## Impact of dispersion profiles of silicon waveguides on optical parametric amplification in the femtosecond regime |

Optics Express, Vol. 19, Issue 24, pp. 24730-24737 (2011)

http://dx.doi.org/10.1364/OE.19.024730

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### Abstract

The impact of dispersion profiles of silicon waveguides on femtosecond optical parametric amplification (OPA) is theoretically investigated. It is found that flat quasi-phase-matching, smooth temporal profiles and separable spectra for 200 fs pulses can be obtained by tailoring the cross-section of silicon rib waveguide. We achieve on-chip parametric gain as high as 26.8 dB and idler conversion gain of 25.6 dB for a low pump peak power over a flat bandwidth of 400 nm in a 10-mm-long dispersion engineered silicon waveguide. Our on-chip OPA can find important potential applications in highly integrated optical circuits for all-optical ultrafast signal processing.

© 2011 OSA

## 1. Introduction

1. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics **4**(8), 535–544 (2010). [CrossRef]

3. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature **433**(7027), 725–728 (2005). [CrossRef] [PubMed]

4. V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, “Parametric Raman wavelength conversion in scaled silicon waveguides,” J. Lightwave Technol. **23**(6), 2094–2102 (2005). [CrossRef]

5. T. K. Liang, L. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. Tsang, “Ultrafast all-optical switching by cross-absorption modulation in silicon wire waveguides,” Opt. Express **13**(19), 7298–7303 (2005). [CrossRef] [PubMed]

6. T. K. Liang, H. K. Tsang, I. E. Day, J. Drake, A. P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for auto-correlation measurements,” Appl. Phys. Lett. **81**(7), 1323–1325 (2002). [CrossRef]

9. H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 um wavelength,” Appl. Phys. Lett. **80**(3), 416–418 (2002). [CrossRef]

10. I.-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood Jr, S. J. McNab, and Y. A. Vlasov, “Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides,” Opt. Express **14**(25), 12380–12387 (2006). [CrossRef] [PubMed]

12. L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. **32**(14), 2031–2033 (2007). [CrossRef] [PubMed]

13. I.-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood Jr, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express **15**(3), 1135–1146 (2007). [CrossRef] [PubMed]

14. L. Yin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Optical switching using nonlinear polarization rotation inside silicon waveguides,” Opt. Lett. **34**(4), 476–478 (2009). [CrossRef] [PubMed]

15. 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**(12), 4629–4637 (2005). [CrossRef] [PubMed]

26. X. Sang and O. Boyraz, “Gain and noise characteristics of high-bit-rate silicon parametric amplifiers,” Opt. Express **16**(17), 13122–13132 (2008). [CrossRef] [PubMed]

*et al*have first reported on-chip optical parametric gain in the telecom-band on picosecond timescale in SOI channel waveguides. They experimentally achieved a net on-chip parametric gain of + 1.8 dB over 60 nm [22

22. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature **441**(7096), 960–963 (2006). [CrossRef] [PubMed]

*et al*have proved mid-infrared optical parametric amplifier in silicon nanophotonic waveguides with picosecond pump pulses and a continuous-wave tunable mid-infrared laser signal, where an on-chip gain of + 25.4 dB over 220 nm was reported [23

23. X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics **4**(8), 557–560 (2010). [CrossRef]

## 2. FWM theory for silicon waveguides

*ω*transporting their energy to a signal wave at frequency

_{p}*ω*and an idler wave at frequency

_{s}*ω*as the relation 2

_{i}*ω*holds. The pump, signal and idler waves are identically polarized in the fundamental quasi-TE mode. To describe the nonlinear optical interaction of the pump, signal and idler in the waveguide, we use the formulism described in [27] and take into account the effects of TPA, FCA, and FCD. Remarkably, the stimulated Raman scattering (SRS) is negligible for femtosecond pulses propagating in silicon waveguides because the Raman response time is about 3 ps and SRS is only effective for pulses longer than this [28

_{p}= ω_{s}+ ω_{i}28. N. C. Panoiu, X. Liu, and R. M. Osgood Jr., “Self-steepening of ultrashort pulses in silicon photonic nanowires,” Opt. Lett. **34**(7), 947–949 (2009). [CrossRef] [PubMed]

29. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express **15**(25), 16604–16644 (2007). [CrossRef] [PubMed]

*A*is the slowly varying amplitude (

_{j}*j = p, s, i*),

*z*is the propagation distance,

*β*

_{2}

*is the group-velocity dispersion (GVD) coefficient and*

_{j}*β*

_{3}

*is the third-order dispersion (TOD) coefficient.*

_{j}*T = t-z/v*is measured in a reference frame moving with pump pulse traveling at speed

