Abstract

A new method for describing the Stimulated Brillouin Scattering (SBS) generated in a fiber ring resonator in dynamic regime is presented. Neglecting the time derivatives of the fields amplitudes, our modeling method describes the lasers steady-state operations as well as their transient characteristics or pulsed emission. The developed approach has shown a very good agreement between the theoretical predictions given by the SBS model and the experimental results.

© 2012 OSA

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  1. A. A. Fotiadi and P. Mégret, “Self-Q-switched Er-Brillouin fiber source with extra-cavity generation of a raman supercontinuum in a dispersion shifted fiber,” Opt. Lett. 31, 1621–1623 (2006).
    [CrossRef] [PubMed]
  2. Z. Pan, L. Meng, Q. Ye, H. Cai, Z. Fang, and R. Qu, “Repetition rate stabilization of the SBS Q-switched fiber laser by external injection,” Opt. Express 17, 3124–3129 (2009).
    [CrossRef] [PubMed]
  3. L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65–70 (1998).
    [CrossRef]
  4. Z. Ou, J. Li, L. Zhang, Z. Dai, and Y. Liu, “An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient,” Opt. Commun. 282, 3812–3816 (2009).
    [CrossRef]
  5. 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]
  6. I. Velchev and W. Ubachs, “Statistical properties of the Stokes signal in stimulated Brillouin scattering pulse compressors,” Phys. Rev. A 71, 043810–043814 (2005).
    [CrossRef]
  7. H. Li and K. Ogusu, “Instability of stimulated brillouin scattering in a fiber ring resonator,” Opt. Rev. 7, 303–308 (2000).
    [CrossRef]
  8. A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
    [CrossRef] [PubMed]
  9. S. Le Floch and P. Cambon, “Theoretical evaluation of the Brillouin threshold and the steady-state Brillouin equations in standard single-mode optical fibers,” J. Opt. Soc. Am. A 20, 1132–1137 (2003).
    [CrossRef]
  10. N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42, 1144–1156 (2006).
    [CrossRef]
  11. I. Velchev, D. Neshev, W. Hogervorst, and W. Ubachs, “Pulse compression to the subphonon lifetime region by half-cycle gain in transient stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1812–1816 (1999).
    [CrossRef]
  12. L. F. Stokes, M. Chodorow, and H. J. Shaw, “All-single-mode fiber resonator,” Opt. Lett. 7, 288–290 (1982).
    [CrossRef] [PubMed]
  13. F. E. Seraji, “Steady-state performance analysis of fiber-optic ring resonator,” Prog. Quantum. Electron. 33, 1–16 (2009).
    [CrossRef]
  14. A. Debut, S. Randoux, and J. Zemmouri, “Experimental and theoretical study of linewidth narrowing in Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 18, 556–567 (2001).
    [CrossRef]
  15. V. V. Spirin, C. A. López, P. Mégret, and A. A. Fotiadi, “Single-mode Brillouin fiber laser passively stabilized at resonance frequency with self-injection locked pump laser,“ Laser Phys. Lett. (to be published), 1–4 (2012).

2012

V. V. Spirin, C. A. López, P. Mégret, and A. A. Fotiadi, “Single-mode Brillouin fiber laser passively stabilized at resonance frequency with self-injection locked pump laser,“ Laser Phys. Lett. (to be published), 1–4 (2012).

2009

Z. Pan, L. Meng, Q. Ye, H. Cai, Z. Fang, and R. Qu, “Repetition rate stabilization of the SBS Q-switched fiber laser by external injection,” Opt. Express 17, 3124–3129 (2009).
[CrossRef] [PubMed]

Z. Ou, J. Li, L. Zhang, Z. Dai, and Y. Liu, “An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient,” Opt. Commun. 282, 3812–3816 (2009).
[CrossRef]

F. E. Seraji, “Steady-state performance analysis of fiber-optic ring resonator,” Prog. Quantum. Electron. 33, 1–16 (2009).
[CrossRef]

2006

N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42, 1144–1156 (2006).
[CrossRef]

A. A. Fotiadi and P. Mégret, “Self-Q-switched Er-Brillouin fiber source with extra-cavity generation of a raman supercontinuum in a dispersion shifted fiber,” Opt. Lett. 31, 1621–1623 (2006).
[CrossRef] [PubMed]

2005

I. Velchev and W. Ubachs, “Statistical properties of the Stokes signal in stimulated Brillouin scattering pulse compressors,” Phys. Rev. A 71, 043810–043814 (2005).
[CrossRef]

2003

2001

2000

H. Li and K. Ogusu, “Instability of stimulated brillouin scattering in a fiber ring resonator,” Opt. Rev. 7, 303–308 (2000).
[CrossRef]

1999

I. Velchev, D. Neshev, W. Hogervorst, and W. Ubachs, “Pulse compression to the subphonon lifetime region by half-cycle gain in transient stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1812–1816 (1999).
[CrossRef]

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]

1998

L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65–70 (1998).
[CrossRef]

1991

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef] [PubMed]

1982

Babin, V.

