## Model for distributed feedback Brillouin lasers |

Optics Express, Vol. 21, Issue 13, pp. 16191-16199 (2013)

http://dx.doi.org/10.1364/OE.21.016191

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### Abstract

We present a propagation model for the dynamics of distributed feedback Brillouin lasers. The model is applied to the recently demonstrated DFB Brillouin laser based on a

© 2013 OSA

## 1. Introduction

1. V. E. Perlin and H. G. Winful, “Distributed feedback fiber Raman laser,” IEEE J. Quantum Electron. **37**(1), 38–47 (2001). [CrossRef]

7. K. S. Abedin, P. S. Westbrook, J. W. Nicholson, J. Porque, T. Kremp, and X. Liu, “Single-frequency Brillouin distributed feedback fiber laser,” Opt. Lett. **37**(4), 605–607 (2012). [CrossRef] [PubMed]

4. P. S. Westbrook, K. S. Abedin, J. W. Nicholson, T. Kremp, and J. Porque, “Raman fiber distributed feedback lasers,” Opt. Lett. **36**(15), 2895–2897 (2011). [CrossRef] [PubMed]

7. K. S. Abedin, P. S. Westbrook, J. W. Nicholson, J. Porque, T. Kremp, and X. Liu, “Single-frequency Brillouin distributed feedback fiber laser,” Opt. Lett. **37**(4), 605–607 (2012). [CrossRef] [PubMed]

1. V. E. Perlin and H. G. Winful, “Distributed feedback fiber Raman laser,” IEEE J. Quantum Electron. **37**(1), 38–47 (2001). [CrossRef]

2. V. E. Perlin and H. G. Winful, “Stimulated Raman scattering in nonlinear periodic structures,” Phys. Rev. A **64**(4), 043804 (2001). [CrossRef]

## 2. The model

*L*containing a

*L*from the input end. The grating is excited at

_{1}*z =*0 by a pump wave of power

8. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A **42**(9), 5514–5521 (1990). [CrossRef] [PubMed]

1. V. E. Perlin and H. G. Winful, “Distributed feedback fiber Raman laser,” IEEE J. Quantum Electron. **37**(1), 38–47 (2001). [CrossRef]

9. K. Ogusu, “Effect of stimulated Brillouin scattering on nonlinear pulse propagation in fiber Bragg gratings,” J. Opt. Soc. Am. B **17**(5), 769–774 (2000). [CrossRef]

10. H. Lee and G. P. Agrawal, “Suppression of stimulated Brillouin scattering in optical fibers using fiber Bragg gratings,” Opt. Express **11**(25), 3467–3472 (2003). [CrossRef] [PubMed]

## 3. Results for pi-phase-shifted DFB Brillouin laser in silica fiber

7. K. S. Abedin, P. S. Westbrook, J. W. Nicholson, J. Porque, T. Kremp, and X. Liu, “Single-frequency Brillouin distributed feedback fiber laser,” Opt. Lett. **37**(4), 605–607 (2012). [CrossRef] [PubMed]

^{−1}. Brillouin lasing could be obtained primarily in the forward or backward direction by displacing the

11. T. Kremp, K. S. Abedin, and P. S. Westbrook, “Closed-form approximations to the threshold quantities of distributed-feedback lasers with varying phase shifts and positions,” IEEE J. Quantum Electron. **49**(3), 281–292 (2013). [CrossRef]

*L*= 12.4 cm,

*l =*9.9 mm,

**37**(4), 605–607 (2012). [CrossRef] [PubMed]

12. C. M. de Sterke, K. R. Jackson, and B. D. Robert, “Nonlinear coupled-mode equations on a finite interval: a numerical procedure,” J. Opt. Soc. Am. B **8**(2), 403–412 (1991). [CrossRef]

**37**(4), 605–607 (2012). [CrossRef] [PubMed]

13. I. C. M. Littler, T. Grujic, and B. J. Eggleton, “Photothermal effects in fiber Bragg gratings,” Appl. Opt. **45**(19), 4679–4685 (2006). [CrossRef] [PubMed]

## 4. DFB Brillouin lasing in chalcogenide glasses

14. C. Florea, M. Bashkansky, Z. Dutton, J. Sanghera, P. Pureza, and I. Aggarwal, “Stimulated Brillouin scattering in single-mode As_{2}S_{3} and As_{2}Se_{3} chalcogenide fibers,” Opt. Express **14**(25), 12063–12070 (2006). [CrossRef] [PubMed]

15. R. Pant, C. G. Poulton, D. Y. Choi, H. Mcfarlane, S. Hile, E. B. Li, L. Thévenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering,” Opt. Express **19**(9), 8285–8290 (2011). [CrossRef] [PubMed]

_{2}S

_{3}[15

15. R. Pant, C. G. Poulton, D. Y. Choi, H. Mcfarlane, S. Hile, E. B. Li, L. Thévenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering,” Opt. Express **19**(9), 8285–8290 (2011). [CrossRef] [PubMed]

