Abstract

Beam combining of phase-modulated kilowatt fiber amplifiers has generated considerable interest recently. We describe in the time domain how stimulated Brillouin scattering (SBS) is generated in an optical fiber under phase-modulated laser conditions, and we analyze different phase modulation techniques. The temporal and spatial evolutions of the acoustic phonon, laser, and Stokes fields are determined by solving the coupled three-wave interaction system. Numerical accuracy is verified through agreement with the analytical solution for the un-modulated case and through the standard photon conservation relation for counter-propagating optical fields. As a test for a modulated laser, a sinusoidal phase modulation is examined for a broad range of modulation amplitudes and frequencies. We show that, at high modulation frequencies, our simulations agree with the analytical results obtained from decomposing the optical power into its frequency components. At low modulation frequencies, there is a significant departure due to the appreciable cross talk among the laser and Stokes sidebands. We also examine SBS suppression for a white noise source and show significant departures for short fibers from analytically derived formulas. Finally, SBS suppression through the application of pseudo-random bit sequence modulation is examined for various patterns. It is shown that for a fiber length of 9 m the patterns at or near n=7 provide the best mitigation of SBS with suppression factors approaching 17 dB at a modulation frequency of 5 GHz.

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  1. I. Dajani, C. Zeringue, and T. Shay, “Investigation of nonlinear effects in multitone-driven narrow linewidth high-power amplifiers,” IEEE J. Sel. Top. Quantum Electron.15(2), 406–414 (2009).
    [CrossRef]
  2. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42(9), 5514–5521 (1990).
    [CrossRef] [PubMed]
  3. M. J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, and L. A. Zenteno, “Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express15(13), 8290–8299 (2007).
    [CrossRef] [PubMed]
  4. C. Robin and I. Dajani, “Acoustically segmented photonic crystal fiber for single-frequency high-power laser applications,” Opt. Lett.36(14), 2641–2643 (2011).
    [CrossRef] [PubMed]
  5. C. Zeringue, C. Vergien, and I. Dajani, “Pump-limited, 203 W single-frequency monolithic fiber amplifier based on laser gain competition,” Opt. Lett.36(5), 618–620 (2011).
    [CrossRef] [PubMed]
  6. F. W. Willems, W. Muys, and J. S. Leong, “Simultaneous Suppression of Stimulated Brillouin Scattering and interferometric noise in externally modulated lightwave AM-SCM systems,” IEEE Photon. Technol. Lett.6(12), 1476–1478 (1994).
    [CrossRef]
  7. G. D. Goodno, S. J. McNaught, J. E. Rothenberg, T. S. McComb, P. A. Thielen, M. G. Wickham, and M. E. Weber, “Active phase and polarization locking of a 1.4 kW fiber amplifier,” Opt. Lett.35(10), 1542–1544 (2010).
    [CrossRef] [PubMed]
  8. C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett.36(14), 2686–2688 (2011).
    [CrossRef] [PubMed]
  9. M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A24(4), 1980–1993 (1981).
    [CrossRef]
  10. R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A2(1), 60–72 (1970).
    [CrossRef]
  11. E. Lichtman, R. G. Waarts, and A. A. Friesem, “Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fibers,” J. Lightwave Technol.7(1), 171–174 (1989).
    [CrossRef]
  12. M. J. Damzen, V. I. Vlad, V. Babin, and A. Mocofanescu, Stimulated Brillouin Scattering Fundamentals and Applications (Institute of Physics Publishing, 2003).
  13. K. E. Gustafson, Partial Differential Equations and Hilbert Space Methods, 2nd ed. (Wiley, 1987).
  14. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).
  15. Y. Liu, Z. Lu, Y. Dong, and Q. Li, “Research on stimulated Brillouin scattering suppression based on multi-frequency phase modulation,” Chin. Opt. Lett.7(1), 29–31 (2009).
    [CrossRef]
  16. R. S. Williamson III, “Laser coherence control using homogeneous linewidth broadening.” U.S. Patent No. 7,280,568, Oct. 9 (2007).
  17. J. Edgecombe, 7 Airport Park Rd, East Granby, CT, 06026 (personal communication, 2011).
  18. D. Brown, M. Dennis, and W. Torruellas, “Improved phase modulation for SBS mitigation in kW-class fiber amplifiers,” Oral Presentation at Photonics West (2011).

2011 (3)

2010 (1)

2009 (2)

I. Dajani, C. Zeringue, and T. Shay, “Investigation of nonlinear effects in multitone-driven narrow linewidth high-power amplifiers,” IEEE J. Sel. Top. Quantum Electron.15(2), 406–414 (2009).
[CrossRef]

Y. Liu, Z. Lu, Y. Dong, and Q. Li, “Research on stimulated Brillouin scattering suppression based on multi-frequency phase modulation,” Chin. Opt. Lett.7(1), 29–31 (2009).
[CrossRef]

2007 (1)

1994 (1)

F. W. Willems, W. Muys, and J. S. Leong, “Simultaneous Suppression of Stimulated Brillouin Scattering and interferometric noise in externally modulated lightwave AM-SCM systems,” IEEE Photon. Technol. Lett.6(12), 1476–1478 (1994).
[CrossRef]

1990 (1)

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42(9), 5514–5521 (1990).
[CrossRef] [PubMed]

1989 (1)

E. Lichtman, R. G. Waarts, and A. A. Friesem, “Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fibers,” J. Lightwave Technol.7(1), 171–174 (1989).
[CrossRef]

1981 (1)

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A24(4), 1980–1993 (1981).
[CrossRef]

1970 (1)

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A2(1), 60–72 (1970).
[CrossRef]

Augst, S. J.

