Abstract

By performing time-resolved experiments and power-dependent measurements using femtosecond pulses inside submicron cross-section Si photonic-wire waveguides, we demonstrate strong cross-phase modulation (XPM) effects. We find that XPM in Si wires can be significant even for low peak pump powers, i.e., ∼15 mW for π phase shift. Our experimental data closely match numerical simulations using a rigorous coupled-wave theoretical treatment. Our results suggest that XPM is a potentially useful approach for all-optical control of photonic devices in Si wires.

© 2007 Optical Society of America

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2006 (15)

X.  Chen, N. C.  Panoiu, and R. M.  Osgood, "Theory of Raman-mediated pulsed amplification in silicon-wire waveguides," IEEE J. Quantum Electron.  42, 160-170 (2006).
[CrossRef]

E.  Dulkeith, F.  Xia, L.  Schares, W. M. J.  Green, and Y. A.  Vlasov, "Group index and group velocity dispersion in silicon on insulator photonic wires," Opt. Express  14, 3853-3863 (2006).
[CrossRef]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous GVD in Si channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

N. C.  Panoiu, X. G.  Chen, and R. M.  Osgood, "Modulation instability in silicon photonic nanowires," Opt. Lett. 31, 3609-3611 (2006).
[CrossRef] [PubMed]

X. Chen, N. Panoiu, I. Hsieh, J. I. Dadap, R. M. Osgood, Jr., "Third-order dispersion and ultrafast pulse propagation in silicon wire waveguides," IEEE Photon. Technol. Lett. 18, 2617-2619 (2006).
[CrossRef]

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

Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, "Ultrabroadband parametric generation and wavelength conversion in silicon waveguides," Opt. Express 14, 4786-4799 (2006).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broadband optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[CrossRef] [PubMed]

H. Rong, Y. -H. Kuo, A. Liu, M. Paniccia, and O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006).
[CrossRef] [PubMed]

A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, "Electrically pumped hybrid AlGaInAs-silicon evanescent laser," Opt. Express 14, 9203-9210 (2006).
[CrossRef] [PubMed]

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
[CrossRef] [PubMed]

I. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. McNab, and Y. A. Vlasov, "Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides," Opt. Express 14, 12380-12387 (2006).
[CrossRef] [PubMed]

R. Dekker, A. Driessen, T. Wahlbrink, C. Moormann, J. Niehusmann, and M. Först, "Ultrafast Kerr-induced all-optical wavelength conversion in silicon waveguides using 1.55 μm femtosecond pulses," Opt. Express 14, 8336-8346 (2006).
[CrossRef] [PubMed]

F. Xia, L. Sekaric, and Y. A. Vlasov, "Mode conversion losses in silicon-on-insulator photonic wire based racetrack resonators," Opt. Express 14, 3872-3886 (2006).
[CrossRef] [PubMed]

J. E. McMillan, X. D. Yang, N. C. Panoiu, R. M. Osgood, and C. W. Wong, "Enhanced stimulated Raman scattering in slow-light photonic crystal waveguides," Opt. Lett. 31, 1235-1237 (2006).
[CrossRef] [PubMed]

2005 (7)

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, 65-69 (2005).
[CrossRef] [PubMed]

D. Dimitripoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, "Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides," Appl. Phys. Lett.  86, 071115 (2005)
[CrossRef]

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 294-296 (2005).
[CrossRef]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature  435, 325-327 (2005).
[CrossRef] [PubMed]

S. Emelett and R. Soref, "Analysis of dual-microring-resonator cross-connect switches and modulators," Opt. Express 13, 7840-7853 (2005).
[CrossRef] [PubMed]

R. Espinola, J. I. Dadap, R. Osgood, Jr., S. McNab, and Y. Vlasov, "C-band wavelength conversion in silicon photonic wire waveguides," Opt. Express 13, 4341-4349 (2005).
[CrossRef] [PubMed]

H.  Fukuda, K.  Yamada, T.  Shoji, M.  Takahashi, T.  Tsuchizawa, T.  Watanabe, J.  Takahashi, and S.  Itabashi, "Four-wave mixing in silicon wire waveguides," Opt. Express  13, 4629-4637 (2005).
[CrossRef] [PubMed]

2004 (8)

2003 (2)

