Abstract

The simultaneous generation of second and third order dispersion is demonstrated using nonlinearly chirped silicon waveguide gratings. The nonlinearly chirped gratings are designed to generate varying signs and magnitudes of group velocity dispersion and dispersion slope. The design, fabrication, and experimental characterization of the silicon waveguide gratings are performed. Second order dispersion as high as −2.3 X 106 ps/nm/km and third order dispersion as high as 1.2 X 105 ps/nm2/km and as low as 1.2 X 104 ps/nm2/km is demonstrated at 1.55µm.

© 2013 Optical Society of America

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2013

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, “Phase-resolved observations of optical pulse propagation in chip-scale silicon nanowires,” Appl. Phys. Lett.103(2), 021103 (2013).
[CrossRef]

2012

2011

2010

2009

2007

2006

2005

P. I. Reyes, N. Litchinitser, M. Sumetsky, and P. S. Westbrook, “160-Gb/s tunable dispersion slope compensator using a chirped fiber Bragg grating and a quadratic heater,” IEEE Photonics Technol. Lett.17(4), 831–833 (2005).
[CrossRef]

2004

S. Matsumoto, M. Takabayashi, K. Yoshiara, T. Sugihara, T. Miyazaki, and F. Kubota, “Tunable dispersion slope compensator with a chirped fiber grating and a divided thin-film heater for 160-Gb/s RZ transmissions,” IEEE Photonics Technol. Lett.16(4), 1095–1097 (2004).
[CrossRef]

2003

2001

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(25), 253902 (2001).
[CrossRef] [PubMed]

2000

M. Nakazawa, T. Yamamoto, and K. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett.36(24), 2027–2029 (2000).
[CrossRef]

1997

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuously-written fibre Bragg gratings for combined second-and third-order dispersion compensation,” Electron. Lett.33(22), 1891–1893 (1997).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature390(6656), 143–145 (1997).
[CrossRef]

1995

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett.31(11), 899–901 (1995).
[CrossRef]

1994

1979

Agarwal, A.

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, A. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy,” IEEE J. Sel. Top. Quantum Electron.18(6), 1799–1806 (2012).
[CrossRef]

Agrawal, G. P.

Albert, J.

Ayache, M.

Beausoleil, R. G.

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, A. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy,” IEEE J. Sel. Top. Quantum Electron.18(6), 1799–1806 (2012).
[CrossRef]

L. Zhang, Y. Yue, R. G. Beausoleil, and A. E. Willner, “Analysis and engineering of chromatic dispersion in silicon waveguide bends and ring resonators,” Opt. Express19(9), 8102–8107 (2011).
[CrossRef] [PubMed]

Bergman, K.

Bilodeau, F.

Chen, X.

Chrostowski, L.

Cole, M. J.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuously-written fibre Bragg gratings for combined second-and third-order dispersion compensation,” Electron. Lett.33(22), 1891–1893 (1997).
[CrossRef]

Cunningham, J. E.

Dadap, J. I.

Dhosi, G.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett.31(11), 899–901 (1995).
[CrossRef]

Driscoll, J. B.

Dulkeith, E.

Durkin, M.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuously-written fibre Bragg gratings for combined second-and third-order dispersion compensation,” Electron. Lett.33(22), 1891–1893 (1997).
[CrossRef]

Eggleton, B.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett.31(11), 899–901 (1995).
[CrossRef]

Fainman, Y.

Fan, S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature390(6656), 143–145 (1997).
[CrossRef]

Feced, R.

Ferrera, J.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature390(6656), 143–145 (1997).
[CrossRef]

Foresi, J. S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature390(6656), 143–145 (1997).
[CrossRef]

Foster, M. A.

Gaeta, A. L.

Green, W. M. J.

Grieco, A.

Grist, S.

Grote, R. R.

Hill, K. O.

Hsieh, I.-W.

Husko, C. A.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, “Phase-resolved observations of optical pulse propagation in chip-scale silicon nanowires,” Appl. Phys. Lett.103(2), 021103 (2013).
[CrossRef]

Ibsen, M.

M. Ibsen and R. Feced, “Fiber Bragg gratings for pure dispersion-slope compensation,” Opt. Lett.28(12), 980–982 (2003).
[CrossRef] [PubMed]

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuously-written fibre Bragg gratings for combined second-and third-order dispersion compensation,” Electron. Lett.33(22), 1891–1893 (1997).
[CrossRef]

Ikeda, K.