Bloembergen, N.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A2(1), 60–72 (1970).
[CrossRef]

Boyd, R. W.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42(9), 5514–5521 (1990).
[CrossRef] [PubMed]

Carman, R. L.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A2(1), 60–72 (1970).
[CrossRef]

Chen, X.

Crowley, A. M.

Dajani, I.

Demeritt, J. A.

Dong, Y.

Fan, T. Y.

Friesem, A. A.

E. Lichtman, R. G. Waarts, and A. A. Friesem, “Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fibers,” J. Lightwave Technol.7(1), 171–174 (1989).
[CrossRef]

Goldizen, K. C.

Goodno, G. D.

Gray, S.

Leong, J. S.

F. W. Willems, W. Muys, and J. S. Leong, “Simultaneous Suppression of Stimulated Brillouin Scattering and interferometric noise in externally modulated lightwave AM-SCM systems,” IEEE Photon. Technol. Lett.6(12), 1476–1478 (1994).
[CrossRef]

Li, M. J.

Li, Q.

Lichtman, E.

E. Lichtman, R. G. Waarts, and A. A. Friesem, “Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fibers,” J. Lightwave Technol.7(1), 171–174 (1989).
[CrossRef]

Liu, A.

Liu, Y.

Lu, Z.

McComb, T. S.

McNaught, S. J.

Mostowski, J.

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A24(4), 1980–1993 (1981).
[CrossRef]

Murphy, D. V.

Muys, W.

F. W. Willems, W. Muys, and J. S. Leong, “Simultaneous Suppression of Stimulated Brillouin Scattering and interferometric noise in externally modulated lightwave AM-SCM systems,” IEEE Photon. Technol. Lett.6(12), 1476–1478 (1994).
[CrossRef]

Narum, P.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42(9), 5514–5521 (1990).
[CrossRef] [PubMed]

Raymer, M. G.

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A24(4), 1980–1993 (1981).
[CrossRef]

Redmond, S. M.

Robin, C.

Rothenberg, J. E.

Ruffin, A. B.

Rzaewski, K.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42(9), 5514–5521 (1990).
[CrossRef] [PubMed]

Sanchez, A.

Shay, T.

I. Dajani, C. Zeringue, and T. Shay, “Investigation of nonlinear effects in multitone-driven narrow linewidth high-power amplifiers,” IEEE J. Sel. Top. Quantum Electron.15(2), 406–414 (2009).
[CrossRef]

Shimizu, F.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A2(1), 60–72 (1970).
[CrossRef]

Thielen, P. A.

Vergien, C.

Waarts, R. G.

E. Lichtman, R. G. Waarts, and A. A. Friesem, “Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fibers,” J. Lightwave Technol.7(1), 171–174 (1989).
[CrossRef]

Walton, D. T.

Wang, C. S.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A2(1), 60–72 (1970).
[CrossRef]

Wang, J.

Weber, M. E.

Wickham, M. G.

Willems, F. W.

F. W. Willems, W. Muys, and J. S. Leong, “Simultaneous Suppression of Stimulated Brillouin Scattering and interferometric noise in externally modulated lightwave AM-SCM systems,” IEEE Photon. Technol. Lett.6(12), 1476–1478 (1994).
[CrossRef]

Yu, C. X.

Zenteno, L. A.

Zeringue, C.

C. Zeringue, C. Vergien, and I. Dajani, “Pump-limited, 203 W single-frequency monolithic fiber amplifier based on laser gain competition,” Opt. Lett.36(5), 618–620 (2011).
[CrossRef] [PubMed]

I. Dajani, C. Zeringue, and T. Shay, “Investigation of nonlinear effects in multitone-driven narrow linewidth high-power amplifiers,” IEEE J. Sel. Top. Quantum Electron.15(2), 406–414 (2009).
[CrossRef]

Chin. Opt. Lett. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

I. Dajani, C. Zeringue, and T. Shay, “Investigation of nonlinear effects in multitone-driven narrow linewidth high-power amplifiers,” IEEE J. Sel. Top. Quantum Electron.15(2), 406–414 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

F. W. Willems, W. Muys, and J. S. Leong, “Simultaneous Suppression of Stimulated Brillouin Scattering and interferometric noise in externally modulated lightwave AM-SCM systems,” IEEE Photon. Technol. Lett.6(12), 1476–1478 (1994).
[CrossRef]

J. Lightwave Technol. (1)

E. Lichtman, R. G. Waarts, and A. A. Friesem, “Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fibers,” J. Lightwave Technol.7(1), 171–174 (1989).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (3)

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42(9), 5514–5521 (1990).
[CrossRef] [PubMed]

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A24(4), 1980–1993 (1981).
[CrossRef]

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient stimulated Raman scattering,” Phys. Rev. A2(1), 60–72 (1970).
[CrossRef]

Other (6)

M. J. Damzen, V. I. Vlad, V. Babin, and A. Mocofanescu, Stimulated Brillouin Scattering Fundamentals and Applications (Institute of Physics Publishing, 2003).

K. E. Gustafson, Partial Differential Equations and Hilbert Space Methods, 2nd ed. (Wiley, 1987).

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

R. S. Williamson III, “Laser coherence control using homogeneous linewidth broadening.” U.S. Patent No. 7,280,568, Oct. 9 (2007).

J. Edgecombe, 7 Airport Park Rd, East Granby, CT, 06026 (personal communication, 2011).

D. Brown, M. Dennis, and W. Torruellas, “Improved phase modulation for SBS mitigation in kW-class fiber amplifiers,” Oral Presentation at Photonics West (2011).

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