## Experimental and theoretical study of longitudinal power distribution in a random DFB fiber laser |

Optics Express, Vol. 20, Issue 10, pp. 11178-11188 (2012)

http://dx.doi.org/10.1364/OE.20.011178

Acrobat PDF (1135 KB)

### Abstract

We have measured the longitudinal power distribution inside a random distributed feedback Raman fiber laser. The observed distribution has a sharp maximum whose position depends on pump power. The spatial distribution profiles are different for the first and the second Stokes waves. Both analytic solution and results of direct numerical modeling are in excellent agreement with experimental observations.

© 2012 OSA

## 1. Introduction

1. S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics **4**(4), 231–235 (2010). [CrossRef]

2. H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A **38**(49), 10497–10535 (2005). [CrossRef]

5. M. Leonetti, C. Conti, and C. Lopez, “The mode-locking transition of random lasers,” Nat. Photonics **5**(10), 615–617 (2011). [CrossRef]

6. D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castanon, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A **82**(3), 033828 (2010). [CrossRef]

8. A. R. Sarmani, M. H. Abu Bakar, A. A. Bakar, F. R. Adikan, and M. A. Mahdi, “Spectral variations of the output spectrum in a random distributed feedback Raman fiber laser,” Opt. Express **19**(15), 14152–14159 (2011). [CrossRef] [PubMed]

9. I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, “Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm,” Opt. Express **19**(19), 18486–18494 (2011). [CrossRef] [PubMed]

10. A. M. R. Pinto, O. Frazão, J. L. Santos, and M. Lopez-Amo, “Multiwavelength fiber laser based on a photonic crystal fiber loop mirror with cooperative Rayleigh scattering,” Appl. Phys. B **99**(3), 391–395 (2010). [CrossRef]

11. A. E. El-Taher, P. Harper, S. A. Babin, D. V. Churkin, E. V. Podivilov, J. D. Ania-Castanon, and S. K. Turitsyn, “Effect of Rayleigh-scattering distributed feedback on multiwavelength Raman fiber laser generation,” Opt. Lett. **36**(2), 130–132 (2011). [CrossRef] [PubMed]

12. S. A. Babin, A. E. El-Taher, P. Harper, E. V. Podivilov, and S. K. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A **84**(2), 021805(R) (2011). [CrossRef]

12. S. A. Babin, A. E. El-Taher, P. Harper, E. V. Podivilov, and S. K. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A **84**(2), 021805(R) (2011). [CrossRef]

13. S. K. Turitsyn, J. D. Ania-Castañón, S. A. Babin, V. Karalekas, P. Harper, D. Churkin, S. I. Kablukov, A. E. El-Taher, E. V. Podivilov, and V. K. Mezentsev, “270-km ultralong Raman fiber laser,” Phys. Rev. Lett. **103**(13), 133901 (2009). [CrossRef] [PubMed]

14. J. D. Ania-Castañón, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Ultralong Raman fiber lasers as virtually lossless optical media,” Phys. Rev. Lett. **96**(2), 023902 (2006). [CrossRef] [PubMed]

## 2. Experimental setup

1. S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics **4**(4), 231–235 (2010). [CrossRef]

1. S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics **4**(4), 231–235 (2010). [CrossRef]

**4**(4), 231–235 (2010). [CrossRef]

## 3. Experimental results

9. I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, “Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm,” Opt. Express **19**(19), 18486–18494 (2011). [CrossRef] [PubMed]

15. 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]

15. 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]

*|z| = L*, see [1

_{RS}**4**(4), 231–235 (2010). [CrossRef]

*|z| = L*defines the boundary of a gain region. The measurements show that with increasing power the position of the power maximum shifts closer to the z = 0, and the distribution becomes correspondingly narrower.

_{RS}*|z|>L*much faster than at lower pump powers owing to the depletion process. At the highest available pump power, when the power of the second Stokes wave becomes high, see Fig. 3(b), the first Stokes wave distribution becomes very narrow, and all the generated first Stokes wave power is localized within the region |z|<10 km. At the same time, the second Stokes wave distribution is much broader with maximum located at longer distances, |z|>10 km.