Bao, X.

L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65–70 (1998).
[CrossRef]

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef] [PubMed]

Cai, H.

Cambon, P.

Chen, L.

L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65–70 (1998).
[CrossRef]

Chodorow, M.

Dai, Z.

Z. Ou, J. Li, L. Zhang, Z. Dai, and Y. Liu, “An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient,” Opt. Commun. 282, 3812–3816 (2009).
[CrossRef]

Damzen, M. J.

Debaes, C.

N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42, 1144–1156 (2006).
[CrossRef]

Debut, A.

Fang, Z.

Fotiadi, A. A.

V. V. Spirin, C. A. López, P. Mégret, and A. A. Fotiadi, “Single-mode Brillouin fiber laser passively stabilized at resonance frequency with self-injection locked pump laser,“ Laser Phys. Lett. (to be published), 1–4 (2012).

N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42, 1144–1156 (2006).
[CrossRef]

A. A. Fotiadi and P. Mégret, “Self-Q-switched Er-Brillouin fiber source with extra-cavity generation of a raman supercontinuum in a dispersion shifted fiber,” Opt. Lett. 31, 1621–1623 (2006).
[CrossRef] [PubMed]

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef] [PubMed]

Hogervorst, W.

I. Velchev, D. Neshev, W. Hogervorst, and W. Ubachs, “Pulse compression to the subphonon lifetime region by half-cycle gain in transient stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1812–1816 (1999).
[CrossRef]

Le Floch, S.

Li, H.

H. Li and K. Ogusu, “Instability of stimulated brillouin scattering in a fiber ring resonator,” Opt. Rev. 7, 303–308 (2000).
[CrossRef]

Li, J.

Z. Ou, J. Li, L. Zhang, Z. Dai, and Y. Liu, “An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient,” Opt. Commun. 282, 3812–3816 (2009).
[CrossRef]

Liu, Y.

Z. Ou, J. Li, L. Zhang, Z. Dai, and Y. Liu, “An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient,” Opt. Commun. 282, 3812–3816 (2009).
[CrossRef]

López, C. A.

V. V. Spirin, C. A. López, P. Mégret, and A. A. Fotiadi, “Single-mode Brillouin fiber laser passively stabilized at resonance frequency with self-injection locked pump laser,“ Laser Phys. Lett. (to be published), 1–4 (2012).

Mégret, P.

V. V. Spirin, C. A. López, P. Mégret, and A. A. Fotiadi, “Single-mode Brillouin fiber laser passively stabilized at resonance frequency with self-injection locked pump laser,“ Laser Phys. Lett. (to be published), 1–4 (2012).

A. A. Fotiadi and P. Mégret, “Self-Q-switched Er-Brillouin fiber source with extra-cavity generation of a raman supercontinuum in a dispersion shifted fiber,” Opt. Lett. 31, 1621–1623 (2006).
[CrossRef] [PubMed]

Meng, L.

Mocofanescu, A.

Neshev, D.

I. Velchev, D. Neshev, W. Hogervorst, and W. Ubachs, “Pulse compression to the subphonon lifetime region by half-cycle gain in transient stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1812–1816 (1999).
[CrossRef]

Ogusu, K.

H. Li and K. Ogusu, “Instability of stimulated brillouin scattering in a fiber ring resonator,” Opt. Rev. 7, 303–308 (2000).
[CrossRef]

Ou, Z.

Z. Ou, J. Li, L. Zhang, Z. Dai, and Y. Liu, “An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient,” Opt. Commun. 282, 3812–3816 (2009).
[CrossRef]

Pan, Z.

Panajotov, K.

N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42, 1144–1156 (2006).
[CrossRef]

Qu, R.

Randoux, S.

Seraji, F. E.

F. E. Seraji, “Steady-state performance analysis of fiber-optic ring resonator,” Prog. Quantum. Electron. 33, 1–16 (2009).
[CrossRef]

Shaw, H. J.

Spirin, V. V.

V. V. Spirin, C. A. López, P. Mégret, and A. A. Fotiadi, “Single-mode Brillouin fiber laser passively stabilized at resonance frequency with self-injection locked pump laser,“ Laser Phys. Lett. (to be published), 1–4 (2012).

Stokes, L. F.

Thienpont, H.

N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42, 1144–1156 (2006).
[CrossRef]

Ubachs, W.

I. Velchev and W. Ubachs, “Statistical properties of the Stokes signal in stimulated Brillouin scattering pulse compressors,” Phys. Rev. A 71, 043810–043814 (2005).
[CrossRef]

I. Velchev, D. Neshev, W. Hogervorst, and W. Ubachs, “Pulse compression to the subphonon lifetime region by half-cycle gain in transient stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1812–1816 (1999).
[CrossRef]

Velchev, I.

