Abstract

The output of high power fiber amplifiers is typically limited by stimulated Brillouin scattering (SBS). An analysis of SBS with a chirped pump laser indicates that a chirp of 2.5 × 1015 Hz/s could raise, by an order of magnitude, the SBS threshold of a 20-m fiber. A diode laser with a constant output power and a linear chirp of 5 × 1015 Hz/s has been previously demonstrated. In a low-power proof-of-concept experiment, the threshold for SBS in a 6-km fiber is increased by a factor of 100 with a chirp of 5 × 1014 Hz/s. A linear chirp will enable straightforward coherent combination of multiple fiber amplifiers, with electronic compensation of path length differences on the order of 0.2 m.

© 2012 OSA

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2011 (2)

C. Robin, I. Dajani, and F. Chiragh, “Experimental studies of segmented acoustically tailored photonic crystal fiber amplifier with 494 W single-frequency output,” Proc. SPIE 7914, 79140B, 79140B-8 (2011).
[CrossRef]

C. G. Carlson, R. B. Ross, J. M. Schafer, J. B. Spring, and B. G. Ward, “Full vectorial analysis of Brillouin gain in random acoustically microstructured photonic crystal fibers,” Phys. Rev. B 83(23), 235110 (2011).
[CrossRef]

2010 (5)

2009 (5)

L. Yingfan, L. Zhiwei, D. Yongkang, and L. Qiang, “Research on stimulated Brillouin scattering suppression based on multi-frequency phase modulation n,” Chin. Opt. Lett. 7, 29–31 (2009).
[CrossRef]

V. Lanticq, S. Jiang, R. Gabet, Y. Jaouën, F. Taillade, G. Moreau, and G. P. Agrawal, “Self-referenced and single-ended method to measure Brillouin gain in monomode optical fibers,” Opt. Lett. 34(7), 1018–1020 (2009).
[CrossRef] [PubMed]

N. Satyan, A. Vasilyev, G. Rakuljic, V. Leyva, and A. Yariv, “Precise control of broadband frequency chirps using optoelectronic feedback,” Opt. Express 17(18), 15991–15999 (2009).
[CrossRef] [PubMed]

S. Gray, D. T. Walton, X. Chen, J. Wang, M.-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[CrossRef]

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers using optical phase-lock loops,” IEEE J. Sel. Top. Quantum Electron. 15(2), 240–247 (2009).
[CrossRef]

2008 (2)

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, and G. Rakuljic, “Tiled-aperture coherent beam combining using optical phase-lock loops,” Electron. Lett. 44(14), 875–876 (2008).
[CrossRef]

N. Satyan, W. Liang, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Phase-controlled apertures using heterodyne optical phase-locked loops,” IEEE Photon. Technol. Lett. 20(11), 897–899 (2008).
[CrossRef]

2007 (1)

2004 (1)

1997 (1)

1995 (1)

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31(8), 668–669 (1995).
[CrossRef]

Aflatouni, F.

N. Satyan, W. Liang, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Phase-controlled apertures using heterodyne optical phase-locked loops,” IEEE Photon. Technol. Lett. 20(11), 897–899 (2008).
[CrossRef]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, G. Rakuljic, F. Aflatouni, H. Hashemi, and J. Ungar, “Coherent power combination of two master-oscillator-power-amplifier (MOPA) semiconductor lasers using optical phase lock loops,” Opt. Express 15(6), 3201–3205 (2007).
[CrossRef] [PubMed]

Agrawal, G. P.

Alic, N.

Andrekson, P. A.

Augst, S. J.

Boggio, J. M. C.

Bres, C.-S.

Caplen, J. E.

Carlson, C. G.

C. G. Carlson, R. B. Ross, J. M. Schafer, J. B. Spring, and B. G. Ward, “Full vectorial analysis of Brillouin gain in random acoustically microstructured photonic crystal fibers,” Phys. Rev. B 83(23), 235110 (2011).
[CrossRef]

Chen, X.