_{RS}16. S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castañón, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A **77**(3), 033803 (2008). [CrossRef]

17. S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, “Four-wave-mixing-induced turbulent spectral broadening in a long Raman fiber laser,” J. Opt. Soc. Am. B **24**(8), 1729–1738 (2007). [CrossRef]

18. S. A. Babin, V. Karalekas, P. Harper, E. V. Podivilov, V. K. Mezentsev, J. D. Ania-Castañón, and S. K. Turitsyn, “Experimental demonstration of mode structure in ultralong Raman fiber lasers,” Opt. Lett. **32**(9), 1135–1137 (2007). [CrossRef] [PubMed]

18. S. A. Babin, V. Karalekas, P. Harper, E. V. Podivilov, V. K. Mezentsev, J. D. Ania-Castañón, and S. K. Turitsyn, “Experimental demonstration of mode structure in ultralong Raman fiber lasers,” Opt. Lett. **32**(9), 1135–1137 (2007). [CrossRef] [PubMed]

19. D. B. Soh, J. P. Koplow, S. W. Moore, K. L. Schroder, and W. L. Hsu, “The effect of dispersion on spectral broadening of incoherent continuous-wave light in optical fibers,” Opt. Express **18**(21), 22393–22405 (2010). [CrossRef] [PubMed]

## 4. Numerical calculation of the power distribution

20. J. D. Ania-Castañón, “Quasi-lossless transmission using second-order Raman amplification and fibre Bragg gratings,” Opt. Express **12**(19), 4372–4377 (2004). [CrossRef] [PubMed]

*P*,

*S*,

*2S*refer the corresponding terms to pump, Stokes and second Stokes waves, while upper indexes + and – refer to forward (“right”) and backward (“left”) propagating waves, respectively. Coefficients

*α*define the attenuation of the corresponding wave,

*g*is the Raman gain coefficient,

*ν*is the radiation frequency,

*Δν*is the Raman amplification bandwidth,

*ε*is the backscattering coefficient, derived as

*α*multiplied by backscattering factor

*Q*. Backscattered factor was measured in special experiments and amounts approximately to

*Q*≈10

^{−3}for the used fiber. As the studied configuration is symmetric against reflection (z→-z) with corresponding changes in upper indexes ( + ↔ -), we can use just the positive arm (z>0) in modeling, with the appropriate boundary conditions:

*L≈*42 km is the length of one fiber arm.

*L*value, Fig. 6(b). At the generation threshold,

_{RS}*L*is defined by the undepleted pump wave distribution, see Fig. 5, so the experimental value is close to the estimation

_{RS}*L*~ 35 km made in [1

_{RS}**4**(4), 231–235 (2010). [CrossRef]

*L*decreases because of the pump power depletion, see Fig. 5. The agreement between the calculated and experimental results remains reasonably good even above the generation threshold of the second Stokes wave, which distorts the first Stokes power distribution at z >

_{RS}*L*, but not near its maximum, see Figs. 3, 5.

_{RS}## 5. Analytical model

*z*≥ 0).

*P*to the pump power depletion, as the left wave is of two orders of magnitude smaller than the right one at positive

_{S}^{-}*z*(see Fig. 3(a)). The resulting simplified set of equations reads as

*g*. These equations should be solved with the following boundary conditions

_{P}= g_{S}·λ_{Stokes}/λ_{pump}*P*is the generation power of the right wave at the pump coupling point (

_{S}(0)*z = 0*). Relationship Eq. (7) defines the generation power of the right wave,

*P*at the pump coupling point (

_{S}(0)*z = 0*) through the integral of the generation power over the fiber length.

*P*=

_{P}(0)*P*is an input pump power.

^{+}_{P}(0)*P*one needs to fit the value of the Stokes wave power

_{S}^{+}(z)*P*at the pump coupling point. However, the value

_{S}(0)*P*can also be found analytically. Indeed, to find the value of

_{S}(0)*P*we substitute Eq. (8) into Eq. (6):

_{S}(0)*g*, that is confirmed by the experimental data and numerical simulations (Fig. 5), we obtainwhere substitution

_{P}P_{S}(0)/g_{S}P_{P}(0) << 1*ξ = (1 - exp(-αz))/α*is used. Here and everywhere below we assume large enough fiber lengths,

*αL >> 1,*such that

*L*

_{eff}= (1 - e^{-αL})/α ≈ 1/α.*P*. Integrating Eq. (11) in this case, one can found implicitly the generation threshold pump power

_{S}(0) = 0*P*:

_{th}*P*could be found in principle. However, it is more insightful to derive a simple approximate solution. Indeed, within the range

_{S}(0)*g*one can neglect the

_{S}P_{P}(0)ξ < ln(g_{S}P_{P}(0)/g_{P}P_{S}(0))*g*term in the denominator of the integral (11). Assuming that

_{S}P_{P}(0)/g_{P}P_{S}(0)*ξ*obeys the relation ln(g

_{S}P

_{P}(0)/g

_{P}P

_{S}(0)) < g

_{S}P

_{P}(0)ξ ≤ g

_{S}P

_{P}(0)/α one can neglect exponential term in the denominator of Eq. (11). In this case the approximate solution of Eq. (11) takes a simple analytical form and the generation power

*P*at pump coupling point can be expressed implicitly as

_{S}(0)*L*.