*Q*resonator in order to achieve threshold with sub-Watt pump power. As it turns out, strong photo-induced gratings with coupling constants larger than 10

^{4}m

^{−1}have already been demonstrated in chalcogenide waveguides [16

16. M. Shokooh-Saremi, V. G. Ta’eed, N. J. Baker, I. C. M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “High-performance Bragg gratings in chalcogenide rib waveguides written with a modified Sagnac interferometer,” J. Opt. Soc. Am. B **23**(7), 1323–1331 (2006). [CrossRef]

17. N. J. Baker, M. A. F. Roelens, S. Madden, B. Luther-Davies, C. M. de Sterke, and B. J. Eggleton, “Pulse train generation by soliton fission in highly nonlinear chalcogenide (As_{2}S_{3}) waveguide Bragg grating,” Electron. Lett. **45**(15), 799–801 (2009). [CrossRef]

*L*= 1 cm yields a coupling strength

*n*= 2.45. This large bandwidth means that if a

*Q*of the resulting resonance is much reduced, however.)

_{2}S

_{3}rib waveguide of Ref. 15

15. R. Pant, C. G. Poulton, D. Y. Choi, H. Mcfarlane, S. Hile, E. B. Li, L. Thévenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering,” Opt. Express **19**(9), 8285–8290 (2011). [CrossRef] [PubMed]

**37**(1), 38–47 (2001). [CrossRef]

^{−1}and hence a threshold pump power

_{2}S

_{3}fiber. The measured Brillouin gain coefficient is

14. C. Florea, M. Bashkansky, Z. Dutton, J. Sanghera, P. Pureza, and I. Aggarwal, “Stimulated Brillouin scattering in single-mode As_{2}S_{3} and As_{2}Se_{3} chalcogenide fibers,” Opt. Express **14**(25), 12063–12070 (2006). [CrossRef] [PubMed]

## 6. Conclusion

18. H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson 3rd, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun **4**, 1944 (2013), doi:. [CrossRef] [PubMed]

19. P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X **2**(1), 011008 (2012). [CrossRef]

## Acknowledgments

## References and links

1. | V. E. Perlin and H. G. Winful, “Distributed feedback fiber Raman laser,” IEEE J. Quantum Electron. |

2. | V. E. Perlin and H. G. Winful, “Stimulated Raman scattering in nonlinear periodic structures,” Phys. Rev. A |

3. | Y. Hu and N. G. R. Broderick, “Improved design of a DFB Raman fibre laser,” Opt. Commun. |

4. | P. S. Westbrook, K. S. Abedin, J. W. Nicholson, T. Kremp, and J. Porque, “Raman fiber distributed feedback lasers,” Opt. Lett. |

5. | J. Shi, S. U. Alam, and M. Ibsen, “Highly efficient Raman distributed feedback fibre lasers,” Opt. Express |

6. | J. Shi, S. Alam, and M. Ibsen, “Sub-watt threshold, kilohertz-linewidth Raman distributed-feedback fiber laser,” Opt. Lett. |

7. | K. S. Abedin, P. S. Westbrook, J. W. Nicholson, J. Porque, T. Kremp, and X. Liu, “Single-frequency Brillouin distributed feedback fiber laser,” Opt. Lett. |

8. | R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A |

9. | K. Ogusu, “Effect of stimulated Brillouin scattering on nonlinear pulse propagation in fiber Bragg gratings,” J. Opt. Soc. Am. B |

10. | H. Lee and G. P. Agrawal, “Suppression of stimulated Brillouin scattering in optical fibers using fiber Bragg gratings,” Opt. Express |

11. | T. Kremp, K. S. Abedin, and P. S. Westbrook, “Closed-form approximations to the threshold quantities of distributed-feedback lasers with varying phase shifts and positions,” IEEE J. Quantum Electron. |

12. | C. M. de Sterke, K. R. Jackson, and B. D. Robert, “Nonlinear coupled-mode equations on a finite interval: a numerical procedure,” J. Opt. Soc. Am. B |

13. | I. C. M. Littler, T. Grujic, and B. J. Eggleton, “Photothermal effects in fiber Bragg gratings,” Appl. Opt. |

14. | C. Florea, M. Bashkansky, Z. Dutton, J. Sanghera, P. Pureza, and I. Aggarwal, “Stimulated Brillouin scattering in single-mode As |

15. | R. Pant, C. G. Poulton, D. Y. Choi, H. Mcfarlane, S. Hile, E. B. Li, L. Thévenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering,” Opt. Express |

16. | M. Shokooh-Saremi, V. G. Ta’eed, N. J. Baker, I. C. M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “High-performance Bragg gratings in chalcogenide rib waveguides written with a modified Sagnac interferometer,” J. Opt. Soc. Am. B |

