Abstract

We propose a new numerical model to analyze heat induced by two-photon absorption and free-carrier absorption, while high intensity optical pulses propagate along silicon-on-insulator (SOI) nanowaveguides (NWGs). Using this model, we demonstrate that such induced heat causes a shift in the amount of wavelength conversion and hence deteriorates the converter output characteristics for pulses in the picosecond regime. The wavelength shift induced by a pulse with maximum input intensity and full width at half-maximum of Imax=1.5×1010W.cm2 and TFWHM=30ps, propagating along a SOI NWG with an effective cross-sectional area of aeff=0.15μm2, is shown to be Δλs8pm. We also demonstrate that such a shift can be compensated by tuning the pump intensity down by approximately 6.33%.

© 2009 Optical Society of America

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  1. 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).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux , S. Beckx, D. Taillaert, B. Luyssaert, J.Van Campenhout, P. Bientsmann, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23, 401-413 (2005).
    [CrossRef]
  6. F. Grillot, L. Vivien, S. Laval, and E. Cassan, “Propagation loss in single-mode ultrasmall square silicon-on-insulator optical waveguides,” J. Lightwave Technol. 24, 891-896 (2006).
    [CrossRef]
  7. Y. H. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia and O. Cohen, “Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides,” Opt. Express 14, 11721-11726(2006).
    [CrossRef] [PubMed]
  8. T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun. 265, 171-174 (2006).
    [CrossRef]
  9. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
    [CrossRef] [PubMed]
  10. T. K. Liang, L. R. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. R. A. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. K. Tsang, “Ultrafast all-optical switching by cross absorption modulation in silicon wire waveguides,” Opt. Express 13, 7298-7303 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. S. Xiao, M. H. Khan, S. Hao, and Q. Minghao, “Two-photon absorption induced thermal-optic effect in high-Qsilicon microring resonators,” in Proceedings of the 20th Annual Meeting of the IEEE, LEOS 2007 (IEEE, 2007), pp. 890-891.
  15. A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists (CRC Press, 2002).
  16. Q. Xu and M. Lipson, “Carrier-induced optical bistability in silicon ring resonators,” Opt. Lett. 31, 341-343 (2006).
    [CrossRef] [PubMed]
  17. K. Biwonjo, S. Sujecki, A. Vukovic, T. M. Benson, and P. Sewell, “Thermal models for silicon-on-insulator-based optical circuits,” Opt. Appl. 34, 149-161 (2004).
  18. G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Narrowband optical filters suitable for various applications in optical communications,” Appl Opt. 47, 5140-5148 (2008).
    [CrossRef] [PubMed]
  19. S. Golmohammadi, M. K. Moravvej-Farshi, A. Rostami, and A. Zarifkar, “Narrowband DWDM filters based on Fibonacci-class quasi-periodic structures,” Opt. Express 15, 10520-10532 (2007).
    [CrossRef] [PubMed]
  20. S. Roy, S. K. Bhadra, and G. P. Agrawal, “Femtosecond pulse propagation in silicon waveguides, variational approach and its advantages,” Opt. Commun. 281, 5889-5893 (2008).
    [CrossRef]
  21. R. Dekker, N. Usechak, M. Först, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D 40, R249-R271 (2007).
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  22. X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. 42, 160-170 (2006).
    [CrossRef]

2008 (2)

G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Narrowband optical filters suitable for various applications in optical communications,” Appl Opt. 47, 5140-5148 (2008).
[CrossRef] [PubMed]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Femtosecond pulse propagation in silicon waveguides, variational approach and its advantages,” Opt. Commun. 281, 5889-5893 (2008).
[CrossRef]

2007 (4)

2006 (8)

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]

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

F. Grillot, L. Vivien, S. Laval, and E. Cassan, “Propagation loss in single-mode ultrasmall square silicon-on-insulator optical waveguides,” J. Lightwave Technol. 24, 891-896 (2006).
[CrossRef]

Y. H. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia and O. Cohen, “Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides,” Opt. Express 14, 11721-11726(2006).
[CrossRef] [PubMed]

T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun. 265, 171-174 (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]

Q. Xu and M. Lipson, “Carrier-induced optical bistability in silicon ring resonators,” Opt. Lett. 31, 341-343 (2006).
[CrossRef] [PubMed]

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

2005 (2)

2004 (3)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

R. L. Espinola, J. I. Dadap, R. M. 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]

K. Biwonjo, S. Sujecki, A. Vukovic, T. M. Benson, and P. Sewell, “Thermal models for silicon-on-insulator-based optical circuits,” Opt. Appl. 34, 149-161 (2004).