_{gp}*v*. The two walk-off parameters of the signal and idler are defined as

_{gp}*d*

_{s}= β_{1}

_{s}-β_{1}

*and*

_{p}*d*

_{i}= β_{1}

_{i}-β_{1}

*, respectively, where*

_{p}*β*

_{1}

*is the inverse of the group velocity. The nonlinear coefficient*

_{j}*γ*is given by [25

_{je}25. Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express **14**(11), 4786–4799 (2006). [CrossRef] [PubMed]

*γ*

_{j}= ω_{j}n_{2}

*/cA*is the effective nonlinearity of the waveguide,

_{eff}*n*

_{2}= 12

*π*

^{2}

*χ*

^{(3)}/

*n*

_{0}

*c*is the nonlinear index coefficient,

*c*is the speed of light in vacuum,

*n*

_{0}is the linear refractive index,

*A*is the effective area of the propagating mode and

_{eff}*β*

_{TPA}is the coefficient of TPA. Here

*n*

_{2}= 6 × 10

^{−18}m

^{2}W

^{−1}and

*β*

_{TPA}= 5 × 10

^{−12}mW

^{−1}in the 1550-nm regime [12

12. L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. **32**(14), 2031–2033 (2007). [CrossRef] [PubMed]

*α*accounts for the linear loss and

_{j}*α*represents FCA, where

_{fcj}= σ_{j}N_{c}*σ*is the free carrier absorption cross section and

_{j}*N*is the free-carrier density. The free-carrier induced index change is

_{c}*δ*. These free-carrier parameters can be obtained by the following equations [25

_{nfcj}= ζ_{j}N_{c}25. Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express **14**(11), 4786–4799 (2006). [CrossRef] [PubMed]

*λ*is the wavelength,

_{j}*λ*1550 nm,

_{ref}=*h*is Planck’s constant, and the carrier lifetime is

*τ*1 ns. Here, free carriers induced by the signal and idler are negligible compared with that induced by the pump in the parametric amplification process.

_{c}≈*β = k*2

_{s}+ k_{i}-*k*is the linear part of the phase mismatch, and

_{p}*k*,

_{p}*k*represent the propagation constants of pump, signal and idler waves, respectively. The second term is the nonlinear part, which results from the SPM and XPM introduced by the pump wave [22

_{s}, k_{i}22. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature **441**(7096), 960–963 (2006). [CrossRef] [PubMed]

*P*represents the pump power. As the nonlinear part is positive, a negative linear part is required to achieve phase matching, which can be realized by locating the pump wavelength in the anomalous dispersion regime.

_{p}## 3. Dispersion tailoring in SOI waveguides

3. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature **433**(7027), 725–728 (2005). [CrossRef] [PubMed]

*A*are 0.09 μm

_{eff}^{2}, 0.12 μm

^{2}and 0.15 μm

^{2}for the above-mentioned waveguides, respectively. The linear propagation losses of the three waveguides are assumed to be 0.3 dB/cm, 0.25 dB/cm and 0.22 dB/cm, respectively [24

24. W. Mathlouthi, H. Rong, and M. Paniccia, “Characterization of efficient wavelength conversion by four-wave mixing in sub-micron silicon waveguides,” Opt. Express **16**(21), 16735–16745 (2008). [CrossRef] [PubMed]

30. J. Y. Lee, L. Yin, G. P. Agrawal, and P. M. Fauchet, “Ultrafast optical switching based on nonlinear polarization rotation in silicon waveguides,” Opt. Express **18**(11), 11514–11523 (2010). [CrossRef] [PubMed]

31. A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Opt. Express **14**(10), 4357–4362 (2006). [CrossRef] [PubMed]

*n*are calculated by using the effective index method as described in [24

_{eff}24. W. Mathlouthi, H. Rong, and M. Paniccia, “Characterization of efficient wavelength conversion by four-wave mixing in sub-micron silicon waveguides,” Opt. Express **16**(21), 16735–16745 (2008). [CrossRef] [PubMed]

*β*(

*ω*)

*= n*(

_{eff}*ω*)

*ω/c*. Higher order dispersion is finally calculated via numerical differentiation from

*β*. From Fig. 2 (c), it can be found that the zero dispersion wavelengths (ZDWL) are 1380 nm, 1445 nm and 1520 nm for the above mentioned waveguides and the corresponding GVD parameters are −0.176 ps

_{n}= d^{n}β/dω^{n}^{2}/m, −0.11 ps

^{2}/m, −0.03 ps

^{2}/m for the 1550 nm wavelength, respectively. In general, the quasi-phase-matching can be satisfied if the pump wavelength is located in the anomalous GVD regime [25

25. Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express **14**(11), 4786–4799 (2006). [CrossRef] [PubMed]

*λ*1550 nm pump pulses for the three waveguides.

