Abstract

We demonstrate a technique for SBS reduction in a nanosecond Yb-fiber amplifier by imposing 1.19 GHz/ns frequency chirp on the seed pulses with a pulse-driven phase modulator. A nearly 9-fold increase in the SBS threshold was observed for 8.4 ns pulses. SBS threshold data and transient SBS gain for various degrees of chirp are reported and compared with theoretical calculations. We further demonstrate the recovery of the input narrowband spectrum by applying an opposite chirp with a second phase modulator after the amplification.

© 2016 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).
  2. R. W. Boyd, Nonlinear Optics (Elsevier Inc., 2008).
  3. K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol. 14(1), 50–57 (1996).
    [Crossref]
  4. T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photonics Technol. Lett. 1(5), 107–108 (1989).
    [Crossref]
  5. J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, “Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” J. Lightwave Technol. 19(11), 1691–1697 (2001).
    [Crossref]
  6. M. D. Mermelstein, “SBS threshold measurements and acoustic beam propagation modeling in guiding and anti-guiding single mode optical fibers,” Opt. Express 17(18), 16225–16237 (2009).
    [Crossref] [PubMed]
  7. Y. Aoki and K. Tajima, “Stimulated Brillouin scattering in a long single-mode fiber excited with a multimode pump laser,” J. Opt. Soc. Am. B 5(2), 358–363 (1988).
    [Crossref]
  8. F. Di Teodoro, J. Morais, T. S. McComb, M. K. Hemmat, E. C. Cheung, M. Weber, and R. Moyer, “SBS-managed high-peak-power nanosecond-pulse fiber-based master oscillator power amplifier,” Opt. Lett. 38(13), 2162–2164 (2013).
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    [Crossref] [PubMed]
  10. N. A. Naderi, I. Dajani, and A. Flores, “High-efficiency, kilowatt 1034 nm all-fiber amplifier operating at 11 pm linewidth,” Opt. Lett. 41(5), 1018–1021 (2016).
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    [Crossref] [PubMed]
  12. C. Weitkamp, Lidar. Range-Resolved Optical Remote Sensing of Atmosphere (Springer, 2005).
  13. J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express 20(14), 15872–15881 (2012).
    [Crossref] [PubMed]
  14. J. O. White, E. Petersen, J. Edgecumbe, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “A linearly chirped seed suppresses SBS in high-power fiber amplifiers, allows coherent combination, and enables long delivery fibers,” Proc. SPIE 8961, 896102 (2014).
    [Crossref]
  15. J. O. White, D. Engin, M. Akbulut, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “Chirped laser seeding for SBS suppression in a 100-W pulsed erbium fiber amplifier,” IEEE J. Quantum Electron. 51(6), 1–10 (2015).
    [Crossref]
  16. L. L. Pendergrass, “Ferroelectric microdomain reversal at room temperature in lithium niobate,” J. Appl. Phys. 62(1), 231–236 (1987).
    [Crossref]
  17. O. V. Bystrov and A. V. Golenishchev-Kutuzov, “Acoustically induced domain structure in lithium niobate,” JETP Lett. 61, 135 (1995).
  18. N. E. Huang and Z. Wu, “A review on Hilbert‐Huang transform: Method and its applications to geophysical studies,” Rev. Geophys. 46(2), RG2006 (2008).
    [Crossref]
  19. M. Ito and T. Kimura, “Carrier density dependence of refractive index in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 16(9), 910–911 (1980).
    [Crossref]
  20. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
    [Crossref] [PubMed]
  21. M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997).
    [Crossref]
  22. I. Dajani, C. Vergien, C. Robin, and C. Zeringue, “Experimental and theoretical investigations of photonic crystal fiber amplifier with 260 W output,” Opt. Express 17(26), 24317–24333 (2009).
    [Crossref] [PubMed]
  23. M. Hildebrandt, S. Büsche, P. Wessels, M. Frede, and D. Kracht, “Brillouin scattering spectra in high-power single-frequency ytterbium doped fiber amplifiers,” Opt. Express 16(20), 15970–15979 (2008).
    [Crossref] [PubMed]
  24. P. N. Brown, G. D. Byrne, and A. C. Hindmarsh, zvod.f on netlib.org, http://www.netlib.org/ode/zvode.f
  25. H. Tünnermann, P. Jahn, V. Quetschke, J. Neumann, D. Kracht, and P. Wessels, “SBS mitigation via phase modulation and demodulation,” in CLEO: Science and Innovations (OSA, 2014), paper SW3N–2.
  26. R. Zhu, J. Wang, J. Zhou, J. Liu, and W. Chen, “Single-frequency pulsed laser source with hybrid MOPA configuration,” Appl. Opt. 51(17), 3826–3831 (2012).
    [Crossref] [PubMed]

