzer. Since there only is a cutoff for TE polarized light, spectral features can be used to recognize the TE polarization. When making the ToF measurements the twister before the polarizer is adjusted for maximal transmission.

Fig. 2.
Fig. 2.

Spectrum of the optical signal modulated with large-amplitude oscillations at 19 GHz. The modulation gives sidebands at λ ± 19 GHz. Hence, the spectral width is less than 0.4 nm. The large amplitude modulation introduces the higher order sidebands due to the non-linear response of the Mach-Zehnder interferometer (MZI). For small modulations the MZI response is linear to first order, i.e. the higher order sidebands are negligible.

Fig. 3.
Fig. 3.

Measured envelope phase (black points) and measured intensity (red curve) for the small amplitude modulated signal transmitted through a buried ridge waveguide and the rest of the experimental setup. The measurement is used for normalization. The phase points are fitted to a 3rd order polynomial and this fitted curve (light blue line) is used to calibrate the measurements for the 20 μm PhCW. The transmission spectrum is that of the 19-GHz modulated signal, and it primarily reflects the spectrum of the fiber amplifiers, which are designed for c-band (1530-1565nm) operation.

Fig. 4.
Fig. 4.

Black curve: Change in the phase ∆ϕelectric due to transmission of the signal through the PhCW. A large change in the phase is observed just before the band gap. Red curve: Transmission spectrum for a cw laser detected with an optical spectrum analyzer. The transmission spectrum is measured when the polarization is adjusted to TE polarized light prior to the envelope phase measurement.

Fig. 5.
Fig. 5.

High-resolution scan of the transmission spectrum for the waveguide containing the PhCW part. The two periodic oscillations originate from the waveguides leading the light to and from the PhCW part. The short period (long waveguide) is 0.07 nm while the long period (short waveguide) is 0.35 nm

Fig. 6.
Fig. 6.

Measured group indices for a 20-μm symmetric W1 PhCW (black line). The curve is averaged over 0.07 nm to remove the contribution from a physical long F-P cavity. Also shown is the corresponding experimental transmission (red line). The blue curve is the group index determined by ToF calculations using 2D FDTD. These data have been shifted to match the wavelength scale for the experimental data. It is noticed that local maxima of the group index coincide with local maxima for the transmission.

Fig. 7.
Fig. 7.

2D band diagram (left) and 2D transmission spectrum (right) calculated for a W1 PhCW. The waveguide parameters are: the triangular lattice constant Λ = 435 nm; hole diameter d = 282 nm; the internal diameter of the air filled silica ring inside the holes ds = 204 nm; length L = 30 μm; refractive index of the Si core n = 3.476. The red lines indicate the borders of the band gap and the blue line the cutoff for the guided defect PBG mode.

Fig. 8.
Fig. 8.

A typical time-of-flight picture of the impulses, recorded at the input (left impulse) and the output (right impulse) detectors.

Fig. 9.
Fig. 9.

3D FDTD calculated group index for the W1 PhCW (red data points). Also shown is the corresponding measured group index (black line) from Fig. 6. The numerical data have been shifted 2.7 % to match the wavelength scale of the experimental data.

Equations (4)

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v g = ω k .
v g = c 2 L Δ λ λ 2 ,
Δ n g = Δ ϕ electric c 360 ° l PhC f electric .
n g = c v g = c Δ t Δ L .

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