_{p}=## 4. Results and discussion

*λ*= 1550 nm and tunable signal pulses in the telecommunication band. The pump and signal pulses are taken to be Gaussian pulses with the same pulse width

_{p}*T*

_{FWHM}

*=*200 fs and same repetition rate

*R*. In simulations, the pump peak power coupled inside the waveguides ranges from 1 W to 10 W, while the signal peak power is kept constant at 1 mW.

^{−1}for the signal wavelength from 1450 nm to 1650 nm for the other two waveguides. According to Eq. (7), the phase mismatch increases as the pump peak power increases because the nonlinear part of the phase mismatch becomes larger, which is illustrated by Fig. 3(b). The phase mismatch increases for the three waveguides, when the pump peak power is 5 W. From Fig. 3, one can find that the phase mismatch curve of the waveguide with the width of 650 nm is more flat than the other two waveguides. Therefore, a flat and broad phase-matching (>300 nm) can be achieved by tailoring the cross-section of the silicon waveguide.

29. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express **15**(25), 16604–16644 (2007). [CrossRef] [PubMed]

*T*

_{0}

*≈T*

_{FWHM}/1.665 is the half-width of the pulse,

*d*is the maximal walk-off parameter between

*d*and

_{s}*d*. The dispersion parameters can be obtained from Fig. 2. The characteristic lengths for the three waveguides are listed in Table 1 . Clearly, the GVD and walk off effects cannot be ignored in the femtosecond OPA process for the waveguide with width of 550 nm, while these effects can be ignored when the width increase to 650 nm. When the width of the waveguide is 550 nm, the interplay between the SPM and GVD compresses the pump pulse in the anomalous GVD regime, and the distortion of the output signal and idler pulses is mainly caused by the combination of XPM and GVD as shown in Fig. 4(a) [27]. With increasing the width of the waveguide, the dispersion length

_{i}*L*becomes longer, and the influence of GVD on the propagation of the femtosecond pulses becomes weaker. Consequently, we can suppress pulse distortion by tailoring the cross-section of the waveguide to change the dispersion profiles of the silicon waveguide.

_{D}*δω*

_{max}induced by SPM, which can estimate the magnitude of spectral broadening. For an unchirped Gaussian pulse, we can get [27]where

*φ*

_{max}

*=*ln(1

*+*2

*rγ*)/2

_{p}P_{p}L_{eff}*r*represents the maximum nonlinear phase shift at the pulse center of the pump,

*r = β*

_{TPA}

*/*(2

*k*

_{p}n_{2}) represents the TPA parameter, and

*L*is the effective length of the waveguide [12

_{eff}12. L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. **32**(14), 2031–2033 (2007). [CrossRef] [PubMed]

*φ*

_{max}of the pump pulses induced by SPM is larger compared with the

*φ*

_{max}of pump pulses from the other two waveguides. The maximum nonlinear phase shift

*φ*

_{ma}

*for the three waveguides are 4.5π, 2.5π and 1.5π, respectively, which can be obtained by counting the number of peaks in the output spectrum of the pump using the relation*

_{x}*φ*

_{max}

*≈*(

*M*-1/2)π, where M is the number of the peaks in the spectrum. A large

*φ*

_{max}means a large

*δω*

_{max}according to Eq. (9), hence the magnitude of spectral broadening of the pump is great and even covers the signal and idler spectra as illustrated in Fig. 5(a). By tailoring the cross-section of the silicon waveguide, the extent of spectral broadening is limited as shown in Fig. 5(c). Therefore, separable spectra can be achieved by tailoring the dispersion profiles of the silicon waveguide. In addition, the spectral broadening of the signal and idler pulses is mainly caused by the interplay between FWM and XPM.

*G*= 10

_{s}*log*

_{10}(

*E*),

_{sout}/E_{sin}*G*= 10

_{s}*log*

_{10}(

*E*). From Fig. 7(a), one can find that a broad bandwidth of the femtosecond OPA can be obtained in the silicon rib waveguide with well gain flatness. As can be seen from Fig. 7(a), when the signal wavelength is 1450 nm, the maximum signal and idler on-chip gains reach 26.8 dB and 25.6 dB, respectively. When the signal wavelength is 1350 nm, the minimal gains are 21.8 dB and 20.5 dB, respectively. It is clear that the on-chip gain is large enough to overcome the fiber-chip coupling losses that are about 13 dB [23

_{iout}/E_{sin}23. X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics **4**(8), 557–560 (2010). [CrossRef]