S. Gray, D. T. Walton, X. Chen, J. Wang, M.-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[CrossRef]

Chiragh, F.

C. Robin, I. Dajani, and F. Chiragh, “Experimental studies of segmented acoustically tailored photonic crystal fiber amplifier with 494 W single-frequency output,” Proc. SPIE 7914, 79140B, 79140B-8 (2011).
[CrossRef]

Coles, J. B.

Dajani, I.

C. Robin, I. Dajani, and F. Chiragh, “Experimental studies of segmented acoustically tailored photonic crystal fiber amplifier with 494 W single-frequency output,” Proc. SPIE 7914, 79140B, 79140B-8 (2011).
[CrossRef]

I. Dajani, C. Zeringue, C. Lu, C. Vergien, L. Henry, and C. Robin, “Stimulated Brillouin scattering suppression through laser gain competition: scalability to high power,” Opt. Lett. 35(18), 3114–3116 (2010).
[CrossRef] [PubMed]

Demeritt, J. A.

S. Gray, D. T. Walton, X. Chen, J. Wang, M.-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[CrossRef]

Dong, L.

Fan, T. Y.

Gabet, R.

Goodno, G. D.

Gray, S.

S. Gray, D. T. Walton, X. Chen, J. Wang, M.-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[CrossRef]

Grosche, G.

Hashemi, H.

N. Satyan, W. Liang, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Phase-controlled apertures using heterodyne optical phase-locked loops,” IEEE Photon. Technol. Lett. 20(11), 897–899 (2008).
[CrossRef]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, G. Rakuljic, F. Aflatouni, H. Hashemi, and J. Ungar, “Coherent power combination of two master-oscillator-power-amplifier (MOPA) semiconductor lasers using optical phase lock loops,” Opt. Express 15(6), 3201–3205 (2007).
[CrossRef] [PubMed]

Henry, L.

Jaouën, Y.

Jiang, S.

Karlsson, M.

Kewitsch, A.

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers using optical phase-lock loops,” IEEE J. Sel. Top. Quantum Electron. 15(2), 240–247 (2009).
[CrossRef]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, and G. Rakuljic, “Tiled-aperture coherent beam combining using optical phase-lock loops,” Electron. Lett. 44(14), 875–876 (2008).
[CrossRef]

N. Satyan, W. Liang, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Phase-controlled apertures using heterodyne optical phase-locked loops,” IEEE Photon. Technol. Lett. 20(11), 897–899 (2008).
[CrossRef]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, G. Rakuljic, F. Aflatouni, H. Hashemi, and J. Ungar, “Coherent power combination of two master-oscillator-power-amplifier (MOPA) semiconductor lasers using optical phase lock loops,” Opt. Express 15(6), 3201–3205 (2007).
[CrossRef] [PubMed]

Kuo, B. P.-P.

Lanticq, V.

Leyva, V.

Li, M.-J.

S. Gray, D. T. Walton, X. Chen, J. Wang, M.-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[CrossRef]

Liang, W.

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers using optical phase-lock loops,” IEEE J. Sel. Top. Quantum Electron. 15(2), 240–247 (2009).
[CrossRef]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, and G. Rakuljic, “Tiled-aperture coherent beam combining using optical phase-lock loops,” Electron. Lett. 44(14), 875–876 (2008).
[CrossRef]

N. Satyan, W. Liang, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Phase-controlled apertures using heterodyne optical phase-locked loops,” IEEE Photon. Technol. Lett. 20(11), 897–899 (2008).
[CrossRef]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, G. Rakuljic, F. Aflatouni, H. Hashemi, and J. Ungar, “Coherent power combination of two master-oscillator-power-amplifier (MOPA) semiconductor lasers using optical phase lock loops,” Opt. Express 15(6), 3201–3205 (2007).
[CrossRef] [PubMed]

Liu, A.

S. Gray, D. T. Walton, X. Chen, J. Wang, M.-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[CrossRef]

Lu, C.

McComb, T. S.

McNaught, S. J.

Moreau, G.

Moro, S.

Ohashi, M.