2016 (1)

2015 (2)

B. Anderson, A. Flores, R. Holten, and I. Dajani, “Comparison of phase modulation schemes for coherently combined fiber amplifiers,” Opt. Express 23(21), 27046–27060 (2015).
[Crossref] [PubMed]

J. O. White, D. Engin, M. Akbulut, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “Chirped laser seeding for SBS suppression in a 100-W pulsed erbium fiber amplifier,” IEEE J. Quantum Electron. 51(6), 1–10 (2015).
[Crossref]

2014 (1)

J. O. White, E. Petersen, J. Edgecumbe, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “A linearly chirped seed suppresses SBS in high-power fiber amplifiers, allows coherent combination, and enables long delivery fibers,” Proc. SPIE 8961, 896102 (2014).
[Crossref]

2013 (1)

2012 (3)

2009 (2)

2008 (2)

2001 (1)

1997 (1)

M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997).
[Crossref]

1996 (1)

K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol. 14(1), 50–57 (1996).
[Crossref]

1995 (1)

O. V. Bystrov and A. V. Golenishchev-Kutuzov, “Acoustically induced domain structure in lithium niobate,” JETP Lett. 61, 135 (1995).

1990 (1)

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[Crossref] [PubMed]

1989 (1)

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photonics Technol. Lett. 1(5), 107–108 (1989).
[Crossref]

1988 (1)

1987 (1)

L. L. Pendergrass, “Ferroelectric microdomain reversal at room temperature in lithium niobate,” J. Appl. Phys. 62(1), 231–236 (1987).
[Crossref]

1980 (1)

M. Ito and T. Kimura, “Carrier density dependence of refractive index in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 16(9), 910–911 (1980).
[Crossref]

Akbulut, M.

J. O. White, D. Engin, M. Akbulut, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “Chirped laser seeding for SBS suppression in a 100-W pulsed erbium fiber amplifier,” IEEE J. Quantum Electron. 51(6), 1–10 (2015).
[Crossref]

Anderson, B.

Andrekson, P. A.

Aoki, Y.

Boyd, R. W.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[Crossref] [PubMed]

Büsche, S.

Bystrov, O. V.

O. V. Bystrov and A. V. Golenishchev-Kutuzov, “Acoustically induced domain structure in lithium niobate,” JETP Lett. 61, 135 (1995).

Cahill, J. P.

Chen, W.

Cheung, E. C.

Dajani, I.

Di Teodoro, F.

Dross, F.

Edgecumbe, J.

J. O. White, E. Petersen, J. Edgecumbe, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “A linearly chirped seed suppresses SBS in high-power fiber amplifiers, allows coherent combination, and enables long delivery fibers,” Proc. SPIE 8961, 896102 (2014).
[Crossref]

Engin, D.

J. O. White, D. Engin, M. Akbulut, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “Chirped laser seeding for SBS suppression in a 100-W pulsed erbium fiber amplifier,” IEEE J. Quantum Electron. 51(6), 1–10 (2015).
[Crossref]

Flores, A.

Frede, M.

Golenishchev-Kutuzov, A. V.

O. V. Bystrov and A. V. Golenishchev-Kutuzov, “Acoustically induced domain structure in lithium niobate,” JETP Lett. 61, 135 (1995).

Hansryd, J.

Hemmat, M. K.

Hildebrandt, M.

Holten, R.

Horiguchi, T.

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photonics Technol. Lett. 1(5), 107–108 (1989).
[Crossref]

Huang, N. E.