17. | N. J. Baker, M. A. F. Roelens, S. Madden, B. Luther-Davies, C. M. de Sterke, and B. J. Eggleton, “Pulse train generation by soliton fission in highly nonlinear chalcogenide (As |

18. | H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson 3rd, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun |

19. | P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X |

**OCIS Codes**

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

(140.3490) Lasers and laser optics : Lasers, distributed-feedback

(190.4360) Nonlinear optics : Nonlinear optics, devices

(290.5900) Scattering : Scattering, stimulated Brillouin

(060.3735) Fiber optics and optical communications : Fiber Bragg gratings

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: June 10, 2013

Revised Manuscript: June 20, 2013

Manuscript Accepted: June 25, 2013

Published: June 28, 2013

**Citation**

Herbert G. Winful, Irina V. Kabakova, and Benjamin J. Eggleton, "Model for distributed feedback Brillouin lasers," Opt. Express **21**, 16191-16199 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-16191

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### References

- V. E. Perlin and H. G. Winful, “Distributed feedback fiber Raman laser,” IEEE J. Quantum Electron.37(1), 38–47 (2001). [CrossRef]
- V. E. Perlin and H. G. Winful, “Stimulated Raman scattering in nonlinear periodic structures,” Phys. Rev. A64(4), 043804 (2001). [CrossRef]
- Y. Hu and N. G. R. Broderick, “Improved design of a DFB Raman fibre laser,” Opt. Commun.282(16), 3356–3359 (2009). [CrossRef]
- P. S. Westbrook, K. S. Abedin, J. W. Nicholson, T. Kremp, and J. Porque, “Raman fiber distributed feedback lasers,” Opt. Lett.36(15), 2895–2897 (2011). [CrossRef] [PubMed]
- J. Shi, S. U. Alam, and M. Ibsen, “Highly efficient Raman distributed feedback fibre lasers,” Opt. Express20(5), 5082–5091 (2012). [CrossRef] [PubMed]
- J. Shi, S. Alam, and M. Ibsen, “Sub-watt threshold, kilohertz-linewidth Raman distributed-feedback fiber laser,” Opt. Lett.37(9), 1544–1546 (2012). [CrossRef] [PubMed]
- K. S. Abedin, P. S. Westbrook, J. W. Nicholson, J. Porque, T. Kremp, and X. Liu, “Single-frequency Brillouin distributed feedback fiber laser,” Opt. Lett.37(4), 605–607 (2012). [CrossRef] [PubMed]
- R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42(9), 5514–5521 (1990). [CrossRef] [PubMed]
- K. Ogusu, “Effect of stimulated Brillouin scattering on nonlinear pulse propagation in fiber Bragg gratings,” J. Opt. Soc. Am. B17(5), 769–774 (2000). [CrossRef]
- H. Lee and G. P. Agrawal, “Suppression of stimulated Brillouin scattering in optical fibers using fiber Bragg gratings,” Opt. Express11(25), 3467–3472 (2003). [CrossRef] [PubMed]
- T. Kremp, K. S. Abedin, and P. S. Westbrook, “Closed-form approximations to the threshold quantities of distributed-feedback lasers with varying phase shifts and positions,” IEEE J. Quantum Electron.49(3), 281–292 (2013). [CrossRef]
- C. M. de Sterke, K. R. Jackson, and B. D. Robert, “Nonlinear coupled-mode equations on a finite interval: a numerical procedure,” J. Opt. Soc. Am. B8(2), 403–412 (1991). [CrossRef]
- I. C. M. Littler, T. Grujic, and B. J. Eggleton, “Photothermal effects in fiber Bragg gratings,” Appl. Opt.45(19), 4679–4685 (2006). [CrossRef] [PubMed]
- C. Florea, M. Bashkansky, Z. Dutton, J. Sanghera, P. Pureza, and I. Aggarwal, “Stimulated Brillouin scattering in single-mode As2S3 and As2Se3 chalcogenide fibers,” Opt. Express14(25), 12063–12070 (2006). [CrossRef] [PubMed]
- R. Pant, C. G. Poulton, D. Y. Choi, H. Mcfarlane, S. Hile, E. B. Li, L. Thévenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering,” Opt. Express19(9), 8285–8290 (2011). [CrossRef] [PubMed]
- M. Shokooh-Saremi, V. G. Ta’eed, N. J. Baker, I. C. M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “High-performance Bragg gratings in chalcogenide rib waveguides written with a modified Sagnac interferometer,” J. Opt. Soc. Am. B23(7), 1323–1331 (2006). [CrossRef]
- N. J. Baker, M. A. F. Roelens, S. Madden, B. Luther-Davies, C. M. de Sterke, and B. J. Eggleton, “Pulse train generation by soliton fission in highly nonlinear chalcogenide (As2S3) waveguide Bragg grating,” Electron. Lett.45(15), 799–801 (2009). [CrossRef]
- H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun4, 1944 (2013), doi:. [CrossRef] [PubMed]
- P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X2(1), 011008 (2012). [CrossRef]

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