Abstract

We report the observation of self-oscillations of the output power in a cascaded Raman fiber laser delivering two Stokes components. Our cascaded Raman fiber laser is made with a highly nonlinear photonic crystal fiber and it oscillates within a Perot-Fabry cavity formed by weak Fresnel reflections from the fiber ends. From our experimental and theoretical study, we identify stimulated Raman scattering as being the physical effect dominant in the emergence of unstable behaviors inside the Perot-Fabry cavity. Mechanisms of laser destabilization are thus found to be very different from polarization mechanisms previously identified as being responsible for unstable behaviors in conventional one-stage Raman fiber lasers [14, 15].

©2008 Optical Society of America

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References

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  1. E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, “Three-cascaded 1407-nm Raman laser based on phosphorus-doped silica fiber,” Opt. Lett. 25, 402–404 (2000).
    [Crossref]
  2. M. D. Mermelstein, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. Eggleton, “Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening,” IEEE. Photon. Technol. Lett. 13, 1286–1288 (2001).
    [Crossref]
  3. Y. Han, C. Kim, J. I. Kang, U. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period gratings,” IEEE. Photon. Technol. Lett. 15, 383–385 (2003).
    [Crossref]
  4. Y. Zhao and S. D. Jackson, “Highly efficient free running cascaded Raman fiber laser that uses broadband pumping,” Opt. Express 13, 4731–4736 (2005).
    [Crossref] [PubMed]
  5. S. Cierullies, H. Renner, and E. Brinkmeyer, “Numerical optimization of multi-wavelength and cascaded Raman fiber lasers,” Opt. Commun. 217, 233–238 (2003).
    [Crossref]
  6. 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, 414–419 (2007).
    [Crossref]
  7. I. A. Bufetov and E. M. Dianov, “A simple analytic model of a cw multicascade fibre Raman laser,” Quantum Electron. 30, 873–877 (2000).
    [Crossref]
  8. 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, 2601–2603 (2004).
    [Crossref]
  9. M. Rini, I. Cristiani, and V. Degiorgio, “Numerical Modeling and Optimization of Cascaded CW Raman Fiber Lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000).
    [Crossref]
  10. B. Burgoyne, N. Godbout, and S. Lacroix, “Theoretical analysis of nth-order cascaded continuous-wave Raman fiber lasers. II. Optimization and design rules,” J. Opt. Soc. Am. B 22, 772–776 (2005).
    [Crossref]
  11. B. Burgoyne, N. Godbout, and S. Lacroix, “Transient regime in a nth-order cascaded CW Raman fiber laser,” Opt. Express 12, 1019–1024 (2004).
    [Crossref] [PubMed]
  12. S. D. Jackson and P. H. Muir “Theory and numerical simulation of nth-order cascaded Raman fiber lasers,” J. Opt. Soc. Am. B 18, 1297–1306 (2001).
    [Crossref]
  13. S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, “Relative Intensity Noise in Cascaded Raman Fiber Lasers,” IEEE Photon. Technol. Lett. 17, 2553–2555 (2005).
    [Crossref]
  14. A. Doutté, P. Suret, and S. Randoux, “Influence of light polarization on dynamics of continuous-wave-pumped Raman fiber lasers,” Opt. Lett. 28, 2464–2466 (2003).
    [Crossref]
  15. P. Suret, A. Doutté, and S. Randoux, “Influence of light polarization on dynamics of all-fiber Raman lasers: theoretical analysis,” Opt. Lett. 29, 2166–2168 (2004).
    [Crossref] [PubMed]
  16. S. Randoux, A. Doutté, and P. Suret, “Polarization-resolved analysis of the characteristics of a Raman laser made with a polarization maintaining fiber,” Opt. Commun. 260, 232–241 (2006).
    [Crossref]
  17. S. Randoux, N. Y. Joly, G. Mélin, A. Fleureau, L. Galkovsky, S. Lempereur, and P. Suret, “Grating-free Raman laser using highly nonlinear photonic crystal fiber” Opt. Express 15, 16035–16043 (2007).
    [Crossref] [PubMed]
  18. S. Randoux, V. Lecoeuche, B. Ségard, and J. Zemmouri, “Dynamical behavior of a Brillouin fiber ring laser emitting two Stokes components” Phys. Rev. A 52, 2327–2334 (1995).
    [Crossref] [PubMed]
  19. V. Babin, A. Mocofanescu, V. I. Vlad, and M. J. Damzen, “Analytical treatment of laser-pulse compression in stimulated Brillouin scattering” J. Opt. Soc. Am. B 16, 155–163 (1999).
    [Crossref]

2007 (2)