1995 (1)

G. Ghosh, “Temperature dispersion of refractive indices in crystalline and amorphous silicon,” Appl. Phys. Lett. 66, 3570-3572 (1995).
[CrossRef]

Abedin, K. S.

T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun. 265, 171-174 (2006).
[CrossRef]

Agrawal, G. P.

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Femtosecond pulse propagation in silicon waveguides, variational approach and its advantages,” Opt. Commun. 281, 5889-5893 (2008).
[CrossRef]

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Baets, R.

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Beckx, S.

Benson, T. M.

K. Biwonjo, S. Sujecki, A. Vukovic, T. M. Benson, and P. Sewell, “Thermal models for silicon-on-insulator-based optical circuits,” Opt. Appl. 34, 149-161 (2004).

Bhadra, S. K.

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Femtosecond pulse propagation in silicon waveguides, variational approach and its advantages,” Opt. Commun. 281, 5889-5893 (2008).
[CrossRef]

Bientsmann, P.

Biwonjo, K.

K. Biwonjo, S. Sujecki, A. Vukovic, T. M. Benson, and P. Sewell, “Thermal models for silicon-on-insulator-based optical circuits,” Opt. Appl. 34, 149-161 (2004).

Bogaerts, W.

T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun. 265, 171-174 (2006).
[CrossRef]

W. Bogaerts, R. Baets, P. Dumon, V. Wiaux , S. Beckx, D. Taillaert, B. Luyssaert, J.Van Campenhout, P. Bientsmann, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23, 401-413 (2005).
[CrossRef]

Cassan, E.

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]

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

Cohen, O.

Dadap, J. I.

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

R. L. Espinola, J. I. Dadap, R. M. 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]

Darvish, G.

G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Narrowband optical filters suitable for various applications in optical communications,” Appl Opt. 47, 5140-5148 (2008).
[CrossRef] [PubMed]

Dekker, R.

Driessen, A.

Dulkeith, E.

Dumon, P.

Espinola, R. L.

Först, M.

Freude, W.

Ghosh, G.

G. Ghosh, “Temperature dispersion of refractive indices in crystalline and amorphous silicon,” Appl. Phys. Lett. 66, 3570-3572 (1995).
[CrossRef]

Golmohammadi, S.

Grillot, F.

Hao, S.

S. Xiao, M. H. Khan, S. Hao, and Q. Minghao, “Two-photon absorption induced thermal-optic effect in high-Qsilicon microring resonators,” in Proceedings of the 20th Annual Meeting of the IEEE, LEOS 2007 (IEEE, 2007), pp. 890-891.

Hsieh, I.

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

Jacome, L.

Kawanishi, T.

Khan, M. H.

S. Xiao, M. H. Khan, S. Hao, and Q. Minghao, “Two-photon absorption induced thermal-optic effect in high-Qsilicon microring resonators,” in Proceedings of the 20th Annual Meeting of the IEEE, LEOS 2007 (IEEE, 2007), pp. 890-891.

Koos, C.

Kuo, Y. H.

Laval, S.

Leuthold, J.

Liang, T. K.

T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun. 265, 171-174 (2006).
[CrossRef]

T. K. Liang, L. R. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. R. A. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. K. Tsang, “Ultrafast all-optical switching by cross absorption modulation in silicon wire waveguides,” Opt. Express 13, 7298-7303 (2005).
[CrossRef] [PubMed]

Lipson, M.

Q. Xu and M. Lipson, “Carrier-induced optical bistability in silicon ring resonators,” Opt. Lett. 31, 341-343 (2006).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Luyssaert, B.

McNab, S. J.

Minghao, Q.

S. Xiao, M. H. Khan, S. Hao, and Q. Minghao, “Two-photon absorption induced thermal-optic effect in high-Qsilicon microring resonators,” in Proceedings of the 20th Annual Meeting of the IEEE, LEOS 2007 (IEEE, 2007), pp. 890-891.

Miyazaki, T.

