Abstract

We show that stimulated Raman scattering is a sufficiently strong effect in silicon waveguides to allow the intensity of a pump input to control the group delay of a weak Stokes-shifted signal. While the fractional change in group delay is minimal in a straight waveguide, microresonator enhancement can produce a fractional increase of 50% with respect to the linear group delay of the resonator.

© 2006 Optical Society of America

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  1. K. Y. Song, M. G. Herraez, and L. Thevenaz "Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering," Opt. Express 13, 82-88 (2005)http://www.opticsexpress.org/abstract.cfm?URI=oe-13-1-82.
    [CrossRef] [PubMed]
  2. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 69, 153902 (2005).
    [CrossRef]
  3. J. E. Sharping, Y. Okawachi, and A. L. Gaeta "Wide bandwidth slow light using a Raman fiber amplifier," Opt. Express 13, 6092-6098 (2005)http://www.opticsexpress.org/abstract.cfm?URI=oe-13-16-6092.
    [CrossRef] [PubMed]
  4. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 1731-1739 (2003)http://www.opticsexpress.org/abstract.cfm?URI=oe-11-15-1731.
    [CrossRef] [PubMed]
  5. H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
    [CrossRef]
  6. R. L. Espinola, J. I. Dadap, J. R. M. Osgood, S. J. McNab, and Y. A. Vlasov "Raman amplification in ultrasmall silicon-on-insulator waveguides," Opt. Express 12, 3713-3718 (2004)http://www.opticsexpress.org/abstract.cfm?URI=oe-12-16-3713.
    [CrossRef] [PubMed]
  7. Q. Xu, V. R. Almeida, and M. Lipson "Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides," Opt. Express 12, 4437-4442 (2004)http://www.opticsexpress.org/abstract.cfm?URI=oe-12-19-4437.
    [CrossRef] [PubMed]
  8. J. Heebner, R. W. Boyd, and Q.-H. Park "SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides," J. Opt. Soc. Am. B 19, 722-731 (2002).
    [CrossRef]
  9. Y. Chen and S. Blair "Nonlinear phase shift of cascaded microring resonators," J. Opt. Soc. Am. B 20, 2125-2132 (2003).
    [CrossRef]
  10. S. BlairOptical Soliton-Based Logic Gates. PhD thesis University of Colorado 1998, http://photonics.ece.utah.edu/files/blair_thesis_98.pdf.
  11. R. A. Soref and B. R. Bennett "Electrooptical effects in silicon," IEEE J. Quantum Electron. QE-23, 123-129 (1987).
    [CrossRef]
  12. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali "Influence of nonlinear absorption on Raman amplification in Silicon waveguides," Opt. Express 12, 2774-2780 (2004)http://www.opticsxpress.org/abstract.cfm?URI=oe-12-12-2774.
    [CrossRef] [PubMed]
  13. H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia "An all-silicon Raman laser," Nature (London) 433, 292-294 (2005).
    [CrossRef] [PubMed]
  14. D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio "Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range," Opt. Lett. 22, 1244-1246 (1997).
    [CrossRef] [PubMed]
  15. Y.-H. Kao, M. N. Islam, J. M. Saylor, R. E. Slusher, and W. S. Hobson "Raman effect in AlGaAs waveguides for subpicosecond pulses," J. Appl. Phys. 78, 2198-2203 (1995).
    [CrossRef]

2005 (4)

K. Y. Song, M. G. Herraez, and L. Thevenaz "Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering," Opt. Express 13, 82-88 (2005)http://www.opticsexpress.org/abstract.cfm?URI=oe-13-1-82.
[CrossRef] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 69, 153902 (2005).
[CrossRef]

J. E. Sharping, Y. Okawachi, and A. L. Gaeta "Wide bandwidth slow light using a Raman fiber amplifier," Opt. Express 13, 6092-6098 (2005)http://www.opticsexpress.org/abstract.cfm?URI=oe-13-16-6092.
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia "An all-silicon Raman laser," Nature (London) 433, 292-294 (2005).
[CrossRef] [PubMed]

2004 (4)

2003 (2)

2002 (1)

1997 (1)

1995 (1)

Y.-H. Kao, M. N. Islam, J. M. Saylor, R. E. Slusher, and W. S. Hobson "Raman effect in AlGaAs waveguides for subpicosecond pulses," J. Appl. Phys. 78, 2198-2203 (1995).
[CrossRef]

1987 (1)

R. A. Soref and B. R. Bennett "Electrooptical effects in silicon," IEEE J. Quantum Electron. QE-23, 123-129 (1987).
[CrossRef]

Almeida, V. R.

Bennett, B. R.

R. A. Soref and B. R. Bennett "Electrooptical effects in silicon," IEEE J. Quantum Electron. QE-23, 123-129 (1987).
[CrossRef]

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 69, 153902 (2005).
[CrossRef]

Blair, S.