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, 414–419 (2007).
[Crossref]

S. Randoux, N. Y. Joly, G. Mélin, A. Fleureau, L. Galkovsky, S. Lempereur, and P. Suret, “Grating-free Raman laser using highly nonlinear photonic crystal fiber” Opt. Express 15, 16035–16043 (2007).
[Crossref] [PubMed]

2006 (1)

S. Randoux, A. Doutté, and P. Suret, “Polarization-resolved analysis of the characteristics of a Raman laser made with a polarization maintaining fiber,” Opt. Commun. 260, 232–241 (2006).
[Crossref]

2005 (3)

2004 (3)

2003 (3)

A. Doutté, P. Suret, and S. Randoux, “Influence of light polarization on dynamics of continuous-wave-pumped Raman fiber lasers,” Opt. Lett. 28, 2464–2466 (2003).
[Crossref]

Y. Han, C. Kim, J. I. Kang, U. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period gratings,” IEEE. Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

S. Cierullies, H. Renner, and E. Brinkmeyer, “Numerical optimization of multi-wavelength and cascaded Raman fiber lasers,” Opt. Commun. 217, 233–238 (2003).
[Crossref]

2001 (2)

M. D. Mermelstein, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. Eggleton, “Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening,” IEEE. Photon. Technol. Lett. 13, 1286–1288 (2001).
[Crossref]

S. D. Jackson and P. H. Muir “Theory and numerical simulation of nth-order cascaded Raman fiber lasers,” J. Opt. Soc. Am. B 18, 1297–1306 (2001).
[Crossref]

2000 (3)

E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, “Three-cascaded 1407-nm Raman laser based on phosphorus-doped silica fiber,” Opt. Lett. 25, 402–404 (2000).
[Crossref]

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical Modeling and Optimization of Cascaded CW Raman Fiber Lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000).
[Crossref]

I. A. Bufetov and E. M. Dianov, “A simple analytic model of a cw multicascade fibre Raman laser,” Quantum Electron. 30, 873–877 (2000).
[Crossref]

1999 (1)

1995 (1)

S. Randoux, V. Lecoeuche, B. Ségard, and J. Zemmouri, “Dynamical behavior of a Brillouin fiber ring laser emitting two Stokes components” Phys. Rev. A 52, 2327–2334 (1995).
[Crossref] [PubMed]

Babin, S. A.

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, “Relative Intensity Noise in Cascaded Raman Fiber Lasers,” IEEE Photon. Technol. Lett. 17, 2553–2555 (2005).
[Crossref]

Babin, V.

Bayart, D.

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, 2601–2603 (2004).
[Crossref]

Borne, S.

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, 2601–2603 (2004).
[Crossref]

Bouteiller, J.-C.

M. D. Mermelstein, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. Eggleton, “Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening,” IEEE. Photon. Technol. Lett. 13, 1286–1288 (2001).
[Crossref]

Brinkmeyer, E.

S. Cierullies, H. Renner, and E. Brinkmeyer, “Numerical optimization of multi-wavelength and cascaded Raman fiber lasers,” Opt. Commun. 217, 233–238 (2003).
[Crossref]

Bubnov, M. M.

Bufetov, I. A.

Burgoyne, B.

Cai, Z.

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, 414–419 (2007).
[Crossref]

Castella, F.

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, 2601–2603 (2004).
[Crossref]

Chartier, P.

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, 2601–2603 (2004).
[Crossref]

Chung, Y.

Y. Han, C. Kim, J. I. Kang, U. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period gratings,” IEEE. Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

Churkin, D. V.

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, “Relative Intensity Noise in Cascaded Raman Fiber Lasers,” IEEE Photon. Technol. Lett. 17, 2553–2555 (2005).
[Crossref]

Cierullies, S.

S. Cierullies, H. Renner, and E. Brinkmeyer, “Numerical optimization of multi-wavelength and cascaded Raman fiber lasers,” Opt. Commun. 217, 233–238 (2003).
[Crossref]

Cristiani, I.

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical Modeling and Optimization of Cascaded CW Raman Fiber Lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000).
[Crossref]

Damzen, M. J.

Degiorgio, V.

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical Modeling and Optimization of Cascaded CW Raman Fiber Lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000).
[Crossref]

Dianov, E. M.

Doutté, A.

Eggleton, B.

M. D. Mermelstein, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. Eggleton, “Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening,” IEEE. Photon. Technol. Lett. 13, 1286–1288 (2001).
[Crossref]

Faou, E.

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, 2601–2603 (2004).
[Crossref]

Feder, K.