T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun. 265, 171-174 (2006).
[CrossRef]

Moormann, C.

Moravvej-Farshi, M. K.

G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Narrowband optical filters suitable for various applications in optical communications,” Appl Opt. 47, 5140-5148 (2008).
[CrossRef] [PubMed]

S. Golmohammadi, M. K. Moravvej-Farshi, A. Rostami, and A. Zarifkar, “Narrowband DWDM filters based on Fibonacci-class quasi-periodic structures,” Opt. Express 15, 10520-10532 (2007).
[CrossRef] [PubMed]

Niehusmann, J.

Nunes, L. R.

T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun. 265, 171-174 (2006).
[CrossRef]

T. K. Liang, L. R. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. R. A. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. K. Tsang, “Ultrafast all-optical switching by cross absorption modulation in silicon wire waveguides,” Opt. Express 13, 7298-7303 (2005).
[CrossRef] [PubMed]

Osgood, R. M.

X. Chen, N. C. Panoiu, I. Hsieh, J. I. Dadap, and R. M. Osgood, “Third-order dispersion and ultrafast-pulse propagation in silicon wire waveguides,” IEEE Photon. Technol. Lett. 18, 2617-2619 (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]

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

R. L. Espinola, J. I. Dadap, R. M. 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]

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Paniccia, M.

Panoiu, N. C.

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, I. Hsieh, J. I. Dadap, and R. M. Osgood, “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, Jr., “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. 42, 160-170 (2006).
[CrossRef]

Polyanin, A. D.

A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists (CRC Press, 2002).

Poulton, C.

Priem, G. R. A.

Rong, H.

Rostami, A.

Roy, S.

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Femtosecond pulse propagation in silicon waveguides, variational approach and its advantages,” Opt. Commun. 281, 5889-5893 (2008).
[CrossRef]

Saghafi, K.

G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Narrowband optical filters suitable for various applications in optical communications,” Appl Opt. 47, 5140-5148 (2008).
[CrossRef] [PubMed]

Sakamoto, T.

Sasagawa, K.

Sewell, P.

K. Biwonjo, S. Sujecki, A. Vukovic, T. M. Benson, and P. Sewell, “Thermal models for silicon-on-insulator-based optical circuits,” Opt. Appl. 34, 149-161 (2004).

Sih, V.

Sujecki, S.

K. Biwonjo, S. Sujecki, A. Vukovic, T. M. Benson, and P. Sewell, “Thermal models for silicon-on-insulator-based optical circuits,” Opt. Appl. 34, 149-161 (2004).

Suzuki, N.

Taillaert, D.

Tsang, H. K.

T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun. 265, 171-174 (2006).
[CrossRef]

T. K. Liang, L. R. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. R. A. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. K. Tsang, “Ultrafast all-optical switching by cross absorption modulation in silicon wire waveguides,” Opt. Express 13, 7298-7303 (2005).
[CrossRef] [PubMed]

Tsuchiya, M.

T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun. 265, 171-174 (2006).
[CrossRef]

T. K. Liang, L. R. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. R. A. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. K. Tsang, “Ultrafast all-optical switching by cross absorption modulation in silicon wire waveguides,” Opt. Express 13, 7298-7303 (2005).
[CrossRef] [PubMed]

Usechak, N.

R. Dekker, N. Usechak, M. Först, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D 40, R249-R271 (2007).
[CrossRef]

Van Campenhout,

Van Thourhout, D.

Vivien, L.

Vlasov, Y. A.

Vukovic, A.

K. Biwonjo, S. Sujecki, A. Vukovic, T. M. Benson, and P. Sewell, “Thermal models for silicon-on-insulator-based optical circuits,” Opt. Appl. 34, 149-161 (2004).

Wahlbrink, T.

Wiaux , V.

Xiao, S.

S. Xiao, M. H. Khan, S. Hao, and Q. Minghao, “Two-photon absorption induced thermal-optic effect in high-Qsilicon microring resonators,” in Proceedings of the 20th Annual Meeting of the IEEE, LEOS 2007 (IEEE, 2007), pp. 890-891.

Xu, Q.

Xu, S.

Zarifkar, A.