_{eff}= 1/α*g*one can define from Eq. (12) the Stokes

_{P}P_{S}(0) = g_{S}P_{P}(0)exp(-g_{S}P_{P}(0)/α),*P*and pump

_{s}*(0)*P*powers as

_{p}*(0)*ln(g*, we easily derive the Stokes power at z = 0 as

_{S}P_{P}(0)/g_{P}P_{S}(0)) = g_{S}P_{th}/α*Ps(0)*Eq. (15) with numerics and the experimental data demonstrates good agreement up to certain power level, as it is seen in Fig. 7 .

*P*can be used in Eq. (9) to plot the longitudinal distribution of the generated power

_{S}(0)*P*. There is a very good agreement between experimentally measured, analytically and numerically calculated power distributions, see Fig. 6(a).

_{S}^{+}(z)*L*depends on pump power. Indeed, using

_{RS}*L*definition

_{RS}*g*, it is straightforward to derive from the Eq. (8) the following equation:

_{S}P_{P}(L_{RS}) = α*L*, Eq. (16) can be simplified using Eq. (15):

_{RS}< 1/α*L*depends on pump power inversely, with the logarithmic accuracy. This analytical result is also in good agreement with both experimental data and numerical simulation, see Fig. 6(b).

_{RS}## 6. Discussion and conclusions

*L*) as well as the spatial longitudinal distribution. The numerical and analytical calculations of the first Stokes wave give very close values which are also in good quantitative agreement with obtained experimental results.

_{RS}*L*corresponding to the boundary of the amplification region. At |z|>

_{RS}*L*the generated power attenuates nearly exponentially with a coefficient defined by linear losses.

_{RS}21. S. Foster and A. Tikhomirov, “Experimental and theoretical characterization of the mode profile of single-mode DFB fiber lasers,” IEEE J. Quantum Electron. **41**(6), 762–766 (2005). [CrossRef]

22. N. Lizárraga, N. P. Puente, E. I. Chaikina, T. A. Leskova, and E. R. Méndez, “Single-mode Er-doped fiber random laser with distributed Bragg grating feedback,” Opt. Express **17**(2), 395–404 (2009). [CrossRef] [PubMed]

23. M. Gagné and R. Kashyap, “Demonstration of a 3 mW threshold Er-doped random fiber laser based on a unique fiber Bragg grating,” Opt. Express **17**(21), 19067–19074 (2009). [CrossRef] [PubMed]

21. S. Foster and A. Tikhomirov, “Experimental and theoretical characterization of the mode profile of single-mode DFB fiber lasers,” IEEE J. Quantum Electron. **41**(6), 762–766 (2005). [CrossRef]

*L*to the center. The model offers the way of power optimization: the half-length of the random DFB fiber laser

_{RS}*L*should be close to

*L*value to eliminate exponential attenuation of the generated wave thus reaching highest possible conversion efficiency (defined by loss factor

_{RS}*η ~ exp(-αL)*[12

12. S. A. Babin, A. E. El-Taher, P. Harper, E. V. Podivilov, and S. K. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A **84**(2), 021805(R) (2011). [CrossRef]

*|z|*=

*L*), exceeding

_{RS}*η*~ 0.6; see Fig. 3. As we have found here, increasing pump power well above the threshold results in reduction of the optimal length nearly inversely with power, down to

*L ~ L*< 5 km in our case. Relevant shortening of the fiber will lead to higher random lasing threshold, however, the conversion efficiency may be further increased because of the loss reduction.