M.  Dinu, F.  Quochi, and H.  Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett.  82, 2954-2956 (2003).
[CrossRef]

R. L. Espinola, M.-C. Tai, J. T. Yardley, and R. M. Osgood, "Fast and low-power thermooptic switch on thin silicon-on-insulator," IEEE Photon. Technol. Lett. 15, 1366-1368 (2003).
[CrossRef]

2002 (1)

H. K.  Tsang, C. S.  Wong, T. K.  Liang, I. E.  Day, S.  Roberts, A.  Harpin, J.  Drake, and M.  Asghari, "Optical dispersion, TPA and SPM in Si waveguides at 1.5 μm wavelength," Appl. Phys. Lett.  80, 416-418 (2002).
[CrossRef]

1989 (1)

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, "Temporal and spectral effects of cross-phase modulation on copropagating ultrashort pulses in optical fibers," Phys. Rev. A 40, 5063-5072 (1989).
[CrossRef] [PubMed]

1987 (1)

R. Soref and B. Bennett, "Electrooptical effects of silicon," IEEE J. Quantum Electron. QE-23123-129 (1987).
[CrossRef]

Agrawal, G. P.

Alfano, R. R.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, "Temporal and spectral effects of cross-phase modulation on copropagating ultrashort pulses in optical fibers," Phys. Rev. A 40, 5063-5072 (1989).
[CrossRef] [PubMed]

Asghari, M.

H. K.  Tsang, C. S.  Wong, T. K.  Liang, I. E.  Day, S.  Roberts, A.  Harpin, J.  Drake, and M.  Asghari, "Optical dispersion, TPA and SPM in Si waveguides at 1.5 μm wavelength," Appl. Phys. Lett.  80, 416-418 (2002).
[CrossRef]

Baldeck, P. L.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, "Temporal and spectral effects of cross-phase modulation on copropagating ultrashort pulses in optical fibers," Phys. Rev. A 40, 5063-5072 (1989).
[CrossRef] [PubMed]

Bennett, B.

R. Soref and B. Bennett, "Electrooptical effects of silicon," IEEE J. Quantum Electron. QE-23123-129 (1987).
[CrossRef]

Bowers, J. E.

Boyraz, O.

Chen, X.

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
[CrossRef] [PubMed]

I. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. McNab, and Y. A. Vlasov, "Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides," Opt. Express 14, 12380-12387 (2006).
[CrossRef] [PubMed]

X. Chen, N. Panoiu, I. Hsieh, J. I. Dadap, R. M. Osgood, Jr., "Third-order dispersion and ultrafast pulse propagation in silicon wire waveguides," IEEE Photon. Technol. Lett. 18, 2617-2619 (2006).
[CrossRef]

X.  Chen, N. C.  Panoiu, and R. M.  Osgood, "Theory of Raman-mediated pulsed amplification in silicon-wire waveguides," IEEE J. Quantum Electron.  42, 160-170 (2006).
[CrossRef]

Chen, X. G.

Claps, R.

D. Dimitripoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, "Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides," Appl. Phys. Lett.  86, 071115 (2005)
[CrossRef]

Cohen, O.

Dadap, J. I.

Day, I. E.

H. K.  Tsang, C. S.  Wong, T. K.  Liang, I. E.  Day, S.  Roberts, A.  Harpin, J.  Drake, and M.  Asghari, "Optical dispersion, TPA and SPM in Si waveguides at 1.5 μm wavelength," Appl. Phys. Lett.  80, 416-418 (2002).
[CrossRef]

Dekker, R.

Dimitripoulos, D.

D. Dimitripoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, "Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides," Appl. Phys. Lett.  86, 071115 (2005)
[CrossRef]

Dinu, M.

M.  Dinu, F.  Quochi, and H.  Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett.  82, 2954-2956 (2003).
[CrossRef]

Drake, J.

H. K.  Tsang, C. S.  Wong, T. K.  Liang, I. E.  Day, S.  Roberts, A.  Harpin, J.  Drake, and M.  Asghari, "Optical dispersion, TPA and SPM in Si waveguides at 1.5 μm wavelength," Appl. Phys. Lett.  80, 416-418 (2002).
[CrossRef]

Driessen, A.

Dulkeith, E.

Emelett, S.

Espinola, R.

Espinola, R. L.