N. E. Huang and Z. Wu, “A review on Hilbert‐Huang transform: Method and its applications to geophysical studies,” Rev. Geophys. 46(2), RG2006 (2008).
[Crossref]

Ito, M.

M. Ito and T. Kimura, “Carrier density dependence of refractive index in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 16(9), 910–911 (1980).
[Crossref]

Kimura, T.

M. Ito and T. Kimura, “Carrier density dependence of refractive index in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 16(9), 910–911 (1980).
[Crossref]

Knudsen, S. N.

Kracht, D.

Kurashima, T.

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photonics Technol. Lett. 1(5), 107–108 (1989).
[Crossref]

Liu, J.

McComb, T. S.

Mermelstein, M. D.

Moore, G. T.

Morais, J.

Moyer, R.

Mungan, C. E.

Naderi, N. A.

Naderi, S.

Narum, P.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[Crossref] [PubMed]

Nikles, M.

M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997).
[Crossref]

Ohashi, M.

K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol. 14(1), 50–57 (1996).
[Crossref]

Okusaga, O.

Pendergrass, L. L.

L. L. Pendergrass, “Ferroelectric microdomain reversal at room temperature in lithium niobate,” J. Appl. Phys. 62(1), 231–236 (1987).
[Crossref]

Petersen, E.

J. O. White, E. Petersen, J. Edgecumbe, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “A linearly chirped seed suppresses SBS in high-power fiber amplifiers, allows coherent combination, and enables long delivery fibers,” Proc. SPIE 8961, 896102 (2014).
[Crossref]

Rakuljic, G.

J. O. White, D. Engin, M. Akbulut, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “Chirped laser seeding for SBS suppression in a 100-W pulsed erbium fiber amplifier,” IEEE J. Quantum Electron. 51(6), 1–10 (2015).
[Crossref]

J. O. White, E. Petersen, J. Edgecumbe, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “A linearly chirped seed suppresses SBS in high-power fiber amplifiers, allows coherent combination, and enables long delivery fibers,” Proc. SPIE 8961, 896102 (2014).
[Crossref]

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express 20(14), 15872–15881 (2012).
[Crossref] [PubMed]

Robert, P. A.

M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997).
[Crossref]

Robin, C.

Rzaewski, K.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[Crossref] [PubMed]

Satyan, N.

J. O. White, D. Engin, M. Akbulut, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “Chirped laser seeding for SBS suppression in a 100-W pulsed erbium fiber amplifier,” IEEE J. Quantum Electron. 51(6), 1–10 (2015).
[Crossref]

J. O. White, E. Petersen, J. Edgecumbe, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “A linearly chirped seed suppresses SBS in high-power fiber amplifiers, allows coherent combination, and enables long delivery fibers,” Proc. SPIE 8961, 896102 (2014).
[Crossref]

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express 20(14), 15872–15881 (2012).
[Crossref] [PubMed]

Shiraki, K.

K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol. 14(1), 50–57 (1996).
[Crossref]

Tajima, K.

Tateda, M.

K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol. 14(1), 50–57 (1996).
[Crossref]

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photonics Technol. Lett. 1(5), 107–108 (1989).
[Crossref]

Thevenaz, L.

M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997).
[Crossref]

Vasilyev, A.

J. O. White, D. Engin, M. Akbulut, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “Chirped laser seeding for SBS suppression in a 100-W pulsed erbium fiber amplifier,” IEEE J. Quantum Electron. 51(6), 1–10 (2015).
[Crossref]

J. O. White, E. Petersen, J. Edgecumbe, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “A linearly chirped seed suppresses SBS in high-power fiber amplifiers, allows coherent combination, and enables long delivery fibers,” Proc. SPIE 8961, 896102 (2014).
[Crossref]

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express 20(14), 15872–15881 (2012).
[Crossref] [PubMed]

Vergien, C.

Wang, J.

Weber, M.

Wessels, P.

Westlund, M.

White, J. O.

