Abstract

We modelled strong slow wave modulation enhancement in a rib corrugated waveguide with respect to a conventional rib waveguide, both embedded in a reverse biased pn junction. This enhancement is characterized in terms of effective index change versus reverse bias variations from 0V to −10V and for moderate group velocities varying in the range 0.02c to 0.15c. Interaction lengths and insertion losses below 750 μm and 3dB are respectively found for voltage variations in the range −8V to −10V. Furthermore, the device electrical modulation bandwidth is expected to be higher than 10 GHz.

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2008

2007

L. O'Faolain, T. P. White, D. O'Brien, X. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15(20), 13129–13138 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-20-13129 .
[CrossRef] [PubMed]

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

L. Gu, W. Jiang, X. Chen, L. Wang, R. T. Chen, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

2006

F. Xia, L. Sekaric, M. O'Boyle, and Y. Vlasov, “Coupled resonator optical waveguides based on silicon-on-insulator photonic wires,” Appl. Phys. Lett. 89(4), 041122 (2006).
[CrossRef]

2005

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

H. Gersen, T. J. Karle, R. J. P. Engelsen, W. Boa, J. P. Korterik, N. F. v. 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]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Opt. Express 13(18), 7145–7159 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-18-7145 .
[CrossRef] [PubMed]

2003

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35(4/5), 365–379 (2003).
[CrossRef]

2002

1987

R. A. Soref and B. R. Bennett, “Electrooptical Effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

Andreani, L. C.

Beggs, D. M.

Bennett, B. R.

R. A. Soref and B. R. Bennett, “Electrooptical Effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

Boa, W.

H. Gersen, T. J. Karle, R. J. P. Engelsen, W. Boa, J. P. Korterik, N. F. v. 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]

Brosi, J. M.

Chen, R. T.

L. Gu, W. Jiang, X. Chen, L. Wang, R. T. Chen, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

L. Gu, W. Jiang, X. Chen, L. Wang, R. T. Chen, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

Chen, X.

L. Gu, W. Jiang, X. Chen, L. Wang, R. T. Chen, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

L. Gu, W. Jiang, X. Chen, L. Wang, R. T. Chen, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

Engelsen, R. J. P.

H. Gersen, T. J. Karle, R. J. P. Engelsen, W. Boa, J. P. Korterik, N. F. v. 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]

Fan, S.

Freude, W.

Garcia, J.

Gersen, H.

H. Gersen, T. J. Karle, R. J. P. Engelsen, W. Boa, J. P. Korterik, N. F. v. 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]

Gu, L.

L. Gu, W. Jiang, X. Chen, L. Wang, R. T. Chen, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Ibanescu, M.

Ippen, E.

Jiang, W.

L. Gu, W. Jiang, X. Chen, L. Wang, R. T. Chen, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

Jiang, Y.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Karle, T. J.

H. Gersen, T. J. Karle, R. J. P. Engelsen, W. Boa, J. P. Korterik, N. F. v. 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]

Koos, C.

Korterik, J. P.

H. Gersen, T. J. Karle, R. J. P. Engelsen, W. Boa, J. P. Korterik, N. F. v. 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]

Krauss, T. F.

Krauss,, T. F.

H. Gersen, T. J. Karle, R. J. P. Engelsen, W. Boa, J. P. Korterik, N. F. v. 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]

Kuipers, L.

H. Gersen, T. J. Karle, R. J. P. Engelsen, W. Boa, J. P. Korterik, N. F. v. 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]

Leuthold, J.

Marti, J.

Martinelli, M.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35(4/5), 365–379 (2003).
[CrossRef]

Martinez, A.

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Melloni, A.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35(4/5), 365–379 (2003).
[CrossRef]

Morichetti, F.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35(4/5), 365–379 (2003).
[CrossRef]

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

O’Faolain, L.

O'Boyle, M.

F. Xia, L. Sekaric, M. O'Boyle, and Y. Vlasov, “Coupled resonator optical waveguides based on silicon-on-insulator photonic wires,” Appl. Phys. Lett. 89(4), 041122 (2006).
[CrossRef]

O'Brien, D.

O'Faolain, L.

Povinelli, M. L.

Sanchis, P.