J. I. Dadap, R. L. Espinola, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, "Spontaneous Raman scattering in ultrasmall silicon waveguides," Opt. Lett. 29, 2755 (2004).
[CrossRef] [PubMed]

R. L. Espinola, M.-C. Tai, J. T. Yardley, and R. M. Osgood, "Fast and low-power thermooptic switch on thin silicon-on-insulator," IEEE Photon. Technol. Lett. 15, 1366-1368 (2003).
[CrossRef]

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 433, 294-296 (2005).
[CrossRef]

Fang, A. W.

Fauchet, P. M.

Först, M.

Foster, M. A.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broadband optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous GVD in Si channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

Fukuda, H.

Gaeta, A. L.

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous GVD in Si channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broadband optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[CrossRef] [PubMed]

Garcia, H.

M.  Dinu, F.  Quochi, and H.  Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett.  82, 2954-2956 (2003).
[CrossRef]

Geis, M. W.

M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, "Submicrosecond, submilliwatt, silicon on insulator thermooptic switch," IEEE Photon. Technol. Lett. 16, 2514-2516 (2004).
[CrossRef]

Green, W. M. J.

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 433, 294-296 (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, 65-69 (2005).
[CrossRef] [PubMed]

Harpin, A.

H. K.  Tsang, C. S.  Wong, T. K.  Liang, I. E.  Day, S.  Roberts, A.  Harpin, J.  Drake, and M.  Asghari, "Optical dispersion, TPA and SPM in Si waveguides at 1.5 μm wavelength," Appl. Phys. Lett.  80, 416-418 (2002).
[CrossRef]

Hsieh, I.

X. Chen, N. Panoiu, I. Hsieh, J. I. Dadap, R. M. Osgood, Jr., "Third-order dispersion and ultrafast pulse propagation in silicon wire waveguides," IEEE Photon. Technol. Lett. 18, 2617-2619 (2006).
[CrossRef]

I. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. McNab, and Y. A. Vlasov, "Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides," Opt. Express 14, 12380-12387 (2006).
[CrossRef] [PubMed]

Indukuri, T.

Itabashi, S.

Jalali, B.

Jhaveri, R.

D. Dimitripoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, "Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides," Appl. Phys. Lett.  86, 071115 (2005)
[CrossRef]

Jones, R.

A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, "Electrically pumped hybrid AlGaInAs-silicon evanescent laser," Opt. Express 14, 9203-9210 (2006).
[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 433, 294-296 (2005).
[CrossRef]

Koonath, P.

Kuo, Y. -H.

Liang, T. K.

H. K.  Tsang, C. S.  Wong, T. K.  Liang, I. E.  Day, S.  Roberts, A.  Harpin, J.  Drake, and M.  Asghari, "Optical dispersion, TPA and SPM in Si waveguides at 1.5 μm wavelength," Appl. Phys. Lett.  80, 416-418 (2002).
[CrossRef]

Lin, Q.

Lipson, M.

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous GVD in Si channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broadband optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[CrossRef] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature  435, 325-327 (2005).
[CrossRef] [PubMed]

Liu, A.

H. Rong, Y. -H. Kuo, A. Liu, M. Paniccia, and O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006).
[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 433, 294-296 (2005).
[CrossRef]

Lyszczarz, T. M.

M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, "Submicrosecond, submilliwatt, silicon on insulator thermooptic switch," IEEE Photon. Technol. Lett. 16, 2514-2516 (2004).
[CrossRef]

Manolatou, C.

McMillan, J. E.

McNab, S.

McNab, S. J.

Moormann, C.

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 433, 294-296 (2005).
[CrossRef]

Niehusmann, J.

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, 65-69 (2005).
[CrossRef] [PubMed]

Osgood, R.

Osgood, R. M.

I. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. McNab, and Y. A. Vlasov, "Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides," Opt. Express 14, 12380-12387 (2006).
[CrossRef] [PubMed]

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
[CrossRef] [PubMed]

X.  Chen, N. C.  Panoiu, and R. M.  Osgood, "Theory of Raman-mediated pulsed amplification in silicon-wire waveguides," IEEE J. Quantum Electron.  42, 160-170 (2006).
[CrossRef]

N. C.  Panoiu, X. G.  Chen, and R. M.  Osgood, "Modulation instability in silicon photonic nanowires," Opt. Lett. 31, 3609-3611 (2006).
[CrossRef] [PubMed]

X. Chen, N. Panoiu, I. Hsieh, J. I. Dadap, R. M. Osgood, Jr., "Third-order dispersion and ultrafast pulse propagation in silicon wire waveguides," IEEE Photon. Technol. Lett. 18, 2617-2619 (2006).
[CrossRef]

J. E. McMillan, X. D. Yang, N. C. Panoiu, R. M. Osgood, and C. W. Wong, "Enhanced stimulated Raman scattering in slow-light photonic crystal waveguides," Opt. Lett. 31, 1235-1237 (2006).
[CrossRef] [PubMed]

J. I. Dadap, R. L. Espinola, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, "Spontaneous Raman scattering in ultrasmall silicon waveguides," Opt. Lett. 29, 2755 (2004).
[CrossRef] [PubMed]

R. L. Espinola, M.-C. Tai, J. T. Yardley, and R. M. Osgood, "Fast and low-power thermooptic switch on thin silicon-on-insulator," IEEE Photon. Technol. Lett. 15, 1366-1368 (2003).
[CrossRef]

Paniccia, M.

H. Rong, Y. -H. Kuo, A. Liu, M. Paniccia, and O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006).
[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 433, 294-296 (2005).
[CrossRef]

Paniccia, M. J.

Panoiu, N.

X. Chen, N. Panoiu, I. Hsieh, J. I. Dadap, R. M. Osgood, Jr., "Third-order dispersion and ultrafast pulse propagation in silicon wire waveguides," IEEE Photon. Technol. Lett. 18, 2617-2619 (2006).
[CrossRef]

Panoiu, N. C.

Park, H.

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature  435, 325-327 (2005).
[CrossRef] [PubMed]

Quochi, F.

M.  Dinu, F.  Quochi, and H.  Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett.  82, 2954-2956 (2003).
[CrossRef]

Raghunathan, V.

Rieger, G. W.

G. W.  Rieger, K. S.  Virk, and J. F.  Young, "Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides," Appl. Phys. Lett.  84, 900-902 (2004).
[CrossRef]

Roberts, S.

H. K.  Tsang, C. S.  Wong, T. K.  Liang, I. E.  Day, S.  Roberts, A.  Harpin, J.  Drake, and M.  Asghari, "Optical dispersion, TPA and SPM in Si waveguides at 1.5 μm wavelength," Appl. Phys. Lett.  80, 416-418 (2002).
[CrossRef]

Rong, H.

H. Rong, Y. -H. Kuo, A. Liu, M. Paniccia, and O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006).
[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 433, 294-296 (2005).
[CrossRef]

Schares, L.

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature  435, 325-327 (2005).
[CrossRef] [PubMed]

Schmidt, B. S.

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous GVD in Si channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broadband optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[CrossRef] [PubMed]

Sekaric, L.

Sharping, J. E.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broadband optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous GVD in Si channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

Shoji, T.

Soref, R.

S. Emelett and R. Soref, "Analysis of dual-microring-resonator cross-connect switches and modulators," Opt. Express 13, 7840-7853 (2005).
[CrossRef] [PubMed]

R. Soref and B. Bennett, "Electrooptical effects of silicon," IEEE J. Quantum Electron. QE-23123-129 (1987).
[CrossRef]

Spector, S. J.

M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, "Submicrosecond, submilliwatt, silicon on insulator thermooptic switch," IEEE Photon. Technol. Lett. 16, 2514-2516 (2004).
[CrossRef]

Tai, M.-C.

R. L. Espinola, M.-C. Tai, J. T. Yardley, and R. M. Osgood, "Fast and low-power thermooptic switch on thin silicon-on-insulator," IEEE Photon. Technol. Lett. 15, 1366-1368 (2003).
[CrossRef]

Takahashi, J.

Takahashi, M.

Tsang, H. K.

H. K.  Tsang, C. S.  Wong, T. K.  Liang, I. E.  Day, S.  Roberts, A.  Harpin, J.  Drake, and M.  Asghari, "Optical dispersion, TPA and SPM in Si waveguides at 1.5 μm wavelength," Appl. Phys. Lett.  80, 416-418 (2002).
[CrossRef]

Tsuchizawa, T.

