## Pump-to-Stokes relative intensity noise transfer and analytical modeling of mid-infrared silicon Raman lasers |

Optics Express, Vol. 20, Issue 16, pp. 17962-17972 (2012)

http://dx.doi.org/10.1364/OE.20.017962

Acrobat PDF (1442 KB)

### Abstract

An analytical model for mid-infrared (mid-IR) silicon Raman lasers (SRLs) is developed. The relative intensity noise (RIN) transfer from the pump to the Stokes in the lasers is also investigated. The analytical model can be used as a versatile and efficient tool for analysis, design and optimization of mid-IR SRLs. It is shown that conversion efficiency of 70% is attainable and the low-frequency RIN transfer may be suppressed to below 1 dB by pumping low-loss waveguides at high intensities.

© 2012 OSA

## 1. Introduction

1. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. **24**(12), 4600–4615 (2006). [CrossRef]

2. B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron. **12**(6), 1618–1627 (2006). [CrossRef]

10. Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J. **4**(1), 104–113 (2012). [CrossRef]

2. B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron. **12**(6), 1618–1627 (2006). [CrossRef]

3. V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a Mid-infrared silicon Raman amplifier,” Opt. Express **15**(22), 14355–14362 (2007). [CrossRef] [PubMed]

4. D. Borlaug, S. Fathpour, and B. Jalali, “Extreme value statistics in silicon photonics,” IEEE Photon. J. **1**(1), 33–39 (2009). [CrossRef]

7. X. Liu, R. M. Osgood, 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]

8. 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 **4**(8), 561–564 (2010). [CrossRef]

5. T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on sapphire integrated waveguides for the mid-infrared,” Opt. Express **18**(12), 12127–12135 (2010). [CrossRef] [PubMed]

9. G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express **19**(8), 7112–7119 (2011). [CrossRef] [PubMed]

10. Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J. **4**(1), 104–113 (2012). [CrossRef]

4. D. Borlaug, S. Fathpour, and B. Jalali, “Extreme value statistics in silicon photonics,” IEEE Photon. J. **1**(1), 33–39 (2009). [CrossRef]

19. M. Krause, S. Cierullies, H. Renner, and E. Brinkmeyer, “Pump-to-Stokes RIN transfer in Raman fiber lasers and its impact on the performance of co-pumped Raman amplifiers,” Opt. Commun. **260**(2), 656–661 (2006). [CrossRef]

20. X. Sang, D. Dimitropoulos, and B. Jalali, “Influence of pump-to-signal RIN transfer on noise figure in silicon Raman amplifiers,” IEEE Photon. Technol. Lett. **20**(24), 2021–2023 (2008). [CrossRef]

## 2. Methodology

23. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express **11**(15), 1731–1739 (2003). [CrossRef] [PubMed]

24. S. Pearl, N. Rotenberg, and H. M. van Driel, “Three-photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett. **93**(13), 131102 (2008). [CrossRef]

13. A. Liu, L. Liao, and H. Rong, “Recent development in silicon photonics: 2.5 Gb/s silicon optical modulator and silicon Raman laser,” Proc. SPIE **5730**, 80–93 (2005). [CrossRef]

15. M. Krause, R. Draheim, H. Renner, and E. Brinkmeyer, “Cascaded silicon Raman lasers as mid-infrared sources,” Electron. Lett. **42**(21), 1224–1225 (2006). [CrossRef]

13. A. Liu, L. Liao, and H. Rong, “Recent development in silicon photonics: 2.5 Gb/s silicon optical modulator and silicon Raman laser,” Proc. SPIE **5730**, 80–93 (2005). [CrossRef]

17. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. **16**(1), 200–215 (2010). [CrossRef]

*L*, whose facets are coated with multilayer dielectric films. A continuous wave (CW) pump laser (

*p*) at wavelength

*λ*is coupled into the LHS (

_{p}*l*) of the cavity and the output Stokes (

*s*) wavelength

*λ*is exited from the RHS (

_{s}*r*) via stimulated Raman scattering. The reflectivities of the left and right mirrors at

*λ*and

_{p}*λ*are

_{s}*R*,

_{pl}*R*,

_{pr}*R*and

_{sl}*R*, respectively.