Sekaric, L.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

F. Xia, L. Sekaric, M. O'Boyle, and Y. Vlasov, “Coupled resonator optical waveguides based on silicon-on-insulator photonic wires,” Appl. Phys. Lett. 89(4), 041122 (2006).
[CrossRef]

Settle, M. D.

Soljacic, M.

Soref, R. A.

R. A. Soref and B. R. Bennett, “Electrooptical Effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

v. Hulst, N. F.

H. Gersen, T. J. Karle, R. J. P. Engelsen, W. Boa, J. P. Korterik, N. F. v. 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]

Vlasov, Y.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

F. Xia, L. Sekaric, M. O'Boyle, and Y. Vlasov, “Coupled resonator optical waveguides based on silicon-on-insulator photonic wires,” Appl. Phys. Lett. 89(4), 041122 (2006).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Waldow, M.

Wang, L.

L. Gu, W. Jiang, X. Chen, L. Wang, R. T. Chen, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

L. Gu, W. Jiang, X. Chen, L. Wang, R. T. Chen, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

White, T. P.

Xia, F.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

F. Xia, L. Sekaric, M. O'Boyle, and Y. Vlasov, “Coupled resonator optical waveguides based on silicon-on-insulator photonic wires,” Appl. Phys. Lett. 89(4), 041122 (2006).
[CrossRef]

Yuan, X.

Appl. Phys. Lett.

F. Xia, L. Sekaric, M. O'Boyle, and Y. Vlasov, “Coupled resonator optical waveguides based on silicon-on-insulator photonic wires,” Appl. Phys. Lett. 89(4), 041122 (2006).
[CrossRef]

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

L. Gu, W. Jiang, X. Chen, L. Wang, R. T. Chen, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

IEEE J. Quantum Electron.

R. A. Soref and B. R. Bennett, “Electrooptical Effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Nature

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35(4/5), 365–379 (2003).
[CrossRef]

Phys. Rev. Lett.

H. Gersen, T. J. Karle, R. J. P. Engelsen, W. Boa, J. P. Korterik, N. F. v. 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]

Other

A. Brimont, F. Y. Gardes, P. Sanchis, D. Marris-Morini, P. Dumon, J. M. Fedeli, L. O'Faolain, W. Bogaert, L. Vivien, J. Martí, G. T. Reed, and T. F. Krauss, “Design of a micro-ring resonator electro-optical modulator embedded in a reverse biased PN junction,” Proc. 14th ECIO, 321–324 (2008).

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Figures (6)

Fig. 1
Fig. 1

Schematics of the 1D PhC corrugated waveguide and the fundamental slow mode Ex component profile respectively in the narrow and wide section.

Fig. 2
Fig. 2

Contour plot of the fundamental mode wavelengths in the slow light regime versus varying periodic elements size for undoped silicon corrugated waveguides. The blue contour line has been derived including the slight refractive index variation at λ = 1.55 μm due to the impurities introduced into the waveguide. Results are plotted at the band edge (k = 0.5*2π/a).

Fig. 3
Fig. 3

Refractive index change Δn under different static voltages ΔV = −10V (a) (d); −6V (b) (e); −2V (c) (f) for the thin and wide sections of the corrugated waveguide, respectively.

Fig. 4
Fig. 4

(a) Refractive index change versus reverse bias variation for varying group velocity. (b) Figure of merit calculated from Eq. (3) versus voltage for varying group velocity

Fig. 5
Fig. 5

(a) Insertion losses and (b) interaction length versus applied reverse bias variation.

Fig. 6
Fig. 6

3 dB cut-off frequency dependence upon varying group velocity and applied voltage variations

Equations (8)

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

n=ne+nh+nSi=(8.8.1022Ne+8.5.1018Nh0.8)+nSi
n(V)=ne(V)+nh(V)+nSi(V)=(8.8.1022Ne(V)+8.5.1018Nh(V)0.8)+nSi
Fmerit=Δneffcorr/Δneffrib
Insertionlosses(dB)=10log10exp(αcarriers.1/VG.Lπαroughness.1/VG.Lπ)
αcarriers(V)=αe(V)+αh(V)=8.5.1018Ne(V)+6.1018Nh(V)
f3dB=0.556VG,optLπ1|1+VG,opt/VG,el|
f3dB=0.556VG,optLπ
f3dB=0.556VG,optLπ1|1VG,opt/VG,el|

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