Turner, A. C.

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous GVD in Si channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broadband optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[CrossRef] [PubMed]

Virk, K. S.

G. W.  Rieger, K. S.  Virk, and J. F.  Young, "Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides," Appl. Phys. Lett.  84, 900-902 (2004).
[CrossRef]

Vlasov, Y.

Vlasov, Y. A.

E.  Dulkeith, F.  Xia, L.  Schares, W. M. J.  Green, and Y. A.  Vlasov, "Group index and group velocity dispersion in silicon on insulator photonic wires," Opt. Express  14, 3853-3863 (2006).
[CrossRef]

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
[CrossRef] [PubMed]

I. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. McNab, and Y. A. Vlasov, "Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides," Opt. Express 14, 12380-12387 (2006).
[CrossRef] [PubMed]

F. Xia, L. Sekaric, and Y. A. Vlasov, "Mode conversion losses in silicon-on-insulator photonic wire based racetrack resonators," Opt. Express 14, 3872-3886 (2006).
[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, 65-69 (2005).
[CrossRef] [PubMed]

J. I. Dadap, R. L. Espinola, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, "Spontaneous Raman scattering in ultrasmall silicon waveguides," Opt. Lett. 29, 2755 (2004).
[CrossRef] [PubMed]

R. Espinola, J. I. Dadap, R. Osgood, Jr., S. J. McNab, and Y. A. Vlasov, "Raman amplification in ultrasmall silicon-on-insulator wire waveguides," Opt. Express 12, 3713-3718 (2004).
[CrossRef] [PubMed]

Y. A.  Vlasov and S. J.  McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends," Opt. Express  12, 1622-1631 (2004).
[CrossRef] [PubMed]

Wahlbrink, T.

Watanabe, T.

Williamson, R. C.

M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, "Submicrosecond, submilliwatt, silicon on insulator thermooptic switch," IEEE Photon. Technol. Lett. 16, 2514-2516 (2004).
[CrossRef]

Wong, C. S.

H. K.  Tsang, C. S.  Wong, T. K.  Liang, I. E.  Day, S.  Roberts, A.  Harpin, J.  Drake, and M.  Asghari, "Optical dispersion, TPA and SPM in Si waveguides at 1.5 μm wavelength," Appl. Phys. Lett.  80, 416-418 (2002).
[CrossRef]

Wong, C. W.

Woo, J. C. S.

D. Dimitripoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, "Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides," Appl. Phys. Lett.  86, 071115 (2005)
[CrossRef]

Xia, F.

Xu, Q.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature  435, 325-327 (2005).
[CrossRef] [PubMed]

Yamada, K.

Yang, X. D.

Yardley, J. T.

R. L. Espinola, M.-C. Tai, J. T. Yardley, and R. M. Osgood, "Fast and low-power thermooptic switch on thin silicon-on-insulator," IEEE Photon. Technol. Lett. 15, 1366-1368 (2003).
[CrossRef]

Yin, L.

Young, J. F.

G. W.  Rieger, K. S.  Virk, and J. F.  Young, "Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides," Appl. Phys. Lett.  84, 900-902 (2004).
[CrossRef]

Zhang, J.

Appl. Phys. Lett. (4)

H. K.  Tsang, C. S.  Wong, T. K.  Liang, I. E.  Day, S.  Roberts, A.  Harpin, J.  Drake, and M.  Asghari, "Optical dispersion, TPA and SPM in Si waveguides at 1.5 μm wavelength," Appl. Phys. Lett.  80, 416-418 (2002).
[CrossRef]

D. Dimitripoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, "Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides," Appl. Phys. Lett.  86, 071115 (2005)
[CrossRef]

G. W.  Rieger, K. S.  Virk, and J. F.  Young, "Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides," Appl. Phys. Lett.  84, 900-902 (2004).
[CrossRef]

M.  Dinu, F.  Quochi, and H.  Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett.  82, 2954-2956 (2003).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. Soref and B. Bennett, "Electrooptical effects of silicon," IEEE J. Quantum Electron. QE-23123-129 (1987).
[CrossRef]

X.  Chen, N. C.  Panoiu, and R. M.  Osgood, "Theory of Raman-mediated pulsed amplification in silicon-wire waveguides," IEEE J. Quantum Electron.  42, 160-170 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