_{sr}2. B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron. **12**(6), 1618–1627 (2006). [CrossRef]

13. A. Liu, L. Liao, and H. Rong, “Recent development in silicon photonics: 2.5 Gb/s silicon optical modulator and silicon Raman laser,” Proc. SPIE **5730**, 80–93 (2005). [CrossRef]

*g*is the Raman gain coefficient,

_{R}*α*and

_{p}*α*are the linear propagation losses at

_{s}*λ*and

_{p}*λ*, respectively. The corresponding boundary conditions arewhere

_{s}*I*is the input pump intensity.

_{in}25. F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. **16**(12), 2601–2603 (2004). [CrossRef]

30. K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun. **271**(1), 257–262 (2007). [CrossRef]

*et al*. simplified the numerical algorithm for solving the equations by transforming the two-point boundary value problem into an initial value problem, but the solution was still fully numerical [25

25. F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. **16**(12), 2601–2603 (2004). [CrossRef]

*et al*. assumed single pass pump, i.e., anti-reflection coated mirrors [26

26. J. Zhou, J. Chen, X. Li, G. Wu, and Y. Wang, “Exact analytical solution for Raman fiber lasers,” IEEE Photon. Technol. Lett. **18**(9), 1097–1099 (2006). [CrossRef]

27. Z. Qin, X. Zhou, Q. Li, H. Wu, and Z. Zhou, “An improved theoretical model of nth-order cascaded Raman fiber lasers,” J. Lightwave Technol. **25**(6), 1555–1560 (2007). [CrossRef]

30. K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun. **271**(1), 257–262 (2007). [CrossRef]

*et al.*made the further simplifying assumption of zero residual pump power reflected back to the input end [27

27. Z. Qin, X. Zhou, Q. Li, H. Wu, and Z. Zhou, “An improved theoretical model of nth-order cascaded Raman fiber lasers,” J. Lightwave Technol. **25**(6), 1555–1560 (2007). [CrossRef]

*et al.*not only assumed zero left-mirror reflectivity but also assumed that the output power increases linearly with the input [28

28. S. A. Babin, D. V. Churkin, and E. V. Podivilov, “Intensity interactions in cascades of a two-stage Raman fiber laser,” Opt. Commun. **226**(1-6), 329–335 (2003). [CrossRef]

25. F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. **16**(12), 2601–2603 (2004). [CrossRef]

30. K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun. **271**(1), 257–262 (2007). [CrossRef]

*z*. As a result, Eqs. (1) and (2) can then be rewritten in terms of

*z*is also assumed, i.e.,

*Ω*in the pump noise spectrum is considered. The intensity fluctuations of the pump and the Stokes wave, normalized to the average intensities, are represented by

*Ω*, i.e.,

*m*is a small real number. The different values of pump and Stokes group velocities,

_{in}*v*and

_{p}*v*, should be accounted for similar to Raman amplifiers [20

_{s}20. X. Sang, D. Dimitropoulos, and B. Jalali, “Influence of pump-to-signal RIN transfer on noise figure in silicon Raman amplifiers,” IEEE Photon. Technol. Lett. **20**(24), 2021–2023 (2008). [CrossRef]

21. I. D. Rukhlenko, I. Udagedara, M. Premaratne, and G. P. Agrawal, “Effect of free carriers on pump-to-signal noise transfer in silicon Raman amplifiers,” Opt. Lett. **35**(14), 2343–2345 (2010). [CrossRef] [PubMed]

20. X. Sang, D. Dimitropoulos, and B. Jalali, “Influence of pump-to-signal RIN transfer on noise figure in silicon Raman amplifiers,” IEEE Photon. Technol. Lett. **20**(24), 2021–2023 (2008). [CrossRef]

