Abstract

We experimentally studied the threshold power for stimulated Brillouin scattering (SBS) in multimode optical fibers as a function of input beam product (a measure of the beam quality), using a Q-switched Nd:YAG laser producing short pulses with a coherence length of at least 8 m. Numerical simulations of the dependence of this threshold on pulse duration were performed to extrapolate the experimental data to the continuous-wave (CW) case. The CW SBS threshold was found to increase with increased beam product (decreased beam quality), with a threshold value of 1 kW, for example, for a beam product of 2.5 mm mrad at the input of a 100-μm core-diameter, 10-m-long fiber. When we compared our measured results with published data for SBS in single-mode fibers recalculated to our core diameter, we found that our CW SBS power threshold values were two to four times higher. Using further numerical simulations, we extrapolated the SBS threshold for the long coherence length to the case of a short coherence length (of the order of centimeters) as in a high-power CW Nd:YAG laser for material processing.

© 2003 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  2. H. J. Eichler, J. Kunde, and B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (2000).
    [CrossRef]
  3. V. Sturm, R. Sattmann, and R. Noll, “Optical fiber transmission of multiple Q-switch Nd: YAG laser pulses with microsecond interpulse separations,” Appl. Phys. B 63, 363–370 (1996).
  4. R. M. Shelby and M. D. Levenson, “Resolved forward Brillouin scattering in optical fibers,” Phys. Rev. Lett. 54, 939–942 (1984).
    [CrossRef]
  5. 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]
  6. C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW cw thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
    [CrossRef]
  7. E. C. Honea, R. J. Beach, S. C. Mitchell, J. A. Skidmore, M. A. Emanuel, S. B. Sutton, S. A. Payne, P. V. Avizonis, R. S. Monroe, and D. G. Harris, “High-power dual-rod Yb:YAG laser,” Opt. Lett. 25, 805–807 (2000).
    [CrossRef]
  8. C.-L. Chen, Elements of Optoelectronics and Fiber Optics (Irwin, Chicago, Ill. 1996).
  9. R. W. Boyd and K. Rzażewski, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
    [CrossRef] [PubMed]
  10. K. Ogusu, “Effect of stimulated Brillouin scattering on nonlinear pulse propagation in fiber Bragg gratings,” J. Opt. Soc. Am. B 17, 769–774 (2000).
    [CrossRef]

2000

H. J. Eichler, J. Kunde, and B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (2000).
[CrossRef]

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW cw thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[CrossRef]

K. Ogusu, “Effect of stimulated Brillouin scattering on nonlinear pulse propagation in fiber Bragg gratings,” J. Opt. Soc. Am. B 17, 769–774 (2000).
[CrossRef]

E. C. Honea, R. J. Beach, S. C. Mitchell, J. A. Skidmore, M. A. Emanuel, S. B. Sutton, S. A. Payne, P. V. Avizonis, R. S. Monroe, and D. G. Harris, “High-power dual-rod Yb:YAG laser,” Opt. Lett. 25, 805–807 (2000).
[CrossRef]

1996

V. Sturm, R. Sattmann, and R. Noll, “Optical fiber transmission of multiple Q-switch Nd: YAG laser pulses with microsecond interpulse separations,” Appl. Phys. B 63, 363–370 (1996).

1990

R. W. Boyd and K. Rzażewski, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

1984

R. M. Shelby and M. D. Levenson, “Resolved forward Brillouin scattering in optical fibers,” Phys. Rev. Lett. 54, 939–942 (1984).
[CrossRef]

1972

Avizonis, P. V.

Beach, R. J.

Boyd, R. W.

R. W. Boyd and K. Rzażewski, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

Contag, K.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW cw thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[CrossRef]

Eichler, H. J.

H. J. Eichler, J. Kunde, and B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (2000).
[CrossRef]

Emanuel, M. A.

Giesen, A.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW cw thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[CrossRef]

Harris, D. G.