J. O. White, D. Engin, M. Akbulut, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “Chirped laser seeding for SBS suppression in a 100-W pulsed erbium fiber amplifier,” IEEE J. Quantum Electron. 51(6), 1–10 (2015).
[Crossref]

J. O. White, E. Petersen, J. Edgecumbe, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “A linearly chirped seed suppresses SBS in high-power fiber amplifiers, allows coherent combination, and enables long delivery fibers,” Proc. SPIE 8961, 896102 (2014).
[Crossref]

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express 20(14), 15872–15881 (2012).
[Crossref] [PubMed]

Wu, Z.

N. E. Huang and Z. Wu, “A review on Hilbert‐Huang transform: Method and its applications to geophysical studies,” Rev. Geophys. 46(2), RG2006 (2008).
[Crossref]

Yariv, A.

J. O. White, D. Engin, M. Akbulut, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “Chirped laser seeding for SBS suppression in a 100-W pulsed erbium fiber amplifier,” IEEE J. Quantum Electron. 51(6), 1–10 (2015).
[Crossref]

J. O. White, E. Petersen, J. Edgecumbe, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “A linearly chirped seed suppresses SBS in high-power fiber amplifiers, allows coherent combination, and enables long delivery fibers,” Proc. SPIE 8961, 896102 (2014).
[Crossref]

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express 20(14), 15872–15881 (2012).
[Crossref] [PubMed]

Zeringue, C.

Zhou, J.

Zhu, R.

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

M. Ito and T. Kimura, “Carrier density dependence of refractive index in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. 16(9), 910–911 (1980).
[Crossref]

J. O. White, D. Engin, M. Akbulut, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “Chirped laser seeding for SBS suppression in a 100-W pulsed erbium fiber amplifier,” IEEE J. Quantum Electron. 51(6), 1–10 (2015).
[Crossref]

IEEE Photonics Technol. Lett. (1)

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fibers,” IEEE Photonics Technol. Lett. 1(5), 107–108 (1989).
[Crossref]

J. Appl. Phys. (1)

L. L. Pendergrass, “Ferroelectric microdomain reversal at room temperature in lithium niobate,” J. Appl. Phys. 62(1), 231–236 (1987).
[Crossref]

J. Lightwave Technol. (3)

J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, “Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” J. Lightwave Technol. 19(11), 1691–1697 (2001).
[Crossref]

K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol. 14(1), 50–57 (1996).
[Crossref]

M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997).
[Crossref]

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

JETP Lett. (1)

O. V. Bystrov and A. V. Golenishchev-Kutuzov, “Acoustically induced domain structure in lithium niobate,” JETP Lett. 61, 135 (1995).

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. A (1)

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
[Crossref] [PubMed]

Proc. SPIE (1)

J. O. White, E. Petersen, J. Edgecumbe, G. Rakuljic, N. Satyan, A. Vasilyev, and A. Yariv, “A linearly chirped seed suppresses SBS in high-power fiber amplifiers, allows coherent combination, and enables long delivery fibers,” Proc. SPIE 8961, 896102 (2014).
[Crossref]

Rev. Geophys. (1)

N. E. Huang and Z. Wu, “A review on Hilbert‐Huang transform: Method and its applications to geophysical studies,” Rev. Geophys. 46(2), RG2006 (2008).
[Crossref]

Other (5)

C. Weitkamp, Lidar. Range-Resolved Optical Remote Sensing of Atmosphere (Springer, 2005).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

R. W. Boyd, Nonlinear Optics (Elsevier Inc., 2008).

P. N. Brown, G. D. Byrne, and A. C. Hindmarsh, zvod.f on netlib.org, http://www.netlib.org/ode/zvode.f

H. Tünnermann, P. Jahn, V. Quetschke, J. Neumann, D. Kracht, and P. Wessels, “SBS mitigation via phase modulation and demodulation,” in CLEO: Science and Innovations (OSA, 2014), paper SW3N–2.