21. I. D. Rukhlenko, I. Udagedara, M. Premaratne, and G. P. Agrawal, “Effect of free carriers on pump-to-signal noise transfer in silicon Raman amplifiers,” Opt. Lett. **35**(14), 2343–2345 (2010). [CrossRef] [PubMed]

*z*are derived as:

## 3. Results and discussion

3. V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a Mid-infrared silicon Raman amplifier,” Opt. Express **15**(22), 14355–14362 (2007). [CrossRef] [PubMed]

4. D. Borlaug, S. Fathpour, and B. Jalali, “Extreme value statistics in silicon photonics,” IEEE Photon. J. **1**(1), 33–39 (2009). [CrossRef]

*g*of 9 cm/GW at these wavelengths was employed [3

_{R}3. V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a Mid-infrared silicon Raman amplifier,” Opt. Express **15**(22), 14355–14362 (2007). [CrossRef] [PubMed]

*I*= 200 MW/cm

_{in}^{2}are plotted using both methods. Such pump intensities can be attained in practice by solid-state mid-IR lasers (e.g., optical parametric oscillators) [3

**15**(22), 14355–14362 (2007). [CrossRef] [PubMed]

**1**(1), 33–39 (2009). [CrossRef]

^{2}. It is reminded that CW near-IR SRLs are not achievable at any pump intensity without using appropriate mirror coatings on top of employing the carrier sweep-out technique to reduce the carrier lifetime [12

12. 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]

*L*for different right facet reflectivities and two different linear propagation losses of 0.5 and 2.0 dB/cm. Unlike near-IR SRLs that have no lasing threshold outside a limited range of lengths [16], mid-IR silicon waveguide cavities can lase for any given length if enough pump power is available. Also, it is evident that for fixed reflectivities, there is an optimum length, where the lasing threshold reaches a minimum. This is more remarkable at the higher studied propagation loss (2.0 dB/cm), as an optimum length of < ~1 cm can be recognized.

*I*/

_{out}*I*. Generating each 3D plot in Fig. 3 was achieved in about 10 minutes with a typical desktop PC (with a 3 GHz Intel(R) Core(TM)2 Duo CPU), while it can take days to make similar plots based on fully numerical methods. However, our analytical model offers an efficient way to optimize the design of mid-IR SRLs. In this case,

_{in}*L*and

*R*could be optimized under certain pump intensities. For linear propagation loss of

_{sr}*α*=

_{p}*α*= 0.5 dB/cm, maximum conversion efficiencies of 55.8% and 45.1% are obtained at input intensities of

_{s}*I*= 200 and 100 MW/cm

_{in}^{2}, respectively (Fig. 3(a) and (c)). Such high conversion efficiency have been previously estimated based on fully numerical simulations and indicate that silicon Raman lasers in the mid-IR can attain performances comparable to near-IR fiber Raman lasers [15

15. M. Krause, R. Draheim, H. Renner, and E. Brinkmeyer, “Cascaded silicon Raman lasers as mid-infrared sources,” Electron. Lett. **42**(21), 1224–1225 (2006). [CrossRef]

*α*=

_{p}*α*= 2.0 dB/cm. The maximum conversion efficiency obtained are 30.5% and 13.5% at input intensities of

_{s}*I*= 200 and 100 MW/cm

_{in}^{2}, respectively (Fig. 3(b) and (d)). The optimum lengths are below 0.4 cm in these two cases. Further increasing the length will result in higher lasing threshold and lower slope efficiency at the same time. Nonetheless, these predictions indicate a key advantage of mid-IR lasers, as compact laser cavities can be demonstrated. In comparison, up to 5 cm lengths are required at near-IR wavelengths [12

12. 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]

31. H. Rong, Y.-H. Kuo, S. Xu, A. Liu, R. Jones, M. Paniccia, O. Cohen, and O. Raday, “Monolithic integrated Raman silicon laser,” Opt. Express **14**(15), 6705–6712 (2006). [CrossRef] [PubMed]

*α*=

_{p}*α*= 0.1 dB/cm, the maximum possible conversion efficiency is ~73%. This could be considered as a practical limit for the efficiency of a mid-IR SRL assuming extremely low-loss silicon waveguides. Pumping the laser with intensities above 200 MW/cm

_{s}^{2}is unnecessary in this case as it could hardly improve the conversion efficiency. For devices with higher loss, i.e.,

*α*=

_{p}*α*= 1.0 or 2.0 dB/cm, the conversion efficiency has not yet reached saturation at an intensity of 500 MW/cm

_{s}^{2}. The minimum achievable lasing thresholds for the four propagation loss values are recognizable by the intersections of the curves with the

*x*-axis.

