Abstract

The threshold for second-order stimulated Brillouin scattering (SBS) in a fiber has been investigated; the study was motivated, in part, by the need to determine the operational dynamic range of SBS fiber beam combiners. Theoretical analysis showed that the second-order Stokes threshold is approximately 130 times the first-order threshold. Experimentally, however, the threshold was found to be only 15 times greater. This dramatic reduction in threshold was determined to be due to the generation of second-order Stokes photons through four-wave mixing, which in turn seeds the second-order SBS process. Suppression of internal Fresnel reflection at the front fiber facet can help to restore the threshold to the higher value.

© 2002 Optical Society of America

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References

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  1. B. C. Rodgers, T. H. Russell, and W. B. Roh, “Laser beam combining and cleanup via stimulated Brillouin scattering in a multimode optical fiber,” Opt. Lett. 24, 1124–1126 (1999).
    [CrossRef]
  2. T. H. Russell, W. B. Roh, and J. R. Marciante, “Incoherent beam combining using stimulated Brillouin scattering in multi-mode fibers,” Opt. Express 8, 246–254 (2001), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  3. E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, “Fiber-optic stimulated-Brillouin-scattering amplifier,” Sov. Phys. Tech. Phys. 33, 206–209 (1988).
  4. H. Bruesselbach, “Beam cleanup using stimulated Brillouin scattering in multimode fibers,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 424.
  5. G. P. Agrawal, Nonlinear Fiber Optics, 3 ed. (Academic, San Diego, Calif., 2001), Chap. 10.
  6. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972).
    [CrossRef] [PubMed]
  7. M. O. van Deventer, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12, 585–590 (1994).
    [CrossRef]
  8. S. J. Garth and R. A. Sammut, “Theory of stimulated Raman scattering in two-mode optical fibers,” J. Opt. Soc. Am. B 10, 2040–2047 (1993).
    [CrossRef]
  9. T. H. Russell, “Laser intensity scaling through stimulated scattering in optical fibers,” Ph.D. dissertation (Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, 2001).

2001 (1)

1999 (1)

1994 (1)

M. O. van Deventer, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12, 585–590 (1994).
[CrossRef]

1993 (1)

1988 (1)

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, “Fiber-optic stimulated-Brillouin-scattering amplifier,” Sov. Phys. Tech. Phys. 33, 206–209 (1988).

1972 (1)

Fotiadi, A. A.

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, “Fiber-optic stimulated-Brillouin-scattering amplifier,” Sov. Phys. Tech. Phys. 33, 206–209 (1988).

Garth, S. J.

Kuzin, E. A.

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, “Fiber-optic stimulated-Brillouin-scattering amplifier,” Sov. Phys. Tech. Phys. 33, 206–209 (1988).

Marciante, J. R.

Petrov, M. P.

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, “Fiber-optic stimulated-Brillouin-scattering amplifier,” Sov. Phys. Tech. Phys. 33, 206–209 (1988).

Rodgers, B. C.

Roh, W. B.

Russell, T. H.

Sammut, R. A.

Smith, R. G.

van Deventer, M. O.

M. O. van Deventer, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12, 585–590 (1994).
[CrossRef]

Appl. Opt. (1)

J. Lightwave Technol. (1)

M. O. van Deventer, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12, 585–590 (1994).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Lett. (1)

Sov. Phys. Tech. Phys. (1)

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, “Fiber-optic stimulated-Brillouin-scattering amplifier,” Sov. Phys. Tech. Phys. 33, 206–209 (1988).

Other (3)

H. Bruesselbach, “Beam cleanup using stimulated Brillouin scattering in multimode fibers,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 424.

G. P. Agrawal, Nonlinear Fiber Optics, 3 ed. (Academic, San Diego, Calif., 2001), Chap. 10.

T. H. Russell, “Laser intensity scaling through stimulated scattering in optical fibers,” Ph.D. dissertation (Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, 2001).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the experimental system: LWE, Lightwave Electronics single-frequency laser.

Fig. 2
Fig. 2

Spectrum transmitted through a long fiber above second-order threshold.

Fig. 3
Fig. 3

(a)–(c) Power transmitted through the SMF-28 fiber as a function of input power at pump, Stokes, and second-order Stokes frequencies. Solid curves, best theoretical fits. (d) Reflected first Stokes power as a function of input power.

Fig. 4
Fig. 4

(a)–(c) Power transmitted through the SMF-28 fiber as a function of input power at pump, Stokes, and second-order Stokes frequencies when the front fiber facet was cleaved at an angle. Solid curves, best theoretical fits. (d) Reflected first Stokes power as a function of input power.

Fig. 5
Fig. 5

(a) Relative Stokes power distribution in a fiber for a 20-mW pump beam (solid curve) and for an 800-mW pump beam (dashed curve). (b) Second-order effective length as a function of input power for a 4.4-km fiber.

Equations (10)

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zAp=-gBε0cnAp|As|2+i2ε0n2ωnAsf2 As2*×exp[i(2ksf-ks2)z]-α2Ap,
zAs=-gBε0cnAs|Ap|2+gBε0cnAs2|As|2+α2As,
zAsf=i4ε0n2ωnAsf* ApAs2×exp[i(kp+ks2-ksf)z]-α2Asf,
zAs2=gBε0cnAs2|As|2+i2ε0n2ωnAsf2 Ap*×exp[i(2ksf-kp)z]-α2As2.
zAp=-ηSBSpgBε0cnAp|As|2+iηFWM2ε0n2ωnAsf2As2*-α2Ap,
zAs=-ηSBSsgBε0cnAs|Ap|2+α2As,
zAsf=iηFWM4ε0n2ωnAsf*ApAs2-α2Asf,
zAs2=ηSBS2gBε0cnAs2|As|2+iηFWM2ε0n2ωnAsf2 Ap*-α2As2,
Psth2=21 AeffgB2Leff,
Leff=1Is(0) 0LIs(z)dz.

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