Boyd, R. W.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 69, 153902 (2005).
[CrossRef]

J. Heebner, R. W. Boyd, and Q.-H. Park "SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides," J. Opt. Soc. Am. B 19, 722-731 (2002).
[CrossRef]

Chen, Y.

Claps, R.

Cohen, O.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia "An all-silicon Raman laser," Nature (London) 433, 292-294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

Dadap, J. I.

Dimitropoulos, D.

Espinola, R. L.

Fang, A.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia "An all-silicon Raman laser," Nature (London) 433, 292-294 (2005).
[CrossRef] [PubMed]

Gaeta, A. L.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 69, 153902 (2005).
[CrossRef]

J. E. Sharping, Y. Okawachi, and A. L. Gaeta "Wide bandwidth slow light using a Raman fiber amplifier," Opt. Express 13, 6092-6098 (2005)http://www.opticsexpress.org/abstract.cfm?URI=oe-13-16-6092.
[CrossRef] [PubMed]

Gauthier, D. J.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 69, 153902 (2005).
[CrossRef]

Hagness, S. C.

Hak, D.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia "An all-silicon Raman laser," Nature (London) 433, 292-294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

Han, Y.

Heebner, J.

Herraez, M. G.

Ho, S. T.

Hobson, W. S.

Y.-H. Kao, M. N. Islam, J. M. Saylor, R. E. Slusher, and W. S. Hobson "Raman effect in AlGaAs waveguides for subpicosecond pulses," J. Appl. Phys. 78, 2198-2203 (1995).
[CrossRef]

Islam, M. N.

Y.-H. Kao, M. N. Islam, J. M. Saylor, R. E. Slusher, and W. S. Hobson "Raman effect in AlGaAs waveguides for subpicosecond pulses," J. Appl. Phys. 78, 2198-2203 (1995).
[CrossRef]

Jalali, B.

Jones, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia "An all-silicon Raman laser," Nature (London) 433, 292-294 (2005).
[CrossRef] [PubMed]

Kao, Y.-H.

Y.-H. Kao, M. N. Islam, J. M. Saylor, R. E. Slusher, and W. S. Hobson "Raman effect in AlGaAs waveguides for subpicosecond pulses," J. Appl. Phys. 78, 2198-2203 (1995).
[CrossRef]

Lipson, M.

Liu, A.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia "An all-silicon Raman laser," Nature (London) 433, 292-294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

McNab, S. J.

Nicolaescu, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia "An all-silicon Raman laser," Nature (London) 433, 292-294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

Okawachi, Y.

J. E. Sharping, Y. Okawachi, and A. L. Gaeta "Wide bandwidth slow light using a Raman fiber amplifier," Opt. Express 13, 6092-6098 (2005)http://www.opticsexpress.org/abstract.cfm?URI=oe-13-16-6092.
[CrossRef] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 69, 153902 (2005).
[CrossRef]

Osgood, J. R. M.

Paniccia, M.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia "An all-silicon Raman laser," Nature (London) 433, 292-294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

Park, Q.-H.

Rafizadeh, D.

Raghunathan, V.

Rong, H.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia "An all-silicon Raman laser," Nature (London) 433, 292-294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

Saylor, J. M.

Y.-H. Kao, M. N. Islam, J. M. Saylor, R. E. Slusher, and W. S. Hobson "Raman effect in AlGaAs waveguides for subpicosecond pulses," J. Appl. Phys. 78, 2198-2203 (1995).
[CrossRef]

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 69, 153902 (2005).
[CrossRef]

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 69, 153902 (2005).
[CrossRef]

J. E. Sharping, Y. Okawachi, and A. L. Gaeta "Wide bandwidth slow light using a Raman fiber amplifier," Opt. Express 13, 6092-6098 (2005)http://www.opticsexpress.org/abstract.cfm?URI=oe-13-16-6092.
[CrossRef] [PubMed]

Slusher, R. E.

Y.-H. Kao, M. N. Islam, J. M. Saylor, R. E. Slusher, and W. S. Hobson "Raman effect in AlGaAs waveguides for subpicosecond pulses," J. Appl. Phys. 78, 2198-2203 (1995).
[CrossRef]

Song, K. Y.

Soref, R. A.

R. A. Soref and B. R. Bennett "Electrooptical effects in silicon," IEEE J. Quantum Electron. QE-23, 123-129 (1987).
[CrossRef]

Stair, K. A.

Taflove, A.

Thevenaz, L.

Tiberio, R. C.

Vlasov, Y. A.

Xu, Q.

Zhang, J. P.