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Figures (16)

Fig. 1
Fig. 1 Experimental block diagram: master oscillator with two-stage fiber amplifier.
Fig. 2
Fig. 2 Measured phase modulator drive voltage and seed laser pulse intensity profile (peak normalized), reflecting relative time position inside the modulator.
Fig. 3
Fig. 3 Fiber modulator phase (drive voltage normalized by nominal Vπ = 2.5 V) and its derivative corresponding to the instantaneous frequency shift. The dashed vertical lines indicate an area of approximately linear chirp where the light pulse was placed.
Fig. 4
Fig. 4 Heterodyne measurement of the instantaneous frequency of the pulse-driven DFB laser with and without driving the phase modulator (42 V peak-to-peak modulator voltage). Dashed lines indicate the section later gated with an SOA.
Fig. 5
Fig. 5 Heterodyne measurement of the instantaneous frequency of the master oscillator (DFB laser, modulator and SOA) for 42 V peak-to-peak modulator driving voltage. Dashed line is the linear regression of the measurement.
Fig. 6
Fig. 6 Measured master oscillator chirp as the function of the modulator driver peak-to-peak voltage.
Fig. 7
Fig. 7 Measured transient SBS gain spectra for 8.4 ns pulse duration, 0.58 µJ pulse energy and 11-µm core diameter double-clad Yb fiber.
Fig. 8
Fig. 8 Full width at half maximum of the logarithm of SBS gain versus frequency chirp for 8.4 ns pulse duration, 0.58 µJ pulse energy and 11 µm diameter core double-clad Yb fiber.
Fig. 9
Fig. 9 Experimental and calculated logarithm of the peak SBS gain versus inverse of chirp for 8.4 ns pulse duration, 11-µm diameter core double-clad Yb fiber and three pulse energies: 0.29 µJ, 0.43 µJ and 0.58 µJ.
Fig. 10
Fig. 10 Calculated growth of the Stokes wave over the duration of the forward propagating 0.58 µJ, 8.4 ns (FWHM) pulse for 11 µm core diameter fiber for several values of frequency chirp and 0 MHz frequency offset of the Stokes seed from the resonance center. The assumed 8.4 ns pulse profile is shown in black.
Fig. 11
Fig. 11 Calculated growth of the Stokes wave over the duration of the forward propagating 0.58 µJ, 8.4 ns (FWHM) pulse for 11 µm core diameter fiber for several values of frequency chirp and 250 MHz frequency offset of the Stokes seed from the resonance center. The assumed 8.4 ns pulse profile is shown in black.
Fig. 12
Fig. 12 Calculated logarithm of SBS gain spectra for 11 µm core diameter, 0.58 µJ, 8.4 ns pulse for several values of frequency chirp.
Fig. 13
Fig. 13 Optical spectrum analyzer spectra at threshold, defined by the SBS peak height of 10 dB above the back-propagating ASE in the 2nd amplifier stage.
Fig. 14
Fig. 14 SBS threshold (10 dB or 20 dB above ASE, see Fig. 13) versus master oscillator frequency chirp.
Fig. 15
Fig. 15 Bulk modulator phase (drive voltage normalized by nominal Vπ = 240 V) and its derivative corresponding to the instantaneous frequency. Dashed vertical lines indicate an area of approximately linear chirp where light pulse was placed.
Fig. 16
Fig. 16 Spectral compressions after amplification by inverting the chirp with the second (bulk) phase modulator. Spectrum before initial application of chirp in the MO (blue): width 240 MHz; after modulation but before compression (green): 2 GHz FWHM width; and after compression (red): width 240 MHz.

Equations (15)

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( / z + v 1 / t ) E p =i k 2 ρ E s ,
( / z + v 1 / t ) E s =i k 2 ρ * E p ,
( / t +Γ/2 ) ρ * =i k 1 E s E p * +f,
Q= kT ρ 0 Γ 2 v s 2 AΔz ,
g 0 = 4 π 2 γ 2 nc λ 2 ρ 0 v s Γ ,
k 1 = 2π ε 0 nγ v s λ = ε 0 n 1.5 g 0 c ρ 0 Γ v s ,
g 0 = 2 k 1 k 2 Γn ε 0 c ,
E p (t,z)= E p (t v 1 z).
E s (t,z)= E s (t v 1 z),
ρ * (t,z)= ρ * (t v 1 z).
d E s / dt =i v 2 k 2 ρ * E p ,
d ρ * / dt =i k 1 E s E p * Γ 2 ρ * .
U=i v 2 k 2 ρ * ,
d E s / dt =U E p ,
dU / dt = 1 4 g 0 Γvn ε 0 c E s E p * Γ 2 U.

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