_{RS}*L*. The second Stokes wave distribution is also more uniform compared to the first Stokes wave distribution at the same average generated powers. It is likely that the higher order schemes could provide an even more flat distribution that could be important for possible telecom applications such as quasi-lossless transmission [14

_{RS}14. J. D. Ania-Castañón, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Ultralong Raman fiber lasers as virtually lossless optical media,” Phys. Rev. Lett. **96**(2), 023902 (2006). [CrossRef] [PubMed]

15. 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]

**226**(1-6), 329–335 (2003). [CrossRef]

## Acknowledgments

## References and links

1. | S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics |

2. | H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A |

3. | D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. |

4. | J. Fallert, R. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photonics |

5. | M. Leonetti, C. Conti, and C. Lopez, “The mode-locking transition of random lasers,” Nat. Photonics |

6. | D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castanon, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A |

7. | A. M. R. Pinto, M. Bravo, M. Fernandez-Vallejo, M. Lopez-Amo, J. Kobelke, and K. Schuster, “Suspended-core fiber Sagnac combined dual-random mirror Raman fiber laser,” Opt. Express |

8. | A. R. Sarmani, M. H. Abu Bakar, A. A. Bakar, F. R. Adikan, and M. A. Mahdi, “Spectral variations of the output spectrum in a random distributed feedback Raman fiber laser,” Opt. Express |

9. | I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, “Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm,” Opt. Express |

10. | A. M. R. Pinto, O. Frazão, J. L. Santos, and M. Lopez-Amo, “Multiwavelength fiber laser based on a photonic crystal fiber loop mirror with cooperative Rayleigh scattering,” Appl. Phys. B |

11. | A. E. El-Taher, P. Harper, S. A. Babin, D. V. Churkin, E. V. Podivilov, J. D. Ania-Castanon, and S. K. Turitsyn, “Effect of Rayleigh-scattering distributed feedback on multiwavelength Raman fiber laser generation,” Opt. Lett. |

12. | S. A. Babin, A. E. El-Taher, P. Harper, E. V. Podivilov, and S. K. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A |

13. | S. K. Turitsyn, J. D. Ania-Castañón, S. A. Babin, V. Karalekas, P. Harper, D. Churkin, S. I. Kablukov, A. E. El-Taher, E. V. Podivilov, and V. K. Mezentsev, “270-km ultralong Raman fiber laser,” Phys. Rev. Lett. |

14. | J. D. Ania-Castañón, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Ultralong Raman fiber lasers as virtually lossless optical media,” Phys. Rev. Lett. |

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

16. | S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castañón, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A |

17. | S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, “Four-wave-mixing-induced turbulent spectral broadening in a long Raman fiber laser,” J. Opt. Soc. Am. B |

18. | S. A. Babin, V. Karalekas, P. Harper, E. V. Podivilov, V. K. Mezentsev, J. D. Ania-Castañón, and S. K. Turitsyn, “Experimental demonstration of mode structure in ultralong Raman fiber lasers,” Opt. Lett. |

19. | D. B. Soh, J. P. Koplow, S. W. Moore, K. L. Schroder, and W. L. Hsu, “The effect of dispersion on spectral broadening of incoherent continuous-wave light in optical fibers,” Opt. Express |

20. | J. D. Ania-Castañón, “Quasi-lossless transmission using second-order Raman amplification and fibre Bragg gratings,” Opt. Express |

21. | S. Foster and A. Tikhomirov, “Experimental and theoretical characterization of the mode profile of single-mode DFB fiber lasers,” IEEE J. Quantum Electron. |

22. | N. Lizárraga, N. P. Puente, E. I. Chaikina, T. A. Leskova, and E. R. Méndez, “Single-mode Er-doped fiber random laser with distributed Bragg grating feedback,” Opt. Express |

23. | M. Gagné and R. Kashyap, “Demonstration of a 3 mW threshold Er-doped random fiber laser based on a unique fiber Bragg grating,” Opt. Express |

**OCIS Codes**

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

(140.3510) Lasers and laser optics : Lasers, fiber

(290.5870) Scattering : Scattering, Rayleigh

(290.5910) Scattering : Scattering, stimulated Raman

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: February 1, 2012

Manuscript Accepted: February 24, 2012

Published: May 1, 2012

**Citation**

Dmitry V. Churkin, Atalla E. El-Taher, Ilya D. Vatnik, Juan Diego Ania-Castañón, Paul Harper, Eugeny V. Podivilov, Sergey A. Babin, and Sergei K. Turitsyn, "Experimental and theoretical study of longitudinal power distribution in a random DFB fiber laser," Opt. Express **20**, 11178-11188 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11178