Ippen, E. P.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature390(6656), 143–145 (1997).
[CrossRef]

Jaeger, N. A. F.

Joannopoulos, J. D.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature390(6656), 143–145 (1997).
[CrossRef]

Johnson, D. C.

Khajavikhan, M.

Kim, H.-C.

Kimerling, L. C.

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, A. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy,” IEEE J. Sel. Top. Quantum Electron.18(6), 1799–1806 (2012).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature390(6656), 143–145 (1997).
[CrossRef]

Kitagawa, T.

Krishnamoorthy, A. V.

Krug, P. A.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett.31(11), 899–901 (1995).
[CrossRef]

Kubota, F.

S. Matsumoto, M. Takabayashi, K. Yoshiara, T. Sugihara, T. Miyazaki, and F. Kubota, “Tunable dispersion slope compensator with a chirped fiber grating and a divided thin-film heater for 160-Gb/s RZ transmissions,” IEEE Photonics Technol. Lett.16(4), 1095–1097 (2004).
[CrossRef]

Kwong, D. L.

Kwong, D.-L.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, “Phase-resolved observations of optical pulse propagation in chip-scale silicon nanowires,” Appl. Phys. Lett.103(2), 021103 (2013).
[CrossRef]

Laming, R. I.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, “1 m long continuously-written fibre Bragg gratings for combined second-and third-order dispersion compensation,” Electron. Lett.33(22), 1891–1893 (1997).
[CrossRef]

Li, X.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, “Phase-resolved observations of optical pulse propagation in chip-scale silicon nanowires,” Appl. Phys. Lett.103(2), 021103 (2013).
[CrossRef]

Liao, J.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, “Phase-resolved observations of optical pulse propagation in chip-scale silicon nanowires,” Appl. Phys. Lett.103(2), 021103 (2013).
[CrossRef]

Lin, Q.

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, A. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy,” IEEE J. Sel. Top. Quantum Electron.18(6), 1799–1806 (2012).
[CrossRef]

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett.31(9), 1295–1297 (2006).
[CrossRef] [PubMed]

Lipson, M.

Litchinitser, N.

P. I. Reyes, N. Litchinitser, M. Sumetsky, and P. S. Westbrook, “160-Gb/s tunable dispersion slope compensator using a chirped fiber Bragg grating and a quadratic heater,” IEEE Photonics Technol. Lett.17(4), 831–833 (2005).
[CrossRef]

Lo, G.-Q.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, “Phase-resolved observations of optical pulse propagation in chip-scale silicon nanowires,” Appl. Phys. Lett.103(2), 021103 (2013).
[CrossRef]

Luo, Y.

Malo, B.

Manolatou, C.

Marko, M. D.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, “Phase-resolved observations of optical pulse propagation in chip-scale silicon nanowires,” Appl. Phys. Lett.103(2), 021103 (2013).
[CrossRef]

Matsumoto, S.

S. Matsumoto, M. Takabayashi, K. Yoshiara, T. Sugihara, T. Miyazaki, and F. Kubota, “Tunable dispersion slope compensator with a chirped fiber grating and a divided thin-film heater for 160-Gb/s RZ transmissions,” IEEE Photonics Technol. Lett.16(4), 1095–1097 (2004).
[CrossRef]

McMillan, J. F.

McNab, S. J.

Michel, J.

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, A. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy,” IEEE J. Sel. Top. Quantum Electron.18(6), 1799–1806 (2012).
[CrossRef]

Miyagi, M.

Miyazaki, T.

S. Matsumoto, M. Takabayashi, K. Yoshiara, T. Sugihara, T. Miyazaki, and F. Kubota, “Tunable dispersion slope compensator with a chirped fiber grating and a divided thin-film heater for 160-Gb/s RZ transmissions,” IEEE Photonics Technol. Lett.16(4), 1095–1097 (2004).
[CrossRef]

Mizrahi, A.

Nakazawa, M.

M. Nakazawa, T. Yamamoto, and K. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett.36(24), 2027–2029 (2000).
[CrossRef]

Nezhad, M. P.

Nishida, S.

Notomi, M.

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(25), 253902 (2001).
[CrossRef] [PubMed]

Ophir, N.

Osgood, R. M.

Ouellette, F.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett.31(11), 899–901 (1995).
[CrossRef]

Panoiu, N. C.

Raj, K.