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31(8), 668–669 (1995).
[CrossRef]

Penty, R. V.

Qiang, L.

Radic, S.

Rakuljic, G.

N. Satyan, G. Rakuljic, and A. Yariv, “Chirp multiplication by four wave mixing for wideband swept-frequency sources for high resolution imaging,” J. Lightwave Technol. 28(14), 2077–2083 (2010).
[CrossRef]

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers using optical phase-lock loops,” IEEE J. Sel. Top. Quantum Electron. 15(2), 240–247 (2009).
[CrossRef]

N. Satyan, A. Vasilyev, G. Rakuljic, V. Leyva, and A. Yariv, “Precise control of broadband frequency chirps using optoelectronic feedback,” Opt. Express 17(18), 15991–15999 (2009).
[CrossRef] [PubMed]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, and G. Rakuljic, “Tiled-aperture coherent beam combining using optical phase-lock loops,” Electron. Lett. 44(14), 875–876 (2008).
[CrossRef]

N. Satyan, W. Liang, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Phase-controlled apertures using heterodyne optical phase-locked loops,” IEEE Photon. Technol. Lett. 20(11), 897–899 (2008).
[CrossRef]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, G. Rakuljic, F. Aflatouni, H. Hashemi, and J. Ungar, “Coherent power combination of two master-oscillator-power-amplifier (MOPA) semiconductor lasers using optical phase lock loops,” Opt. Express 15(6), 3201–3205 (2007).
[CrossRef] [PubMed]

Richardson, D. J.

Robin, C.

C. Robin, I. Dajani, and F. Chiragh, “Experimental studies of segmented acoustically tailored photonic crystal fiber amplifier with 494 W single-frequency output,” Proc. SPIE 7914, 79140B, 79140B-8 (2011).
[CrossRef]

I. Dajani, C. Zeringue, C. Lu, C. Vergien, L. Henry, and C. Robin, “Stimulated Brillouin scattering suppression through laser gain competition: scalability to high power,” Opt. Lett. 35(18), 3114–3116 (2010).
[CrossRef] [PubMed]

Ross, R. B.

C. G. Carlson, R. B. Ross, J. M. Schafer, J. B. Spring, and B. G. Ward, “Full vectorial analysis of Brillouin gain in random acoustically microstructured photonic crystal fibers,” Phys. Rev. B 83(23), 235110 (2011).
[CrossRef]

Rothenberg, J. E.

Ruffin, A. B.

S. Gray, D. T. Walton, X. Chen, J. Wang, M.-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[CrossRef]

Sanchez, A.

Satyan, N.

N. Satyan, G. Rakuljic, and A. Yariv, “Chirp multiplication by four wave mixing for wideband swept-frequency sources for high resolution imaging,” J. Lightwave Technol. 28(14), 2077–2083 (2010).
[CrossRef]

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers using optical phase-lock loops,” IEEE J. Sel. Top. Quantum Electron. 15(2), 240–247 (2009).
[CrossRef]

N. Satyan, A. Vasilyev, G. Rakuljic, V. Leyva, and A. Yariv, “Precise control of broadband frequency chirps using optoelectronic feedback,” Opt. Express 17(18), 15991–15999 (2009).
[CrossRef] [PubMed]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, and G. Rakuljic, “Tiled-aperture coherent beam combining using optical phase-lock loops,” Electron. Lett. 44(14), 875–876 (2008).
[CrossRef]

N. Satyan, W. Liang, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Phase-controlled apertures using heterodyne optical phase-locked loops,” IEEE Photon. Technol. Lett. 20(11), 897–899 (2008).
[CrossRef]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, G. Rakuljic, F. Aflatouni, H. Hashemi, and J. Ungar, “Coherent power combination of two master-oscillator-power-amplifier (MOPA) semiconductor lasers using optical phase lock loops,” Opt. Express 15(6), 3201–3205 (2007).
[CrossRef] [PubMed]

Schafer, J. M.