Honea, E. C.

Hugel, H.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW cw thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[CrossRef]

Kunde, J.

H. J. Eichler, J. Kunde, and B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (2000).
[CrossRef]

Larionov, M.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW cw thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[CrossRef]

Levenson, M. D.

R. M. Shelby and M. D. Levenson, “Resolved forward Brillouin scattering in optical fibers,” Phys. Rev. Lett. 54, 939–942 (1984).
[CrossRef]

Liu, B.

H. J. Eichler, J. Kunde, and B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (2000).
[CrossRef]

Mitchell, S. C.

Monroe, R. S.

Noll, R.

V. Sturm, R. Sattmann, and R. Noll, “Optical fiber transmission of multiple Q-switch Nd: YAG laser pulses with microsecond interpulse separations,” Appl. Phys. B 63, 363–370 (1996).

Ogusu, K.

Payne, S. A.

Rzazewski, K.

R. W. Boyd and K. Rzażewski, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

Sattmann, R.

V. Sturm, R. Sattmann, and R. Noll, “Optical fiber transmission of multiple Q-switch Nd: YAG laser pulses with microsecond interpulse separations,” Appl. Phys. B 63, 363–370 (1996).

Shelby, R. M.

R. M. Shelby and M. D. Levenson, “Resolved forward Brillouin scattering in optical fibers,” Phys. Rev. Lett. 54, 939–942 (1984).
[CrossRef]

Skidmore, J. A.

Smith, R. G.

Stewen, C.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW cw thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[CrossRef]

Sturm, V.

V. Sturm, R. Sattmann, and R. Noll, “Optical fiber transmission of multiple Q-switch Nd: YAG laser pulses with microsecond interpulse separations,” Appl. Phys. B 63, 363–370 (1996).

Sutton, S. B.

Appl. Opt.

Appl. Phys. B

V. Sturm, R. Sattmann, and R. Noll, “Optical fiber transmission of multiple Q-switch Nd: YAG laser pulses with microsecond interpulse separations,” Appl. Phys. B 63, 363–370 (1996).

IEEE J. Sel. Top. Quantum Electron.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW cw thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

H. J. Eichler, J. Kunde, and B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (2000).
[CrossRef]

Opt. Lett.

Phys. Rev. A

R. W. Boyd and K. Rzażewski, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett.

R. M. Shelby and M. D. Levenson, “Resolved forward Brillouin scattering in optical fibers,” Phys. Rev. Lett. 54, 939–942 (1984).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

C.-L. Chen, Elements of Optoelectronics and Fiber Optics (Irwin, Chicago, Ill. 1996).

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Figures (12)

Fig. 1
Fig. 1

ω1 is the beam radius at the focus, and the angle θ can be calculated from the beam radius at the lens, ω2, and from the distance from the lens to the focus, z.

Fig. 2
Fig. 2

Schematic of experimental setup: F, Q-switch filter; BW, Brewster window; NDs, neutral-density filters; BS, beam splitter with splitting ratio 1:10; L1, focusing lens; L2, output lens, D1–D3, optical detectors. Core diameter of the optical fiber 100, 200, or 300 μm. Fiber length, 10 m.

Fig. 3
Fig. 3

Power returned from the fiber and received by detector D3 as a function of time for a 50-ns-long input pulse with a BP of 1.4 mm mrad. (a) Below threshold; input power of 1.1 kW. Note the two peaks from the reflections at the input and output surfaces of the fiber. (b) At the SBS threshold; input power of 1.8 kW. Note the additional peak that is due to SBS between the two end surface reflection peaks. (c) Far above SBS threshold; input power of 3.8-kW. The power scale is the same for all three figures, normalized to the peak power of the reflection from the input surface in (a).