M. D. Mermelstein, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. Eggleton, “Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening,” IEEE. Photon. Technol. Lett. 13, 1286–1288 (2001).
[Crossref]

Fleureau, A.

Fotiadi, A. A.

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, “Relative Intensity Noise in Cascaded Raman Fiber Lasers,” IEEE Photon. Technol. Lett. 17, 2553–2555 (2005).
[Crossref]

Galkovsky, L.

Godbout, N.

Grekov, M. V.

Han, Y.

Y. Han, C. Kim, J. I. Kang, U. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period gratings,” IEEE. Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

Horn, C.

M. D. Mermelstein, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. Eggleton, “Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening,” IEEE. Photon. Technol. Lett. 13, 1286–1288 (2001).
[Crossref]

Huang, C.

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, 414–419 (2007).
[Crossref]

Jackson, S. D.

Joly, N. Y.

Kablukov, S. I.

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, “Relative Intensity Noise in Cascaded Raman Fiber Lasers,” IEEE Photon. Technol. Lett. 17, 2553–2555 (2005).
[Crossref]

Kang, J. I.

Y. Han, C. Kim, J. I. Kang, U. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period gratings,” IEEE. Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

Kim, C.

Y. Han, C. Kim, J. I. Kang, U. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period gratings,” IEEE. Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

Lacroix, S.

Lecoeuche, V.

S. Randoux, V. Lecoeuche, B. Ségard, and J. Zemmouri, “Dynamical behavior of a Brillouin fiber ring laser emitting two Stokes components” Phys. Rev. A 52, 2327–2334 (1995).
[Crossref] [PubMed]

Lempereur, S.

Leplingard, F.

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, 2601–2603 (2004).
[Crossref]

Lorcy, L.

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, 2601–2603 (2004).
[Crossref]

Luo, Z.

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, 414–419 (2007).
[Crossref]

Martinelli, C.

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, 2601–2603 (2004).
[Crossref]

Medvedkov, O. I.

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, “Relative Intensity Noise in Cascaded Raman Fiber Lasers,” IEEE Photon. Technol. Lett. 17, 2553–2555 (2005).
[Crossref]

E. M. Dianov, I. A. Bufetov, M. M. Bubnov, M. V. Grekov, S. A. Vasiliev, and O. I. Medvedkov, “Three-cascaded 1407-nm Raman laser based on phosphorus-doped silica fiber,” Opt. Lett. 25, 402–404 (2000).
[Crossref]

Mélin, G.

Mermelstein, M. D.

M. D. Mermelstein, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. Eggleton, “Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening,” IEEE. Photon. Technol. Lett. 13, 1286–1288 (2001).
[Crossref]

Mocofanescu, A.

Muir, P. H.

Paek, U.

Y. Han, C. Kim, J. I. Kang, U. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period gratings,” IEEE. Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

Podivilov, E. V.

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, “Relative Intensity Noise in Cascaded Raman Fiber Lasers,” IEEE Photon. Technol. Lett. 17, 2553–2555 (2005).
[Crossref]

Randoux, S.

Renner, H.

S. Cierullies, H. Renner, and E. Brinkmeyer, “Numerical optimization of multi-wavelength and cascaded Raman fiber lasers,” Opt. Commun. 217, 233–238 (2003).
[Crossref]

Rini, M.

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical Modeling and Optimization of Cascaded CW Raman Fiber Lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000).
[Crossref]

Ségard, B.

S. Randoux, V. Lecoeuche, B. Ségard, and J. Zemmouri, “Dynamical behavior of a Brillouin fiber ring laser emitting two Stokes components” Phys. Rev. A 52, 2327–2334 (1995).
[Crossref] [PubMed]

Steinvurzel, P.

M. D. Mermelstein, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. Eggleton, “Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening,” IEEE. Photon. Technol. Lett. 13, 1286–1288 (2001).
[Crossref]

Suret, P.

Vasiliev, S. A.

Vlad, V. I.

Xu, H.

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, 414–419 (2007).
[Crossref]

Ye, C.

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, 414–419 (2007).
[Crossref]

Zemmouri, J.

S. Randoux, V. Lecoeuche, B. Ségard, and J. Zemmouri, “Dynamical behavior of a Brillouin fiber ring laser emitting two Stokes components” Phys. Rev. A 52, 2327–2334 (1995).
[Crossref] [PubMed]

Zhao, Y.