Zhu, Z.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 69, 153902 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. A. Soref and B. R. Bennett "Electrooptical effects in silicon," IEEE J. Quantum Electron. QE-23, 123-129 (1987).
[CrossRef]

J. Appl. Phys. (1)

Y.-H. Kao, M. N. Islam, J. M. Saylor, R. E. Slusher, and W. S. Hobson "Raman effect in AlGaAs waveguides for subpicosecond pulses," J. Appl. Phys. 78, 2198-2203 (1995).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nature (London) (1)

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia "An all-silicon Raman laser," Nature (London) 433, 292-294 (2005).
[CrossRef] [PubMed]

Opt. Express (6)

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali "Influence of nonlinear absorption on Raman amplification in Silicon waveguides," Opt. Express 12, 2774-2780 (2004)http://www.opticsxpress.org/abstract.cfm?URI=oe-12-12-2774.
[CrossRef] [PubMed]

R. L. Espinola, J. I. Dadap, J. R. M. Osgood, S. J. McNab, and Y. A. Vlasov "Raman amplification in ultrasmall silicon-on-insulator waveguides," Opt. Express 12, 3713-3718 (2004)http://www.opticsexpress.org/abstract.cfm?URI=oe-12-16-3713.
[CrossRef] [PubMed]

Q. Xu, V. R. Almeida, and M. Lipson "Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides," Opt. Express 12, 4437-4442 (2004)http://www.opticsexpress.org/abstract.cfm?URI=oe-12-19-4437.
[CrossRef] [PubMed]

K. Y. Song, M. G. Herraez, and L. Thevenaz "Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering," Opt. Express 13, 82-88 (2005)http://www.opticsexpress.org/abstract.cfm?URI=oe-13-1-82.
[CrossRef] [PubMed]

J. E. Sharping, Y. Okawachi, and A. L. Gaeta "Wide bandwidth slow light using a Raman fiber amplifier," Opt. Express 13, 6092-6098 (2005)http://www.opticsexpress.org/abstract.cfm?URI=oe-13-16-6092.
[CrossRef] [PubMed]

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 1731-1739 (2003)http://www.opticsexpress.org/abstract.cfm?URI=oe-11-15-1731.
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 69, 153902 (2005).
[CrossRef]

Other (1)

S. BlairOptical Soliton-Based Logic Gates. PhD thesis University of Colorado 1998, http://photonics.ece.utah.edu/files/blair_thesis_98.pdf.

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Figures (7)

Fig. 1.
Fig. 1.

Cascaded microring resonator (CMRR) geometry.

Fig. 2.
Fig. 2.

Raman susceptibility for silicon leading to gain gR (left), nonlinear refraction nR (middle), and intensity-dependent group delay (right). The pump and signal wavelengths λp = 1.428 μm and λs = 1.545 μm.

Fig. 3.
Fig. 3.

Raman gain (left) and group delay (right) for a straight waveguide of 5.75 mm length versus pump intensity and normalized signal frequency.

Fig. 4.
Fig. 4.

Raman gain (left) and group delay (right) for a straight waveguide of 1.18 cm length versus pump intensity and normalized signal frequency.

Fig. 5.
Fig. 5.

Raman gain (left) and group delay (right) for a single resonator of 50 μm length and 50 GHz bandwidth versus pump intensity and normalized signal frequency.

Fig. 6.
Fig. 6.

Raman gain (left) and group delay (right) for a single resonator of 50 μm length and 25 GHz bandwidth versus pump intensity and normalized signal frequency.

Fig. 7.
Fig. 7.

Raman-induced group delay for N = 5 cascaded resonators of 50 GHz (left) and 25 GHz (right) bandwidths for input pump intensities n 2 Ip = 0 (lower series of symbols) and n 2 Ip = 1×10-6 (upper series). The lines represent total group delay of straight waveguides of the same effective lengths 1.15N mm (left) and 2.35N mm (right) at n 2 Ip = 1×10-6, showing virtually no change.

Equations (7)

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

E out E in = [ t a exp ( ) 1 t a exp ( ) ] N ,
dE p dz = 1 2 [ α + β 2 ( I p + 2 I s ) + g R ( Ω ) I s + σN ] E p + i ω p c [ n 2 ( I p + 2 I s ) + n R ( Ω ) I s + ρN ] E p
dE S dz = 1 2 [ α + β 2 ( I S + 2 I p ) + g R ( Ω ) I p + σN ] E S + i ω s c [ n 2 ( I S + 2 I p ) + n R ( Ω ) I p + ρN ] E S ,
g R ( ω ; Ω ) = R 0 ω ε 0 c 2 n ( ω ± Ω ) n 2 ( ω ) . Ω γ [ Ω f 2 Ω 2 ] 2 + Ω 2 γ 2
n R ( ω ; Ω ) = 1 4 n ( ω ) . R 0 ( Ω f 2 Ω 2 ) [ Ω f 2 Ω 2 ] 2 + Ω 2 γ 2 .
ϕ NL ( ω s ) = ω s c [ 2 n 2 + n R ( ω p ω s ) + ρτ β 2 2 ω p ] I p L ,
τ gd NL = NL ( ω s ) s = ω s c dn R ( ω p ω s ) s I p L ,

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