Abstract

We theoretically analyze a high-efficiency single-frequency Brillouin all-fiber ring laser at 1.5 µm wavelength, taking pump depletion into account. The output pump and Stokes intensities are calculated as functions of the cavity coupling coefficient and of the input pump intensity. Lasing threshold and pump-to-Stokes conversion efficiency are predicted. Furthermore, we demonstrate good agreement between model results and measurements. Applications to the improvement of optoelectronic links for radio-frequency signals by use of stimulated Brillouin scattering fiber lasers are also presented.

© 2004 Optical Society of America

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References

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  1. D. Cotter, “Stimulated Brillouin scattering in monomode optical fiber,” J. Opt. Commun. 4, 10–19 (1983).
    [CrossRef]
  2. L. F. Stokes, M. Chodorow, and H. J. Shaw, “All-fiber stimulated Brillouin ring laser with submilliwatt pump threshold,” Opt. Lett. 7, 509–511 (1982).
    [CrossRef] [PubMed]
  3. P. Bayvel and I. P. Giles, “Evaluation of performance parameters of single-mode all-fiber Brillouin ring laser,” Opt. Lett. 14, 581–583 (1989).
    [CrossRef] [PubMed]
  4. F. Zarinetchi, S. P. Smith, and S. Ezekiel, “Stimulated Brillouin fiber-optic laser gyroscope,” Opt. Lett. 16, 229–231 (1991).
    [CrossRef] [PubMed]
  5. N. A. Olsson and J. P. Van Der Ziel, “Characteristics of a semiconductor laser pumped Brillouin amplifier with electronically controlled bandwidth,” J. Lightwave Technol. LT-5, 147–153 (1987).
    [CrossRef]
  6. R. W. Tkach and A. R. Chraplyvy, “Fiber Brillouin amplifier,” Opt. Quantum Electron. 21, S105–S112 (1989).
    [CrossRef]
  7. A. Küng, P. A. Nicati, and Ph. A. Robert, “Reciprocal and quasi-reciprocal Brillouin fiber-optic current sensors,” IEEE Photonics Technol. Lett. 8, 1680–1682 (1996).
    [CrossRef]
  8. K. J. Williams and R. D. Esman, “Stimulated Brillouin scattering for improvement of microwave fiber-optic link efficiency,” Electron. Lett. 30, 1965–1966 (1994).
    [CrossRef]
  9. A. Loayssa, D. Benito, and M. J. Garde, “Optical carrier-suppression technique with a Brillouin-erbium fiber laser,” Opt. Lett. 25, 197–199 (2000).
    [CrossRef]
  10. S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, “Stimulated Brillouin scattering for microwave signal modulation depth increase in optical links,” Electron. Lett. 36, 944–946 (2000).
    [CrossRef]
  11. T. Tanemura, Y. Takushima, and K. Kikuchi, “Narrowband optical filter, with a variable transmission spectrum, using stimulated Brillouin scattering in optical fiber,” Opt. Lett. 27, 1552–1554 (2002).
    [CrossRef]
  12. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).
  13. S. Norcia, S. Tonda-Goldstein, R. Frey, D. Dolfi, and J.-P. Huignard, “Efficient single-mode Brillouin fiber laser for low noise optical carrier reduction of microwave signals,” Opt. Lett. 28, 1888–1890 (2003).
    [CrossRef] [PubMed]
  14. L. F. Stokes, M. Chodorow, and H. J. Shaw, “All-single-mode fiber resonator,” Opt. Lett. 7, 288–290 (1982).
    [CrossRef] [PubMed]
  15. C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945–2955 (1966).
    [CrossRef]
  16. S. Tonda-Goldstein, S. Norcia, D. Dolfi, and J.-P. Huignard, “40 dB dynamic enhancement of modulation depth for optically carried microwave signals,” Electron. Lett. 39, 790–792 (2003).
    [CrossRef]
  17. 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]
  18. L. Stépien, S. Randoux, and J. Zemmouri, “Intensity noise in Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 19, 1055–1066 (2002).
    [CrossRef]

2003 (2)