C. G. Carlson, R. B. Ross, J. M. Schafer, J. B. Spring, and B. G. Ward, “Full vectorial analysis of Brillouin gain in random acoustically microstructured photonic crystal fibers,” Phys. Rev. B 83(23), 235110 (2011).
[CrossRef]

Schnatz, H.

Shiraki, K.

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31(8), 668–669 (1995).
[CrossRef]

Spring, J. B.

C. G. Carlson, R. B. Ross, J. M. Schafer, J. B. Spring, and B. G. Ward, “Full vectorial analysis of Brillouin gain in random acoustically microstructured photonic crystal fibers,” Phys. Rev. B 83(23), 235110 (2011).
[CrossRef]

Taillade, F.

Tateda, M.

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31(8), 668–669 (1995).
[CrossRef]

Taverner, D.

Terra, O.

Thielen, P. A.

Ungar, J.

Vasilyev, A.

Vergien, C.

Walton, D. T.

S. Gray, D. T. Walton, X. Chen, J. Wang, M.-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[CrossRef]

Wang, J.

S. Gray, D. T. Walton, X. Chen, J. Wang, M.-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[CrossRef]

Ward, B. G.

C. G. Carlson, R. B. Ross, J. M. Schafer, J. B. Spring, and B. G. Ward, “Full vectorial analysis of Brillouin gain in random acoustically microstructured photonic crystal fibers,” Phys. Rev. B 83(23), 235110 (2011).
[CrossRef]

Weber, M. E.

Wickham, M. G.

Williams, K.

Yariv, A.

N. Satyan, G. Rakuljic, and A. Yariv, “Chirp multiplication by four wave mixing for wideband swept-frequency sources for high resolution imaging,” J. Lightwave Technol. 28(14), 2077–2083 (2010).
[CrossRef]

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers using optical phase-lock loops,” IEEE J. Sel. Top. Quantum Electron. 15(2), 240–247 (2009).
[CrossRef]

N. Satyan, A. Vasilyev, G. Rakuljic, V. Leyva, and A. Yariv, “Precise control of broadband frequency chirps using optoelectronic feedback,” Opt. Express 17(18), 15991–15999 (2009).
[CrossRef] [PubMed]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, and G. Rakuljic, “Tiled-aperture coherent beam combining using optical phase-lock loops,” Electron. Lett. 44(14), 875–876 (2008).
[CrossRef]

N. Satyan, W. Liang, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Phase-controlled apertures using heterodyne optical phase-locked loops,” IEEE Photon. Technol. Lett. 20(11), 897–899 (2008).
[CrossRef]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, G. Rakuljic, F. Aflatouni, H. Hashemi, and J. Ungar, “Coherent power combination of two master-oscillator-power-amplifier (MOPA) semiconductor lasers using optical phase lock loops,” Opt. Express 15(6), 3201–3205 (2007).
[CrossRef] [PubMed]

Yingfan, L.

Yongkang, D.

Zenteno, L. A.

S. Gray, D. T. Walton, X. Chen, J. Wang, M.-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[CrossRef]

Zeringue, C.

Zhiwei, L.

Chin. Opt. Lett. (1)

Electron. Lett. (2)

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31(8), 668–669 (1995).
[CrossRef]

W. Liang, N. Satyan, A. Yariv, A. Kewitsch, and G. Rakuljic, “Tiled-aperture coherent beam combining using optical phase-lock loops,” Electron. Lett. 44(14), 875–876 (2008).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

S. Gray, D. T. Walton, X. Chen, J. Wang, M.-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[CrossRef]

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers using optical phase-lock loops,” IEEE J. Sel. Top. Quantum Electron. 15(2), 240–247 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

N. Satyan, W. Liang, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Phase-controlled apertures using heterodyne optical phase-locked loops,” IEEE Photon. Technol. Lett. 20(11), 897–899 (2008).
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J. Lightwave Technol. (1)

Opt. Express (4)

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Phys. Rev. B (1)