X. Chen, N. Panoiu, I. Hsieh, J. I. Dadap, R. M. Osgood, Jr., "Third-order dispersion and ultrafast pulse propagation in silicon wire waveguides," IEEE Photon. Technol. Lett. 18, 2617-2619 (2006).
[CrossRef]

R. L. Espinola, M.-C. Tai, J. T. Yardley, and R. M. Osgood, "Fast and low-power thermooptic switch on thin silicon-on-insulator," IEEE Photon. Technol. Lett. 15, 1366-1368 (2003).
[CrossRef]

M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, "Submicrosecond, submilliwatt, silicon on insulator thermooptic switch," IEEE Photon. Technol. Lett. 16, 2514-2516 (2004).
[CrossRef]

Nature (4)

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broadband optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
[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 433, 294-296 (2005).
[CrossRef]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature  435, 325-327 (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, 65-69 (2005).
[CrossRef] [PubMed]

Opt. Express (17)

O.  Boyraz, T.  Indukuri, and B.  Jalali, "Self-phase-modulation induced spectral broadening in silicon waveguides," Opt. Express  12, 829-834 (2004).
[CrossRef] [PubMed]

Y. A.  Vlasov and S. J.  McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends," Opt. Express  12, 1622-1631 (2004).
[CrossRef] [PubMed]

R. Espinola, J. I. Dadap, R. Osgood, Jr., S. J. McNab, and Y. A. Vlasov, "Raman amplification in ultrasmall silicon-on-insulator wire waveguides," Opt. Express 12, 3713-3718 (2004).
[CrossRef] [PubMed]

O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, "All optical switching and continuum generation in silicon waveguides," Opt. Express 12, 4094-4102 (2004).
[CrossRef] [PubMed]

O. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004).
[CrossRef] [PubMed]

R. Espinola, J. I. Dadap, R. Osgood, Jr., S. McNab, and Y. Vlasov, "C-band wavelength conversion in silicon photonic wire waveguides," Opt. Express 13, 4341-4349 (2005).
[CrossRef] [PubMed]

H.  Fukuda, K.  Yamada, T.  Shoji, M.  Takahashi, T.  Tsuchizawa, T.  Watanabe, J.  Takahashi, and S.  Itabashi, "Four-wave mixing in silicon wire waveguides," Opt. Express  13, 4629-4637 (2005).
[CrossRef] [PubMed]

S. Emelett and R. Soref, "Analysis of dual-microring-resonator cross-connect switches and modulators," Opt. Express 13, 7840-7853 (2005).
[CrossRef] [PubMed]

H. Rong, Y. -H. Kuo, A. Liu, M. Paniccia, and O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006).
[CrossRef] [PubMed]

E.  Dulkeith, F.  Xia, L.  Schares, W. M. J.  Green, and Y. A.  Vlasov, "Group index and group velocity dispersion in silicon on insulator photonic wires," Opt. Express  14, 3853-3863 (2006).
[CrossRef]

F. Xia, L. Sekaric, and Y. A. Vlasov, "Mode conversion losses in silicon-on-insulator photonic wire based racetrack resonators," Opt. Express 14, 3872-3886 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous GVD in Si channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, "Ultrabroadband parametric generation and wavelength conversion in silicon waveguides," Opt. Express 14, 4786-4799 (2006).
[CrossRef] [PubMed]

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
[CrossRef] [PubMed]

R. Dekker, A. Driessen, T. Wahlbrink, C. Moormann, J. Niehusmann, and M. Först, "Ultrafast Kerr-induced all-optical wavelength conversion in silicon waveguides using 1.55 μm femtosecond pulses," Opt. Express 14, 8336-8346 (2006).
[CrossRef] [PubMed]

A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, "Electrically pumped hybrid AlGaInAs-silicon evanescent laser," Opt. Express 14, 9203-9210 (2006).
[CrossRef] [PubMed]

I. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. McNab, and Y. A. Vlasov, "Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides," Opt. Express 14, 12380-12387 (2006).
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Rev. A (1)

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, "Temporal and spectral effects of cross-phase modulation on copropagating ultrashort pulses in optical fibers," Phys. Rev. A 40, 5063-5072 (1989).
[CrossRef] [PubMed]

Other (4)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999).
[CrossRef]

I. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, S. McNab, Y. A. Vlasov, and R. M. Osgood, "Cross-phase modulation in Si Photonic Wire Waveguides," CLEO Conference Proceedings, Anaheim, CA (2006).