G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Narrowband optical filters suitable for various applications in optical communications,” Appl Opt. 47, 5140-5148 (2008).
[CrossRef] [PubMed]

S. Golmohammadi, M. K. Moravvej-Farshi, A. Rostami, and A. Zarifkar, “Narrowband DWDM filters based on Fibonacci-class quasi-periodic structures,” Opt. Express 15, 10520-10532 (2007).
[CrossRef] [PubMed]

Appl Opt. (1)

G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Narrowband optical filters suitable for various applications in optical communications,” Appl Opt. 47, 5140-5148 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

G. Ghosh, “Temperature dispersion of refractive indices in crystalline and amorphous silicon,” Appl. Phys. Lett. 66, 3570-3572 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

IEEE Photon. Technol. Lett. (1)

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

J. Lightwave Technol. (3)

J. Phys. D (1)

R. Dekker, N. Usechak, M. Först, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D 40, R249-R271 (2007).
[CrossRef]

Nature (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004).
[CrossRef] [PubMed]

Opt. Appl. (1)

K. Biwonjo, S. Sujecki, A. Vukovic, T. M. Benson, and P. Sewell, “Thermal models for silicon-on-insulator-based optical circuits,” Opt. Appl. 34, 149-161 (2004).

Opt. Commun. (2)

T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides,” Opt. Commun. 265, 171-174 (2006).
[CrossRef]

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Femtosecond pulse propagation in silicon waveguides, variational approach and its advantages,” Opt. Commun. 281, 5889-5893 (2008).
[CrossRef]

Opt. Express (7)

S. Golmohammadi, M. K. Moravvej-Farshi, A. Rostami, and A. Zarifkar, “Narrowband DWDM filters based on Fibonacci-class quasi-periodic structures,” Opt. Express 15, 10520-10532 (2007).
[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]

Y. H. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia and O. Cohen, “Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides,” Opt. Express 14, 11721-11726(2006).
[CrossRef] [PubMed]

T. K. Liang, L. R. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. R. A. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. K. Tsang, “Ultrafast all-optical switching by cross absorption modulation in silicon wire waveguides,” Opt. Express 13, 7298-7303 (2005).
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C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15, 5976-5990 (2007).
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[CrossRef] [PubMed]

Opt. Lett. (1)

Other (2)

S. Xiao, M. H. Khan, S. Hao, and Q. Minghao, “Two-photon absorption induced thermal-optic effect in high-Qsilicon microring resonators,” in Proceedings of the 20th Annual Meeting of the IEEE, LEOS 2007 (IEEE, 2007), pp. 890-891.

A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists (CRC Press, 2002).

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Figures (6)

Fig. 1
Fig. 1

Top view of a SOI NWG in a wavelength conversion pump–probe experimental setup.

Fig. 2
Fig. 2

Comparison of normalized pulse intensities at three locations: z = 0 , L / 2 , and L for (a)  P 1 and P 2 , (b)  P 3 and P 4 , (c)  P 5 and P 6 . Maximum pulse intensities at the input and their T FWHM are listed in Table 1.

Fig. 3
Fig. 3

Temperature variation induced by TPA and FCA at three points, z = 0 , L / 2 , and L, along the waveguide during propagation of (a)  P 1 and P 2 , (b)  P 3 and P 4 , (c)  P 5 and P 6 .

Fig. 4
Fig. 4

Variation in probe wavelength that is due to conversion as well as induced shift ( λ s + Δ λ s λ s 0 ) versus delay time between pump and probe with and without taking into consideration the effect of the heat induced by pulses (a)  P 1 and P 2 , (b)  P 3 and P 4 , (c)  P 5 and P 6 .

Fig. 5
Fig. 5

Variation of the tuned wavelength shift δ λ T versus intensity of a variable pump pulse tuned around that of P 4 with the same T FWHM .

Fig. 6
Fig. 6

Wavelength shift Δ λ s (left axis), and the difference between the maximum and the minimum wavelength conversion δ λ , both experienced by the probe pulse, due to induced heat by pulse P 4 propagating in SOI NGWs of various lengths in the range of 1 mm L 7 mm .