S. Tonda-Goldstein, S. Norcia, D. Dolfi, and J.-P. Huignard, “40 dB dynamic enhancement of modulation depth for optically carried microwave signals,” Electron. Lett. 39, 790–792 (2003).
[CrossRef]

S. Norcia, S. Tonda-Goldstein, R. Frey, D. Dolfi, and J.-P. Huignard, “Efficient single-mode Brillouin fiber laser for low noise optical carrier reduction of microwave signals,” Opt. Lett. 28, 1888–1890 (2003).
[CrossRef] [PubMed]

2002 (2)

2001 (1)

2000 (2)

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, “Stimulated Brillouin scattering for microwave signal modulation depth increase in optical links,” Electron. Lett. 36, 944–946 (2000).
[CrossRef]

A. Loayssa, D. Benito, and M. J. Garde, “Optical carrier-suppression technique with a Brillouin-erbium fiber laser,” Opt. Lett. 25, 197–199 (2000).
[CrossRef]

1996 (1)

A. Küng, P. A. Nicati, and Ph. A. Robert, “Reciprocal and quasi-reciprocal Brillouin fiber-optic current sensors,” IEEE Photonics Technol. Lett. 8, 1680–1682 (1996).
[CrossRef]

1994 (1)

K. J. Williams and R. D. Esman, “Stimulated Brillouin scattering for improvement of microwave fiber-optic link efficiency,” Electron. Lett. 30, 1965–1966 (1994).
[CrossRef]

1991 (1)

1989 (2)

1987 (1)

N. A. Olsson and J. P. Van Der Ziel, “Characteristics of a semiconductor laser pumped Brillouin amplifier with electronically controlled bandwidth,” J. Lightwave Technol. LT-5, 147–153 (1987).
[CrossRef]

1983 (1)

D. Cotter, “Stimulated Brillouin scattering in monomode optical fiber,” J. Opt. Commun. 4, 10–19 (1983).
[CrossRef]

1982 (2)

1966 (1)

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945–2955 (1966).
[CrossRef]

Bayvel, P.

Benito, D.

Charlet, G.

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, “Stimulated Brillouin scattering for microwave signal modulation depth increase in optical links,” Electron. Lett. 36, 944–946 (2000).
[CrossRef]

Chazelas, J.

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, “Stimulated Brillouin scattering for microwave signal modulation depth increase in optical links,” Electron. Lett. 36, 944–946 (2000).
[CrossRef]

Chodorow, M.

Chraplyvy, A. R.

R. W. Tkach and A. R. Chraplyvy, “Fiber Brillouin amplifier,” Opt. Quantum Electron. 21, S105–S112 (1989).
[CrossRef]

Cotter, D.

D. Cotter, “Stimulated Brillouin scattering in monomode optical fiber,” J. Opt. Commun. 4, 10–19 (1983).
[CrossRef]

Debut, A.

Dolfi, D.

S. Tonda-Goldstein, S. Norcia, D. Dolfi, and J.-P. Huignard, “40 dB dynamic enhancement of modulation depth for optically carried microwave signals,” Electron. Lett. 39, 790–792 (2003).
[CrossRef]

S. Norcia, S. Tonda-Goldstein, R. Frey, D. Dolfi, and J.-P. Huignard, “Efficient single-mode Brillouin fiber laser for low noise optical carrier reduction of microwave signals,” Opt. Lett. 28, 1888–1890 (2003).
[CrossRef] [PubMed]

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, “Stimulated Brillouin scattering for microwave signal modulation depth increase in optical links,” Electron. Lett. 36, 944–946 (2000).
[CrossRef]

Esman, R. D.

K. J. Williams and R. D. Esman, “Stimulated Brillouin scattering for improvement of microwave fiber-optic link efficiency,” Electron. Lett. 30, 1965–1966 (1994).
[CrossRef]

Ezekiel, S.

Frey, R.

Garde, M. J.

Giles, I. P.

Huignard, J.-P.