Reyes, P. I.

P. I. Reyes, N. Litchinitser, M. Sumetsky, and P. S. Westbrook, “160-Gb/s tunable dispersion slope compensator using a chirped fiber Bragg grating and a quadratic heater,” IEEE Photonics Technol. Lett.17(4), 831–833 (2005).
[CrossRef]

Schares, L.

Schmidt, B. S.

Sharping, J. E.

Shi, W.

Shinya, A.

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(25), 253902 (2001).
[CrossRef] [PubMed]

Shubin, I.

Slutsky, B.

Smith, H. I.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature390(6656), 143–145 (1997).
[CrossRef]

Steinmeyer, G.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature390(6656), 143–145 (1997).
[CrossRef]

Stephens, T.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett.31(11), 899–901 (1995).
[CrossRef]

Sugihara, T.

S. Matsumoto, M. Takabayashi, K. Yoshiara, T. Sugihara, T. Miyazaki, and F. Kubota, “Tunable dispersion slope compensator with a chirped fiber grating and a divided thin-film heater for 160-Gb/s RZ transmissions,” IEEE Photonics Technol. Lett.16(4), 1095–1097 (2004).
[CrossRef]

Sumetsky, M.

P. I. Reyes, N. Litchinitser, M. Sumetsky, and P. S. Westbrook, “160-Gb/s tunable dispersion slope compensator using a chirped fiber Bragg grating and a quadratic heater,” IEEE Photonics Technol. Lett.17(4), 831–833 (2005).
[CrossRef]

Sun, P. C.

D. T. H. Tan, P. C. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat. Commun.1(8), 116 (2010).
[CrossRef] [PubMed]

Takabayashi, M.

S. Matsumoto, M. Takabayashi, K. Yoshiara, T. Sugihara, T. Miyazaki, and F. Kubota, “Tunable dispersion slope compensator with a chirped fiber grating and a divided thin-film heater for 160-Gb/s RZ transmissions,” IEEE Photonics Technol. Lett.16(4), 1095–1097 (2004).
[CrossRef]

Takahashi, C.

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(25), 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

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(25), 253902 (2001).
[CrossRef] [PubMed]

Takiguchi, K.

Tamura, K.

M. Nakazawa, T. Yamamoto, and K. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett.36(24), 2027–2029 (2000).
[CrossRef]

Tan, D. T. H.

Thériault, S.

Thoen, E. R.

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the device generating third order group velocity dispersion. Inset shows a scanning electron micrograph of a device. (b) 2D FDTD modeling for the grating reflectivity with inputs at port 2 and (c) Simulated group delay for different values of ∆Λ with the input at port 1 (dashed lines) and port 2 (solid lines). (d) Group delay (green – without apodization and red – with apodization) and reflecivity (blue – without apodization and black – without apodization) for ∆Λ = 4nm, launched from port 1. (e) Extracted values of D and S plotted as a function of ∆Λ for inputs at ports 1 and 2.

Fig. 2
Fig. 2

Reflection spectrum for ∆Λ = 2nm, 4nm, 7nm and 10nm (port 2). Inset shows the transmission spectrum for ∆Λ = 2nm in linear units showing ~90% extinction.

Fig. 3
Fig. 3

(a) Calculated group index as a function of wavelength used to extract the group delay. (b) Group delay and reflectivity for device with ∆Λ = 2nm with light launched from port 2. (c) Group delay vs. wavelength for light launched into Ports 1 and 2 and for different values of ∆Λ. Circles denote group delay for light launched from port 1 (black - ∆Λ = 4nm, blue, ∆Λ = 7nm, red, ∆Λ = 10nm) Diamonds denote group delay for light launched form port 2 (yellow - ∆Λ = 4nm, purple - ∆Λ = 7nm, green - ∆Λ = 10nm).

Fig. 4
Fig. 4

(a) Fabry Perot oscillations arising from a device with L = 500µm with light launched into Port 2. (b) Measured S and D for light launched into Ports 1 and 2.

Equations (3)

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β(ω)= β 0 (ω)+ β ω (ω ω 0 )+ 1 2 2 β ω 2 (ω ω 0 ) 2 + 1 6 3 β ω 3 (ω ω 0 ) 3 +...
τ(λ)= S 2 (λ λ 0 ) 2 +D(λ λ 0 )+ τ 0 .,
Δλ(λ)= λ 2 2. n g (λ).L(λ) .

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