Fig. 4
Fig. 4

SBS threshold power as a function of input BP for a 10-m-long, 100-μm core-diameter fiber. Pulse durations are 19–26 ns (circles) and 48–58 ns (crosses). The CW SBS threshold power for a single-mode fiber, according to Refs. 1 and 5, recalculated to fiber diameter 100 μm is marked by an asterisk (lower left), where the BP is at its theoretical minimum of λ/π.

Fig. 5
Fig. 5

SBS threshold power as a function of input BP for three 10-m-long fibers with core diameters 100 μm (circles), 200 μm (diamonds), and 300 μm (triangles). The pulse duration for all points was 19–26 ns.

Fig. 6
Fig. 6

SBS threshold power as a function of pulse duration for three 10-m-long fibers of core diameters 100 μm (circles), 200 μm (diamonds), and 300 μm (triangles). The input beam product was approximately 1.1 mm mrad for all points; it was 1.0 mm mrad for the shorter pulses and 1.2 mm mrad for the longer pulses.

Fig. 7
Fig. 7

Simulation of SBS threshold power dependence on pulse duration, under the assumption that all power is confined to the fundamental mode, scaled to a fiber diameter of 100 μm. The threshold power is normalized to the CW value of Refs. 1 and 5. Infinite coherence length was assumed. Arrow, time of flight for an optical pulse through a 10-m fiber, for comparison.

Fig. 8
Fig. 8

SBS threshold power as a function of input BP for a 100-μm core-diameter fiber, from Fig. 4, adjusted to the CW case using the same pulse-duration dependence from the simulations in Fig. 7. The pulse durations of the original data were 19–26 ns (circles) and 48–58 ns (crosses). The asterisk (lower left) marks the CW published data.1,5

Fig. 9
Fig. 9

BP at the output end of the fiber as a function of input BP for three 10-m long fibers, of core diameters 100 μm (circles), 200 μm (diamonds), and 300 μm (triangles). The pulse duration here was 19–26 ns. All measurements were taken below SBS threshold.  

Fig. 10
Fig. 10

Output radiance from the fiber at SBS threshold as a function of input BP for three 10-m-long fibers, of core diameters 100 μm (circles), 200 μm (diamonds), and 300 μm (triangles). The pulse duration here was 19–26 ns. The points represent averages of three measurements.

Fig. 11
Fig. 11

Simulation of SBS threshold power dependence on coherence length. Threshold Pth is normalized to that for an infinite coherence length and coherence length Lcoh is normalized to the fiber length. It is assumed here that all power is confined to the fundamental mode, scaled to a fiber diameter of 100 μm.  

Fig. 12
Fig. 12

Numerically simulated reflectivity as a function of pump power. The value of the initial noise level was chosen such that the threshold would match the threshold for single-mode transmission through the fiber.  

Tables (1)

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Table 1 Values of Physical Parameters Used in the Numerical Simulations

Equations (14)

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BP=ω1θ.
Le=Pπ2(BPout)2,
zup+1v tup=-gBeusρ+iκ(|up|2+2|us|2)up-Γup,
zus-1v tus=-gBeupρ*-iκ(|us|2+2|up|2)us+Γus
τAtρ=-ρ+upus*+ρ0,
gBe=τAg1g2=n04η0 gB,
g1=πn03p122λ0ρav,
g2=πn05p120λ0vA,
t¯u¯p=-z¯u¯p-gu¯sρ¯+iκ¯(|u¯p|2+2|u¯s|2)u¯p-γu¯p,
t¯u¯s=z¯u¯s+gu¯pρ¯*+iκ¯(|u¯s|2+2|u¯p|2)u¯s-γu¯s,
t¯ρ¯=-Ωρ¯+u¯pu¯s*+Ωρ¯(z¯, 0),
t¯u¯p+z¯u¯p=0,z¯=0,
t¯u¯s-z¯u¯s=0,z¯=L¯,
f(t¯)=U04 {1+tanh[α(t¯-t¯0)]}×{1-tanh[α(t¯-3t¯0-t¯p)]},

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