^{2}, i.e.,

*L*= 1.20 cm,

*R*= 38% (assuming

_{sr}*R*= 10% and

_{pl}*R*=

_{pr}*R*= 90%), was numerically evaluated. Noise frequencies ranging from zero to tens of gigahertz were included. The group velocity at the pump wavelength in Eqs. (13a) and 14(a) was calculated as

_{sl}*v*=

_{p}*c*/

*n*, where

_{eff}*c*is the speed of light in vacuum and

*n*is the effective index of the silicon waveguide at pump wavelength. The group velocity at the Stokes wavelength was obtained from

_{eff}*v*= 1/[(

_{s}*λ*̶

_{s}*λ*)

_{p}*D*+ 1/

*v*], where

_{p}*D*= ̶ 120 ps/(nm.km) is the local group-velocity dispersion in silicon calculated by the Sellmeier equation. This material dispersion dominates the waveguide dispersion in the studied large cross-section waveguides. This was validated by RSoft calculations and is consistent with previous works [20

**20**(24), 2021–2023 (2008). [CrossRef]

*m*= 0.01 is assumed in our simulation but even higher values for this quantity changes the following calculations insignificantly.

_{in}^{2}. It is evident that the RIN transfer remains constant at low frequencies, then starts to oscillate at the free spectral range (FSR) of the laser cavity, i.e., Δυ =

*c*/(2

*n*) = 3.6 GHz. The observed strong oscillations at higher frequencies suggest that laser sources with RIN spectra no wider than a few GHz are required for pumping mid-IR lasers with cavity lengths of ~1 cm. The low-frequency transferred RIN, as well as the magnitude of the high-frequency oscillations, drop as the pump power increases. This is consistent with theoretical and experimental RIN transfer spectrum of Raman fiber lasers [19

_{eff}L19. M. Krause, S. Cierullies, H. Renner, and E. Brinkmeyer, “Pump-to-Stokes RIN transfer in Raman fiber lasers and its impact on the performance of co-pumped Raman amplifiers,” Opt. Commun. **260**(2), 656–661 (2006). [CrossRef]

^{2}, and drops to below 1 dB at a pump intensity of 200 MW/cm

^{2}.

**20**(24), 2021–2023 (2008). [CrossRef]

21. I. D. Rukhlenko, I. Udagedara, M. Premaratne, and G. P. Agrawal, “Effect of free carriers on pump-to-signal noise transfer in silicon Raman amplifiers,” Opt. Lett. **35**(14), 2343–2345 (2010). [CrossRef] [PubMed]

## 4. Conclusions

^{2}, the optimized cavity length and output facet reflectivity are 1.04 cm and 22%, respectively. The maximum possible conversion efficiency is ~56%, and the pump-to-Stokes RIN transfer is ~1 dB. For a linear propagation loss of 2.0 dB/cm and same pump intensity, the corresponding values will be 0.34 cm (length), 58% (

*R*), 31% (conversion efficiency) and 4 dB (RIN transfer). The results of this study predict strong prospects for mid-IR silicon Raman lasers for high-performance biochemical and communication applications provided that low-noise mid-IR pump sources with high beam-quality and efficient waveguiding schemes exist.