C. G. Carlson, R. B. Ross, J. M. Schafer, J. B. Spring, and B. G. Ward, “Full vectorial analysis of Brillouin gain in random acoustically microstructured photonic crystal fibers,” Phys. Rev. B 83(23), 235110 (2011).
[CrossRef]

Proc. SPIE (1)

C. Robin, I. Dajani, and F. Chiragh, “Experimental studies of segmented acoustically tailored photonic crystal fiber amplifier with 494 W single-frequency output,” Proc. SPIE 7914, 79140B, 79140B-8 (2011).
[CrossRef]

Other (6)

D. Brown, M. Dennis, and W. Torruellas, “Improved phase modulation for SBS mitigation in kW-class fiber amplifiers,” SPIE Photonics West, San Francisco, CA, 24 Jan. 2011.

J. Edgecumbe, T. Ehrenreich, C.-H. Wang, K. Farley, J. Galipeau, R. Leveille, D. Björk, I. Majid, and K. Tankala, “kW class, narrow-linewidth, counter pumped fiber amplifiers,” Solid State and Diode Laser Technical Review, 17 June 2010.

Model YLS-10000-SM, IPG Photonics

DARPA ADHELS contract No. HR0011-060C-0029, final report (2008).

N. Satyan, A. Vasilyev, G. Rakuljic, J.O. White, and A. Yariv, manuscript submitted for publication.

D. Brown, M. Dennis, and W. Torruellas, “Improved phase modulation for SBS mitigation in kW-class fiber amplifiers,” Photonics West, 24 Jan. 2011.

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Figures (9)

Fig. 1
Fig. 1

Normalized SBS gain coefficient vs. position in a 17.5-m fiber, for various chirps and ΔνΒ = 20 MHz. The Stokes wave propagates from z = L to z = 0. The dashed line shows the gain for a chirp of 1015 Hz/s, at a Stokes frequency, which is resonant with the laser at z = L. The solid lines correspond to the Stokes frequencies that experience the highest integrated gain for each value of the chirp.

Fig. 2
Fig. 2

Plot of Leff vs. chirp, at δopt, for several values of ΔνB and L.

Fig. 3
Fig. 3

Plot of Leff vs. Stokes offset frequency, for ΔνΒ = 20 MHz and L = 17.5 m.

Fig. 4
Fig. 4

SBS threshold vs. chirp, for ΔνB = 20 MHz and three different fiber lengths.

Fig. 5
Fig. 5

Experimental layout for observing SBS suppression. A chirped diode laser is amplified in an erbium-doped fiber amplifier and then directed to the fiber under test (FUT) using a circulator.

Fig. 6
Fig. 6

Power spectrum of the chirped diode laser.

Fig. 7
Fig. 7

Backscattered power vs incident power for a 6-km single mode fiber with an 8-µm mode field diameter. The symbols are the experimental data taken at chirps of β = 0, 1014, 2 × 1014, and 5 × 1014 Hz/s. The curves are calculations of the backscattered Brillouin power for β = 1011 ‒ 1015 Hz/s (left to right). The dashed line is the backscattered Rayleigh power.

Fig. 8
Fig. 8

Spontaneous Brillouin power spectrum for the 6-km single mode fiber.

Fig. 9
Fig. 9

Frequency dependence of Im(ρ), normalized to the zero-chirp steady-state value, for different values of the chirp, and τ = 10 ns.

Equations (7)

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g( ν )= g 0 1+ ( ν ν L +Ω Δ ν B /2 ) 2 ,
ν L ( z,t )= ν 0 +β( t+ Lz c/n ),
g( δ,z )= g 0 1+ ( δ2βn( Lz )/c Δ ν B /2 ) 2 ,
L eff ( δ )= 1 g 0 0 L g( δ,z ) dz= Δ ν B  c 4nβ  ( tan 1 δ Δ ν B /2 tan 1 δ2βτ Δ ν B /2   ).
P B = ρ seed exp[   g 0   I pump   L eff  ( δ )  ] dδ.
Δ L max < cΔ ν max nβ .
dρ dt = ρ τ +iΛ E L E S * exp( iπβ t 2 ),

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