I. Velchev and W. Ubachs, “Statistical properties of the Stokes signal in stimulated Brillouin scattering pulse compressors,” Phys. Rev. A 71, 043810–043814 (2005).
[CrossRef]

I. Velchev, D. Neshev, W. Hogervorst, and W. Ubachs, “Pulse compression to the subphonon lifetime region by half-cycle gain in transient stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1812–1816 (1999).
[CrossRef]

Vermeulen, N.

N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42, 1144–1156 (2006).
[CrossRef]

Vlad, V. I.

Ye, Q.

Zemmouri, J.

Zhang, L.

Z. Ou, J. Li, L. Zhang, Z. Dai, and Y. Liu, “An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient,” Opt. Commun. 282, 3812–3816 (2009).
[CrossRef]

IEEE J. Quantum Electron.

N. Vermeulen, C. Debaes, A. A. Fotiadi, K. Panajotov, and H. Thienpont, “Stokes-anti-Stokes iterative resonator method for modeling Raman lasers,” IEEE J. Quantum Electron. 42, 1144–1156 (2006).
[CrossRef]

I. Velchev, D. Neshev, W. Hogervorst, and W. Ubachs, “Pulse compression to the subphonon lifetime region by half-cycle gain in transient stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1812–1816 (1999).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Laser Phys. Lett.

V. V. Spirin, C. A. López, P. Mégret, and A. A. Fotiadi, “Single-mode Brillouin fiber laser passively stabilized at resonance frequency with self-injection locked pump laser,“ Laser Phys. Lett. (to be published), 1–4 (2012).

Opt. Commun.

L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152, 65–70 (1998).
[CrossRef]

Z. Ou, J. Li, L. Zhang, Z. Dai, and Y. Liu, “An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient,” Opt. Commun. 282, 3812–3816 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Rev.

H. Li and K. Ogusu, “Instability of stimulated brillouin scattering in a fiber ring resonator,” Opt. Rev. 7, 303–308 (2000).
[CrossRef]

Phys. Rev. A

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef] [PubMed]

I. Velchev and W. Ubachs, “Statistical properties of the Stokes signal in stimulated Brillouin scattering pulse compressors,” Phys. Rev. A 71, 043810–043814 (2005).
[CrossRef]

Prog. Quantum. Electron.

F. E. Seraji, “Steady-state performance analysis of fiber-optic ring resonator,” Prog. Quantum. Electron. 33, 1–16 (2009).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic representation of pulsed pumping Brillouin fiber ring laser with a zoom on the time evolution of the incident field Ein(t). (b) Schematic representation of the integration method with Δz the integration step.

Fig. 2
Fig. 2

Experimental setup of the Brillouin fiber ring laser with all the fiber components with polarization maintaining (PM).

Fig. 3
Fig. 3

(a) Experimental results. (b) Simulation results obtained on the resonance conditions Δϕp = 0. Transmitted signals (black) and SBS signals (red).

Equations (9)

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E p z + n c E p t = α 2 E p + i γ ω p 4 ρ 0 n c ρ E s , E s z n c E s t = α 2 E s i γ ω s 4 ρ 0 n c ρ * E p , ρ t + Γ 2 ρ = i γ q 2 16 π Ω E p E s * + f ,
ρ ( z ) = 2 Γ ( i γ q 2 16 π Ω E p ( z ) E s ( z ) * + f ( z ) ) .
d E p ( z ) d z = α 2 E p ( z ) g E | E s ( z ) | 2 E p ( z ) + i b E s ( z ) f ( z ) , d E s ( z ) d z = α 2 E s ( z ) g E | E p ( z ) | 2 E s ( z ) i b E p ( z ) f * ( z ) ,
d E p ( m ) ( z ) d z = α 2 E p ( m ) ( z ) g E | E s ( m ) ( z ) | 2 E p ( m ) ( z ) b E s ( m ) ( z ) f ( z ) , d E p ( m ) ( z ) d z = α 2 E p ( m ) ( z ) g E | E s ( m ) ( z ) | 2 E p ( m ) ( z ) + b E s ( m ) ( z ) f ( z ) ,
E p ( m ) ( 0 ) = i 1 κ E in ( m t r ) + κ E p ( m 1 ) ( L ) e i Δ ϕ p ,
d E s ( m ) ( z ) d z = α 2 E s ( m ) ( z ) + g E | E p ( m ) ( z ) | 2 E s ( m ) ( z ) b E p ( m ) ( z ) f * ( z ) , d E s ( m ) ( z ) d z = α 2 E s ( m ) ( z ) + g E | E p ( m ) ( z ) | 2 E s ( m ) ( z ) + b E p ( m ) ( z ) f * ( z ) ,
E s ( m ) ( 0 ) = κ E s ( m 1 ) ( L ) e i Δ ϕ s ,
E p out ( m t r ) = κ E in ( m t r ) + i 1 κ E p ( L , m t r ) e i Δ ϕ p ,
E s out ( m t r ) = i 1 κ E s ( 0 , m t r ) e i Δ ϕ s .

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