IEEE J. Quantum Electron. (1)

M. Rini, I. Cristiani, and V. Degiorgio, “Numerical Modeling and Optimization of Cascaded CW Raman Fiber Lasers,” IEEE J. Quantum Electron. 36, 1117–1122 (2000).
[Crossref]

IEEE Photon. Technol. Lett. (2)

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, 2601–2603 (2004).
[Crossref]

S. A. Babin, D. V. Churkin, A. A. Fotiadi, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov, “Relative Intensity Noise in Cascaded Raman Fiber Lasers,” IEEE Photon. Technol. Lett. 17, 2553–2555 (2005).
[Crossref]

IEEE. Photon. Technol. Lett. (2)

M. D. Mermelstein, J.-C. Bouteiller, P. Steinvurzel, C. Horn, K. Feder, and B. Eggleton, “Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening,” IEEE. Photon. Technol. Lett. 13, 1286–1288 (2001).
[Crossref]

Y. Han, C. Kim, J. I. Kang, U. Paek, and Y. Chung, “Multiwavelength Raman fiber-ring laser based on tunable cascaded long-period gratings,” IEEE. Photon. Technol. Lett. 15, 383–385 (2003).
[Crossref]

J. Opt. Soc. Am. B (3)

Opt. Commun. (3)

S. Randoux, A. Doutté, and P. Suret, “Polarization-resolved analysis of the characteristics of a Raman laser made with a polarization maintaining fiber,” Opt. Commun. 260, 232–241 (2006).
[Crossref]

S. Cierullies, H. Renner, and E. Brinkmeyer, “Numerical optimization of multi-wavelength and cascaded Raman fiber lasers,” Opt. Commun. 217, 233–238 (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, 414–419 (2007).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. A (1)

S. Randoux, V. Lecoeuche, B. Ségard, and J. Zemmouri, “Dynamical behavior of a Brillouin fiber ring laser emitting two Stokes components” Phys. Rev. A 52, 2327–2334 (1995).
[Crossref] [PubMed]

Quantum Electron. (1)

I. A. Bufetov and E. M. Dianov, “A simple analytic model of a cw multicascade fibre Raman laser,” Quantum Electron. 30, 873–877 (2000).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Schematic representation of the experimental setup.
Fig. 2.
Fig. 2. Characteristics of the linearly-polarized grating-free RFL.
Fig. 3.
Fig. 3. Self-oscillations experimentally recorded at input pump powers Pinc ∼ 3 W: (a)-(c) and ∼ 3.5 W: (d)-(f). Time evolution of the optical power of second-order Stokes wave:(a),(d). Time evolution of the optical power of first-order Stokes wave:(b),(e). Time evolution of the optical power of transmitted pump wave:(c)-(f).
Fig. 4.
Fig. 4. Numerical simulations : Self-oscillations numerically computed from integration of Eqs. (1)-(8) at incident pump powers Pinc = 2.5 W: (a)–(c) and Pinc = 2.75 W: (d)–(f). Time evolution of the optical power of second-order Stokes wave:(a),(d). Time evolution of the optical power of first-order Stokes wave:(b),(e). Time evolution of the optical power of transmitted pump wave: (c)–(f). Parameters used in numerical simulations are: αp = 2.21 km-1, α 1 = 2.12 km-1, α 2 = 2.03 km-1, GR 1 = 41.9 km-1W-1, GR2 = 37.8 km-1W-1 (i.e.αp = 9.6 dB km-1, α 1 = 9.2 dB km-1, α 2 = 8.8 dB km-1, GR 1 = 184 dB km-1W-1, GR 2 = 164. dB km-1W-1) , R = 0.03, L = 220 m, λp = 1064 nm, λ 1 = 1118 nm and λ 2 = 1177 nm.
Fig. 5.
Fig. 5. Numerical simulations : Laser characteristics numerically computed from integration of Eqs. (1)-(8) with parameters identical to those given in the caption of Fig. 4.
Fig. 6.
Fig. 6. Typical optical spectrum recorded at the output of the grating-free RFL for input pump powers ranging between ∼ 2 W and ∼ 4 W.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

P z + n c P t = α p P G R 1 λ 1 λ p ( F 1 + B 1 ) P ,
F 1 z + n c F 1 t = α 1 F 1 + G R 1 PF 1 G R 2 λ 2 λ 2 ( F 2 + B 2 ) F 1 ,
B 1 z + n c B 1 t = α 1 B 1 + G R 1 PB 1 G R 2 λ 2 λ 1 ( F 2 + B 2 ) B 2 ,
F 2 z + n c F 2 t = α 2 F 2 + G R 2 ( F 1 + B 1 ) F 2 ,
B 2 z + n c B 2 t = α 2 B 2 + G R 2 ( F 1 + B 1 ) B 2 .
P ( z = 0 , t ) = P inc
F i ( z = 0 , t ) = R in , i B i ( z = 0 , t )
B i ( z = L , t ) = R out , i F i ( z = L , t )

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