_{sr}## Appendix A

*z*is proved first. Substituting Eq. (1) into

*z*, the integration in Eq. (22) can be approximated as

## References and links

1. | B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. |

2. | B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron. |

3. | V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a Mid-infrared silicon Raman amplifier,” Opt. Express |

4. | D. Borlaug, S. Fathpour, and B. Jalali, “Extreme value statistics in silicon photonics,” IEEE Photon. J. |

5. | T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on sapphire integrated waveguides for the mid-infrared,” Opt. Express |

6. | R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics |

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

8. | 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 |

9. | G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express |

10. | Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J. |

11. | O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express |

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

13. | A. Liu, L. Liao, and H. Rong, “Recent development in silicon photonics: 2.5 Gb/s silicon optical modulator and silicon Raman laser,” Proc. SPIE |

14. | X. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. |

15. | M. Krause, R. Draheim, H. Renner, and E. Brinkmeyer, “Cascaded silicon Raman lasers as mid-infrared sources,” Electron. Lett. |

16. | M. Krause, H. Renner, and E. Brinkmeyer, “Theory of silicon Raman amplifiers and lasers,” in |

17. | I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. |

18. | H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics |

19. | M. Krause, S. Cierullies, H. Renner, and E. Brinkmeyer, “Pump-to-Stokes RIN transfer in Raman fiber lasers and its impact on the performance of co-pumped Raman amplifiers,” Opt. Commun. |

20. | X. Sang, D. Dimitropoulos, and B. Jalali, “Influence of pump-to-signal RIN transfer on noise figure in silicon Raman amplifiers,” IEEE Photon. Technol. Lett. |

21. | I. D. Rukhlenko, I. Udagedara, M. Premaratne, and G. P. Agrawal, “Effect of free carriers on pump-to-signal noise transfer in silicon Raman amplifiers,” Opt. Lett. |

22. | X. Liu, X. Sang, B. Yan, K. Wang, C. Yu, and W. Dou, “Influences of pump-to-Stokes RIN transfer on the single order silicon Raman lasers,” J. Optoelectron. Adv. Mater. |

23. | R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express |

24. | S. Pearl, N. Rotenberg, and H. M. van Driel, “Three-photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett. |

25. | F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett. |

26. | J. Zhou, J. Chen, X. Li, G. Wu, and Y. Wang, “Exact analytical solution for Raman fiber lasers,” IEEE Photon. Technol. Lett. |

27. | Z. Qin, X. Zhou, Q. Li, H. Wu, and Z. Zhou, “An improved theoretical model of nth-order cascaded Raman fiber lasers,” J. Lightwave Technol. |

28. | S. A. Babin, D. V. Churkin, and E. V. Podivilov, “Intensity interactions in cascades of a two-stage Raman fiber laser,” Opt. Commun. |

29. | C. Huang, Z. Cai, C. Ye, H. Xu, and Z. Luo, “Optimization of dual-wavelength cascaded Raman fiber lasers using an analytic approach,” Opt. Commun. |

30. | K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun. |

31. | H. Rong, Y.-H. Kuo, S. Xu, A. Liu, R. Jones, M. Paniccia, O. Cohen, and O. Raday, “Monolithic integrated Raman silicon laser,” Opt. Express |

**OCIS Codes**

(130.0130) Integrated optics : Integrated optics

(190.5650) Nonlinear optics : Raman effect

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: April 5, 2012

Revised Manuscript: June 15, 2012

Manuscript Accepted: July 13, 2012

Published: July 23, 2012

**Citation**

J. Ma and S. Fathpour, "Pump-to-Stokes relative intensity noise transfer and analytical modeling of mid-infrared silicon Raman lasers," Opt. Express **20**, 17962-17972 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-17962