S. Norcia, S. Tonda-Goldstein, R. Frey, D. Dolfi, and J.-P. Huignard, “Efficient single-mode Brillouin fiber laser for low noise optical carrier reduction of microwave signals,” Opt. Lett. 28, 1888–1890 (2003).
[CrossRef] [PubMed]

S. Tonda-Goldstein, S. Norcia, D. Dolfi, and J.-P. Huignard, “40 dB dynamic enhancement of modulation depth for optically carried microwave signals,” Electron. Lett. 39, 790–792 (2003).
[CrossRef]

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, “Stimulated Brillouin scattering for microwave signal modulation depth increase in optical links,” Electron. Lett. 36, 944–946 (2000).
[CrossRef]

Kikuchi, K.

Küng, A.

A. Küng, P. A. Nicati, and Ph. A. Robert, “Reciprocal and quasi-reciprocal Brillouin fiber-optic current sensors,” IEEE Photonics Technol. Lett. 8, 1680–1682 (1996).
[CrossRef]

Loayssa, A.

Nicati, P. A.

A. Küng, P. A. Nicati, and Ph. A. Robert, “Reciprocal and quasi-reciprocal Brillouin fiber-optic current sensors,” IEEE Photonics Technol. Lett. 8, 1680–1682 (1996).
[CrossRef]

Norcia, S.

S. Tonda-Goldstein, S. Norcia, D. Dolfi, and J.-P. Huignard, “40 dB dynamic enhancement of modulation depth for optically carried microwave signals,” Electron. Lett. 39, 790–792 (2003).
[CrossRef]

S. Norcia, S. Tonda-Goldstein, R. Frey, D. Dolfi, and J.-P. Huignard, “Efficient single-mode Brillouin fiber laser for low noise optical carrier reduction of microwave signals,” Opt. Lett. 28, 1888–1890 (2003).
[CrossRef] [PubMed]

Olsson, N. A.

N. A. Olsson and J. P. Van Der Ziel, “Characteristics of a semiconductor laser pumped Brillouin amplifier with electronically controlled bandwidth,” J. Lightwave Technol. LT-5, 147–153 (1987).
[CrossRef]

Randoux, S.

Robert, Ph. A.

A. Küng, P. A. Nicati, and Ph. A. Robert, “Reciprocal and quasi-reciprocal Brillouin fiber-optic current sensors,” IEEE Photonics Technol. Lett. 8, 1680–1682 (1996).
[CrossRef]

Shaw, H. J.

Smith, S. P.

Stépien, L.

Stokes, L. F.

Takushima, Y.

Tanemura, T.

Tang, C. L.

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945–2955 (1966).
[CrossRef]

Tkach, R. W.

R. W. Tkach and A. R. Chraplyvy, “Fiber Brillouin amplifier,” Opt. Quantum Electron. 21, S105–S112 (1989).
[CrossRef]

Tonda-Goldstein, S.

S. Norcia, S. Tonda-Goldstein, R. Frey, D. Dolfi, and J.-P. Huignard, “Efficient single-mode Brillouin fiber laser for low noise optical carrier reduction of microwave signals,” Opt. Lett. 28, 1888–1890 (2003).
[CrossRef] [PubMed]

S. Tonda-Goldstein, S. Norcia, D. Dolfi, and J.-P. Huignard, “40 dB dynamic enhancement of modulation depth for optically carried microwave signals,” Electron. Lett. 39, 790–792 (2003).
[CrossRef]

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, “Stimulated Brillouin scattering for microwave signal modulation depth increase in optical links,” Electron. Lett. 36, 944–946 (2000).
[CrossRef]

Van Der Ziel, J. P.

N. A. Olsson and J. P. Van Der Ziel, “Characteristics of a semiconductor laser pumped Brillouin amplifier with electronically controlled bandwidth,” J. Lightwave Technol. LT-5, 147–153 (1987).
[CrossRef]

Williams, K. J.

K. J. Williams and R. D. Esman, “Stimulated Brillouin scattering for improvement of microwave fiber-optic link efficiency,” Electron. Lett. 30, 1965–1966 (1994).
[CrossRef]

Zarinetchi, F.

Zemmouri, J.