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1989).

"BeamProp," RSoftDesign, Inc., .

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Figures (8)

Fig. 1.
Fig. 1.

(a) Effective and group indices of the silicon photonic wire waveguide; in (b) second-(solid) and third-order (dashed) dispersion coefficients of the silicon photonic wire.

Fig. 2.
Fig. 2.

Comparison between experimental and theoretical normalized pump spectra, corresponding to Pp = 40mW. Figures in inset show experimental results of pump spectra corresponding to peak pump powers of (i) 5 mW, (ii) 20 mW, and (iii) 35 mW.

Fig. 3.
Fig. 3.

Experimental spectra showing the dependence of the probe spectrum on the peak pump power for Td = 200 fs. For each subplot, the red curve shows the probe spectrum without the presence of the pump and the blue curve shows the probe spectrum with the pump. Strong pump power dependence is observed.

Fig. 4.
Fig. 4.

Experimental spectra showing the dependence of the probe spectrum on the probe power for a fixed pump-probe delay and a fixed pump power of Pp = 20 mW.

Fig. 5.
Fig. 5.

Panel (a): Simulated probe spectra in linear scale for different values of peak pump powers (Note: probe spectra are vertically offset for clarity). Inset in panel (a): probe spectra in logarithmic scale. Panel (b): Dependence of probe spectra on probe power (in logarithmic scale) at a fixed pump power Pp = 100 mW. Note that the shape of the output spectrum remains unchanged with increasing peak probe power by 10×.

Fig. 6.
Fig. 6.

Experimental (a) and numerical simulation (b) results showing the dependence of the XPM on the time delay. The sub-plots show the output probe spectra measured at several time delays. For each sub-plot, on the y-axis, the optical power is normalized to the peak of the output at Td = 2000 fs. The center wavelength of the probe is 1590 nm.

Fig. 7.
Fig. 7.

Temporal (a) and spectral (b) profiles of the probe pulse. Red line: experiment; blue dotted line: numerical simulation.

Fig 8.
Fig 8.

Center wavelength shift as a function of time delay, Td. Td is positive (negative) when the pump is trailing (leading) the probe at the input of Si-wire waveguide.

Equations (7)

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i ( u p z + 1 v g , p u p t ) β 2 , p 2 2 u p t 2 i β 3 , p 6 3 u p t 3 = icκ p 2 nv g , p ( α in + α FC p ) u p ω p κ p nv g , p δn FC p u p 3 ω p ε 0 A 0 v g , p ( P p Γ p v g , p u p 2 + 2 P s Γ sp v g , s u s 2 ) u p ,
i ( u s z + 1 v g , s u s t ) β 2 , s 2 2 u s t 2 i β 3 , s 6 3 u s t 3 = icκ s 2 nv g , s ( α in + α FC s ) u s ω s κ s nv g , s δ n FC s u s 3 ω s ε 0 A 0 v g , s ( P s Γ s v g , s u s 2 + 2 P p Γ ps v g , p u p 2 ) u s ,
N t = N t c + 3 ε 0 A 0 2 [ P p 2 Γ p " v g , p 2 u p 4 + P s 2 Γ s " v g , s 2 u s 4 + 4 ( ω p Γ sp " + ω s Γ ps " ) P p P s ( ω p + ω s ) v g , p v g , s u p u s 2 ] ,
ϕ s z T = z γ s P s u s 0 T 2 + 2 γ ps P p 0 z u p ( 0 , T + z ' Δ ) 2 dz ' .
ϕ s z τ = γ ps P p z π δ [ erf ( τ τ d + δ ) erf ( τ τ d ) ] ,
δω s z τ = 1 T p ϕ s ( z , τ ) τ = 2 γ ps P p z T p δ { exp [ ( τ τ d + δ ) 2 ] exp [ ( τ τ d ) 2 ] } .
u s 0 T = P s { exp [ 1 2 ( T T s ) 2 T αT s ] + A exp [ 1 2 ( T αT s ) 2 ] }

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