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### References

- B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol.24(12), 4600–4615 (2006). [CrossRef]
- B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron.12(6), 1618–1627 (2006). [CrossRef]
- V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a Mid-infrared silicon Raman amplifier,” Opt. Express15(22), 14355–14362 (2007). [CrossRef] [PubMed]
- D. Borlaug, S. Fathpour, and B. Jalali, “Extreme value statistics in silicon photonics,” IEEE Photon. J.1(1), 33–39 (2009). [CrossRef]
- T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on sapphire integrated waveguides for the mid-infrared,” Opt. Express18(12), 12127–12135 (2010). [CrossRef] [PubMed]
- R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics4(8), 495–497 (2010). [CrossRef]
- X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4(8), 557–560 (2010). [CrossRef]
- 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. Photonics4(8), 561–564 (2010). [CrossRef]
- G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express19(8), 7112–7119 (2011). [CrossRef] [PubMed]
- Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J.4(1), 104–113 (2012). [CrossRef]
- O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express12(21), 5269–5273 (2004). [CrossRef] [PubMed]
- 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]
- A. Liu, L. Liao, and H. Rong, “Recent development in silicon photonics: 2.5 Gb/s silicon optical modulator and silicon Raman laser,” Proc. SPIE5730, 80–93 (2005). [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(2), 160–170 (2006). [CrossRef]
- M. Krause, R. Draheim, H. Renner, and E. Brinkmeyer, “Cascaded silicon Raman lasers as mid-infrared sources,” Electron. Lett.42(21), 1224–1225 (2006). [CrossRef]
- M. Krause, H. Renner, and E. Brinkmeyer, “Theory of silicon Raman amplifiers and lasers,” in Silicon Photonics for Telecommunications and Biomedicine, S. Fathpour and B. Jalali, eds. (CRC Press, 2012), pp.131–200.
- I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron.16(1), 200–215 (2010). [CrossRef]
- H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2(3), 170–174 (2008). [CrossRef]
- M. Krause, S. Cierullies, H. Renner, and E. Brinkmeyer, “Pump-to-Stokes RIN transfer in Raman fiber lasers and its impact on the performance of co-pumped Raman amplifiers,” Opt. Commun.260(2), 656–661 (2006). [CrossRef]
- X. Sang, D. Dimitropoulos, and B. Jalali, “Influence of pump-to-signal RIN transfer on noise figure in silicon Raman amplifiers,” IEEE Photon. Technol. Lett.20(24), 2021–2023 (2008). [CrossRef]
- I. D. Rukhlenko, I. Udagedara, M. Premaratne, and G. P. Agrawal, “Effect of free carriers on pump-to-signal noise transfer in silicon Raman amplifiers,” Opt. Lett.35(14), 2343–2345 (2010). [CrossRef] [PubMed]
- X. Liu, X. Sang, B. Yan, K. Wang, C. Yu, and W. Dou, “Influences of pump-to-Stokes RIN transfer on the single order silicon Raman lasers,” J. Optoelectron. Adv. Mater.4, 1284–1288 (2010).
- R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express11(15), 1731–1739 (2003). [CrossRef] [PubMed]
- S. Pearl, N. Rotenberg, and H. M. van Driel, “Three-photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett.93(13), 131102 (2008). [CrossRef]
- F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett.16(12), 2601–2603 (2004). [CrossRef]
- J. Zhou, J. Chen, X. Li, G. Wu, and Y. Wang, “Exact analytical solution for Raman fiber lasers,” IEEE Photon. Technol. Lett.18(9), 1097–1099 (2006). [CrossRef]
- Z. Qin, X. Zhou, Q. Li, H. Wu, and Z. Zhou, “An improved theoretical model of nth-order cascaded Raman fiber lasers,” J. Lightwave Technol.25(6), 1555–1560 (2007). [CrossRef]
- S. A. Babin, D. V. Churkin, and E. V. Podivilov, “Intensity interactions in cascades of a two-stage Raman fiber laser,” Opt. Commun.226(1-6), 329–335 (2003). [CrossRef]
- C. Huang, Z. Cai, C. Ye, H. Xu, and Z. Luo, “Optimization of dual-wavelength cascaded Raman fiber lasers using an analytic approach,” Opt. Commun.272(2), 414–419 (2007). [CrossRef]
- K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun.271(1), 257–262 (2007). [CrossRef]
- H. Rong, Y.-H. Kuo, S. Xu, A. Liu, R. Jones, M. Paniccia, O. Cohen, and O. Raday, “Monolithic integrated Raman silicon laser,” Opt. Express14(15), 6705–6712 (2006). [CrossRef] [PubMed]

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