Electron. Lett. (3)

S. Tonda-Goldstein, S. Norcia, D. Dolfi, and J.-P. Huignard, “40 dB dynamic enhancement of modulation depth for optically carried microwave signals,” Electron. Lett. 39, 790–792 (2003).
[CrossRef]

K. J. Williams and R. D. Esman, “Stimulated Brillouin scattering for improvement of microwave fiber-optic link efficiency,” Electron. Lett. 30, 1965–1966 (1994).
[CrossRef]

S. Tonda-Goldstein, D. Dolfi, J.-P. Huignard, G. Charlet, and J. Chazelas, “Stimulated Brillouin scattering for microwave signal modulation depth increase in optical links,” Electron. Lett. 36, 944–946 (2000).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

A. Küng, P. A. Nicati, and Ph. A. Robert, “Reciprocal and quasi-reciprocal Brillouin fiber-optic current sensors,” IEEE Photonics Technol. Lett. 8, 1680–1682 (1996).
[CrossRef]

J. Appl. Phys. (1)

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945–2955 (1966).
[CrossRef]

J. Lightwave Technol. (1)

N. A. Olsson and J. P. Van Der Ziel, “Characteristics of a semiconductor laser pumped Brillouin amplifier with electronically controlled bandwidth,” J. Lightwave Technol. LT-5, 147–153 (1987).
[CrossRef]

J. Opt. Commun. (1)

D. Cotter, “Stimulated Brillouin scattering in monomode optical fiber,” J. Opt. Commun. 4, 10–19 (1983).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (7)

Opt. Quantum Electron. (1)

R. W. Tkach and A. R. Chraplyvy, “Fiber Brillouin amplifier,” Opt. Quantum Electron. 21, S105–S112 (1989).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).

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Figures (9)

Fig. 1
Fig. 1

Efficient single-frequency Brillouin fiber laser.

Fig. 2
Fig. 2

Resolution method for determination of (a) np0 and (b) Npt and Nst.

Fig. 3
Fig. 3

Normalized pump and Stokes output power as functions of coupling coefficient R; αcpl and αf, coupler and fiber losses, respectively.

Fig. 4
Fig. 4

Normalized output pump and Stokes power as functions of coupling coefficient R for various input pump powers Pin.

Fig. 5
Fig. 5

Pump-to-Stokes conversion efficiency for αcpl=0.10; and αf=0.12 and (filled circles) for a cavity without losses.

Fig. 6
Fig. 6

Normalized output pump, Stokes, and 2-Stokes (2×Stokes) powers as a function of coupling coefficient R for various input pump powers Pin.

Fig. 7
Fig. 7

Values of coupling coefficient R that correspond to extreme output pump and Stokes powers and to the 2-Stoke threshold as a function of input pump power Pin.

Fig. 8
Fig. 8

Use of the SBS laser for modulation depth enhancement of an optically carried rf signal: MZM, Mach–Zehnder modulator; O.F., optical fiber.

Fig. 9
Fig. 9

rf output power of a SBS laser as a function of modulation frequency fmod.

Equations (20)

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dns(z)dz=-gns(z)np(z)exp(-αz),
dnp(z)dz=-gns(z)np(z)exp(αz).
ns(z)=ns0(np0-ns0)exp[-gz(np0-ns0)]np0-ns0 exp[-gz(np0-ns0)],
np(z)=ns(z)+np0-ns0,
np(0)=dNpi+cnp(L)+2[dcNpinp(L)]1/2,
Npt=aNpi+bnp(L)-2[abNpinp(L)]1/2,
Nst=dns(0),
Ns(L)=cns(0).
np(L)=(np0-dNpi)2c.
ns0=cnp0-(np0-dNpi)2c(1-c)=f(np0).
exp[-gL(np0-ns0)]=cnp0[ns0(c-1)+np0].
G(np0)=H(np0),
G(np0)=exp{-gL[np0-f(np0)]},
H(np0)=cnp0[f(np0)(c-1)+np0].
Nst=d cnp0-(np0-dNpi)2c(1-c),
Npt=[aNpi]1/2-b (np0-dNpi)2c1/22.
dn2s(z)dz=+gn2s(z)ns(z),
c expg0Lns(z)dzL=1.
Pth_SRes{[(1-R)/R]+αcpl+αf}AeffgLeff(1-R)(1-αcpl)×{1+[R(1-αcpl)(1-αf)]2}1/2,
(1-R)(1-αcpl){1-[R(1-αcpl)(1-αf)]2}1/2

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