Tables (2)

Tables Icon

Table 1 Maximum Intensities and Widths of the TM Mode Optical Pulses of Wavelength λ p = 1554 nm

Tables Icon

Table 2 Parameters Used in our Simulations with the Optical Pulses in Table 1 a

Equations (43)

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d I p ( z , t ) d z = ( α 0 + α TPA I p ( z , t ) + σ N c ( z , t ) ) I p ( z , t ) ,
d N c ( z , t ) d t = N c ( z , t ) τ c + α TPA 2 ω p I p 2 ( z , t ) ,
ρ C ( T t + T τ θ ) = Φ + ( K Si T ) ,
P ( z , t ) = I p ( z , t ) a eff ,
P ( z + Δ z , t ) = I p ( z + Δ z , t ) a eff .
Δ P = ( I p ( z , t ) I p ( z + Δ z , t ) ) a eff .
Φ = Δ P V = I p ( z + Δ z , t ) I p ( z , t ) Δ z .
Φ ( z , t ) = d I p ( z , t ) d z .
Φ = d I p d z α I p .
Φ = ( α rough + α TPA I p + σ N c ) I p .
ρ C T ( z , t ) t = ( K Si T ( z , t ) ) + ( α rough + α TPA I p ( z , t ) + σ N c ) I p ( z , t ) .
Q = K air T z | z = 0 , L ,
T z | z = 0 T z | z = L 0 ,
λ s + Δ λ s = λ s 0 1 L int c d Δ n ( z , t ) d t .
δ λ T | λ s ( P t ) + Δ λ s ( P t ) λ s ( P ) |
d ψ p d z = Δ d ψ p d t + i j 1. ( i ) j j ! β i d j ψ p d t j ( 1 2 α 0 + Γ | ψ p | 2 + σ 2 N c ) ψ p + i γ p | ψ p | 2 ψ p + i γ p ψ s + g R ( t ) ψ p ( z , t t ) ψ s * ( z , t t ) e i Ω p s t d t ,
d N c ( z , t ) d t = N c ( z , t ) τ c + Γ a eff . ω p | ψ p ( z , t ) | 4 ,
σ ( cm 2 ) = 1.45 × 10 17 ( λ ( μm ) 1.55 ) 2 .
γ p = 2 π n 2 λ p a eff ,
n 2 = 3 χ Re ( 3 ) 4 c ε 0 n 0 2 ,
Δ = ( β 1 p β 1 s ) / 2.
α TPA = 2 Γ a eff .
L NL = 1 γ p I p a eff
L w = T FWHM | β 1 s β 1 p |
L D = T FWHM 2 β 2
L D L NL 1 , L D L 1 , L L NL 1 ,
d ψ p d z = ( α 0 2 + Γ | ψ p | 2 + σ 2 N c + i γ p | ψ p | 2 ) ψ p .
I p ( z , t ) ( ψ p ( z , t ) ψ p * ( z , t ) ) / a eff = | ψ p ( z , t ) | 2 / a eff ( W · cm 2 ) .
ψ p ( z , t ) d ψ p * ( z , t ) d z + ψ p * ( z , t ) d ψ p ( z , t ) d z = a eff d I p ( z , t ) d z .
a eff d I p ( z , t ) d z = 2 ( α 0 2 + Γ I p ( z , t ) a eff + σ 2 N c ( z , t ) ) I p ( z , t ) a eff .
d I p ( z , t ) d z = ( α 0 + α TPA I p ( z , t ) + σ N c ( z , t ) ) I p ( z , t ) .
d N c ( z , t ) d t = N c ( z , t ) τ c + α TPA 2 ω p I p 2 ( z , t ) .
d ψ p d z = i γ p | ψ p | 2 ψ p .
ψ p = A exp ( i γ p | ψ p | 2 z ) ,
ψ p = A exp ( i k NL z ) ,
k NL = γ p | ψ p | 2 .
k NL = 2 π n 2 λ p I p .
Δ n Kerr ( z , t ) = n 2 I p ( z , t ) .
Δ n FC ( z , t ) = ( 8.8 × 10 22 N e ( z , t ) + 8.5 × 10 18 N h 0.8 ( z , t ) ) ,
Δ n th = ( n T | λ = 1550 nm = 1.84 × 10 4 ) Δ T .
Δ ϕ ( z , t ) = 2 π L int λ s 0 [ Δ n = ( Δ n Kerr ( z , t ) + Δ n FC ( z , t ) + Δ n th ( z , t ) ) ] ,
Δ ω ( z , t ) = d d t Δ ϕ ( z , t ) .
λ s + Δ λ s = λ s 0 1 L int c · d Δ n ( z , t ) d t ,

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