26. X. Sang and O. Boyraz, “Gain and noise characteristics of high-bit-rate silicon parametric amplifiers,” Opt. Express **16**(17), 13122–13132 (2008). [CrossRef] [PubMed]

## 5. Conclusion

## Acknowledgments

## References and links

1. | J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics |

2. | V. Raghunathan, O. Boyraz, and B. Jalali, “20 dB on-off Raman amplification in silicon waveguides,” Proc.CLEO |

3. | H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature |

4. | V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, “Parametric Raman wavelength conversion in scaled silicon waveguides,” J. Lightwave Technol. |

5. | T. K. Liang, L. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. Tsang, “Ultrafast all-optical switching by cross-absorption modulation in silicon wire waveguides,” Opt. Express |

6. | T. K. Liang, H. K. Tsang, I. E. Day, J. Drake, A. P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for auto-correlation measurements,” Appl. Phys. Lett. |

7. | 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. |

8. | Y. Liu and H. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. |

9. | H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 um wavelength,” Appl. Phys. Lett. |

10. | I.-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood Jr, S. J. McNab, and Y. A. Vlasov, “Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides,” Opt. Express |

11. | L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. |

12. | L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. |

13. | I.-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood Jr, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express |

14. | L. Yin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Optical switching using nonlinear polarization rotation inside silicon waveguides,” Opt. Lett. |

15. | 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 |

16. | Q. Lin, T. J. Johnson, R. Perahia, C. P. Michael, and O. J. Painter, “A proposal for highly tunable optical parametric oscillation in silicon micro-resonators,” Opt. Express |

17. | 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 |

18. | A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express |

19. | S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics |

20. | R. L. Espinola, J. I. Dadap, R. M. Osgood Jr, S. McNab, and Y. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express |

21. | 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 |

22. | M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature |

23. | X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics |

24. | W. Mathlouthi, H. Rong, and M. Paniccia, “Characterization of efficient wavelength conversion by four-wave mixing in sub-micron silicon waveguides,” Opt. Express |

25. | Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express |

26. | X. Sang and O. Boyraz, “Gain and noise characteristics of high-bit-rate silicon parametric amplifiers,” Opt. Express |

27. | G. P. Agrawal, |

28. | N. C. Panoiu, X. Liu, and R. M. Osgood Jr., “Self-steepening of ultrashort pulses in silicon photonic nanowires,” Opt. Lett. |

29. | Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express |

30. | J. Y. Lee, L. Yin, G. P. Agrawal, and P. M. Fauchet, “Ultrafast optical switching based on nonlinear polarization rotation in silicon waveguides,” Opt. Express |

31. | A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Opt. Express |

**OCIS Codes**

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

(190.7110) Nonlinear optics : Ultrafast nonlinear optics

(230.7370) Optical devices : Waveguides

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: September 19, 2011

Manuscript Accepted: October 18, 2011

Published: November 17, 2011

**Citation**

Zhaolu Wang, Hongjun Liu, Nan Huang, Qibing Sun, and Jin Wen, "Impact of dispersion profiles of silicon waveguides on optical parametric amplification in the femtosecond regime," Opt. Express **19**, 24730-24737 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24730

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### References

- J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics4(8), 535–544 (2010). [CrossRef]
- V. Raghunathan, O. Boyraz, and B. Jalali, “20 dB on-off Raman amplification in silicon waveguides,” Proc.CLEO 1, 349–351 (2005).
- H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005). [CrossRef] [PubMed]
- V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, “Parametric Raman wavelength conversion in scaled silicon waveguides,” J. Lightwave Technol.23(6), 2094–2102 (2005). [CrossRef]
- T. K. Liang, L. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. Tsang, “Ultrafast all-optical switching by cross-absorption modulation in silicon wire waveguides,” Opt. Express13(19), 7298–7303 (2005). [CrossRef] [PubMed]
- T. K. Liang, H. K. Tsang, I. E. Day, J. Drake, A. P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for auto-correlation measurements,” Appl. Phys. Lett.81(7), 1323–1325 (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(7), 071115–071117 (2005). [CrossRef]
- Y. Liu and H. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett.90(21), 211105 (2007). [CrossRef]
- H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 um wavelength,” Appl. Phys. Lett.80(3), 416–418 (2002). [CrossRef]
- I.-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides,” Opt. Express14(25), 12380–12387 (2006). [CrossRef] [PubMed]
- L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett.32(4), 391–393 (2007). [CrossRef] [PubMed]
- L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett.32(14), 2031–2033 (2007). [CrossRef] [PubMed]
- I.-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express15(3), 1135–1146 (2007). [CrossRef] [PubMed]
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