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### References

- S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics4(4), 231–235 (2010). [CrossRef]
- H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A38(49), 10497–10535 (2005). [CrossRef]
- D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys.4(5), 359–367 (2008). [CrossRef]
- J. Fallert, R. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photonics3(5), 279–282 (2009). [CrossRef]
- M. Leonetti, C. Conti, and C. Lopez, “The mode-locking transition of random lasers,” Nat. Photonics5(10), 615–617 (2011). [CrossRef]
- D. V. Churkin, S. A. Babin, A. E. El-Taher, P. Harper, S. I. Kablukov, V. Karalekas, J. D. Ania-Castanon, E. V. Podivilov, and S. K. Turitsyn, “Raman fiber lasers with a random distributed feedback based on Rayleigh scattering,” Phys. Rev. A82(3), 033828 (2010). [CrossRef]
- A. M. R. Pinto, M. Bravo, M. Fernandez-Vallejo, M. Lopez-Amo, J. Kobelke, and K. Schuster, “Suspended-core fiber Sagnac combined dual-random mirror Raman fiber laser,” Opt. Express19(12), 11906–11915 (2011). [CrossRef] [PubMed]
- A. R. Sarmani, M. H. Abu Bakar, A. A. Bakar, F. R. Adikan, and M. A. Mahdi, “Spectral variations of the output spectrum in a random distributed feedback Raman fiber laser,” Opt. Express19(15), 14152–14159 (2011). [CrossRef] [PubMed]
- I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, “Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm,” Opt. Express19(19), 18486–18494 (2011). [CrossRef] [PubMed]
- A. M. R. Pinto, O. Frazão, J. L. Santos, and M. Lopez-Amo, “Multiwavelength fiber laser based on a photonic crystal fiber loop mirror with cooperative Rayleigh scattering,” Appl. Phys. B99(3), 391–395 (2010). [CrossRef]
- A. E. El-Taher, P. Harper, S. A. Babin, D. V. Churkin, E. V. Podivilov, J. D. Ania-Castanon, and S. K. Turitsyn, “Effect of Rayleigh-scattering distributed feedback on multiwavelength Raman fiber laser generation,” Opt. Lett.36(2), 130–132 (2011). [CrossRef] [PubMed]
- S. A. Babin, A. E. El-Taher, P. Harper, E. V. Podivilov, and S. K. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A84(2), 021805(R) (2011). [CrossRef]
- S. K. Turitsyn, J. D. Ania-Castañón, S. A. Babin, V. Karalekas, P. Harper, D. Churkin, S. I. Kablukov, A. E. El-Taher, E. V. Podivilov, and V. K. Mezentsev, “270-km ultralong Raman fiber laser,” Phys. Rev. Lett.103(13), 133901 (2009). [CrossRef] [PubMed]
- J. D. Ania-Castañón, T. J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and S. K. Turitsyn, “Ultralong Raman fiber lasers as virtually lossless optical media,” Phys. Rev. Lett.96(2), 023902 (2006). [CrossRef] [PubMed]
- 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]
- S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castañón, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A77(3), 033803 (2008). [CrossRef]
- S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, “Four-wave-mixing-induced turbulent spectral broadening in a long Raman fiber laser,” J. Opt. Soc. Am. B24(8), 1729–1738 (2007). [CrossRef]
- S. A. Babin, V. Karalekas, P. Harper, E. V. Podivilov, V. K. Mezentsev, J. D. Ania-Castañón, and S. K. Turitsyn, “Experimental demonstration of mode structure in ultralong Raman fiber lasers,” Opt. Lett.32(9), 1135–1137 (2007). [CrossRef] [PubMed]
- D. B. Soh, J. P. Koplow, S. W. Moore, K. L. Schroder, and W. L. Hsu, “The effect of dispersion on spectral broadening of incoherent continuous-wave light in optical fibers,” Opt. Express18(21), 22393–22405 (2010). [CrossRef] [PubMed]
- J. D. Ania-Castañón, “Quasi-lossless transmission using second-order Raman amplification and fibre Bragg gratings,” Opt. Express12(19), 4372–4377 (2004). [CrossRef] [PubMed]
- S. Foster and A. Tikhomirov, “Experimental and theoretical characterization of the mode profile of single-mode DFB fiber lasers,” IEEE J. Quantum Electron.41(6), 762–766 (2005). [CrossRef]
- N. Lizárraga, N. P. Puente, E. I. Chaikina, T. A. Leskova, and E. R. Méndez, “Single-mode Er-doped fiber random laser with distributed Bragg grating feedback,” Opt. Express17(2), 395–404 (2009). [CrossRef] [PubMed]
- M. Gagné and R. Kashyap, “Demonstration of a 3 mW threshold Er-doped random fiber laser based on a unique fiber Bragg grating,” Opt. Express17(21), 19067–19074 (2009). [CrossRef] [PubMed]

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