Abstract

We propose using piecewise parabolic phase modulation of the seed laser for suppressing stimulated Brillouin scattering (SBS) in a fiber amplifier. Simulations are run with a 9 m passive fiber. Compared with random phase modulation and 0-π pseudo-random phase modulation, the piecewise parabolic phase waveform yields a higher SBS threshold per unit bandwidth. If the bandwidth is defined as the range of frequencies containing 85% of the total power, the threshold for parabolic phase modulation is 1.4 times higher than the threshold for the five- or seven-bit pseudo-random modulation format. If the bandwidth is defined more tightly, e.g., the range of frequencies containing 95% of the total power, the threshold for parabolic phase modulation is three times higher. For both cases, achieving a bandwidth of 1.5 GHz requires a maximum phase shift of ~30 radians. All of the waveforms are compared on the basis of the bandwidth required of the phase moduator. The coherence functions are calculated in order to compare their suitability for coherent combining.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combination of narrow-linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
    [Crossref]
  2. M. Vorontsov, G. Filimonov, V. Ovchinnikov, E. Polnau, S. Lachinova, T. Weyrauch, and J. Mangano, “Comparative efficiency analysis of fiber-array and conventional beam director systems in volume turbulence,” Appl. Opt. 55(15), 4170–4185 (2016).
    [Crossref] [PubMed]
  3. 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]
  4. A. Mussot, M. Le Parquier, and P. Szriftgiser, “Thermal noise for SBS suppression in fiber optical parametric amplifiers,” Opt. Commun. 283(12), 2607–2610 (2010).
    [Crossref]
  5. 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]
  6. V. R. Supradeepa, “Stimulated Brillouin scattering thresholds in optical fibers for lasers linewidth broadened with noise,” Opt. Express 21(4), 4677–4687 (2013).
    [Crossref] [PubMed]
  7. D. Brown, M. Dennis, and W. Torruellas, “Improved phase modulation for SBS mitigation in kW-class fiber amplifiers,” presented at SPIE Photonics West, San Francisco, CA (January 24, 2011).
  8. A. Flores, T. Ehrehreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
    [Crossref]
  9. C. Zeringue, I. Dajani, S. Naderi, G. T. Moore, and C. Robin, “A theoretical study of transient stimulated Brillouin scattering in optical fibers seeded with phase-modulated light,” Opt. Express 20(19), 21196–21213 (2012).
    [Crossref] [PubMed]
  10. P. I. Ionov and T. S. Rose, “SBS reduction in nanosecond fiber amplifiers by frequency chirping,” Opt. Express 24(13), 13763–13777 (2016).
    [Crossref] [PubMed]
  11. . B. Coles, B. P.-P. Kuo, N. Alic, S. Moro, C.-S. Bres, J. M. C. Boggio, P. A. Andrekson, M. Karlsson, and S. Radic, “Bandwidth-efficient phase modulation techniques for stimulated Brillouin scattering suppression in fiber optic parametric amplifiers,” Opt. Express 18(17), 18138–18150 (2010).
    [Crossref] [PubMed]
  12. J. O. White, M. Harfouche, J. Edgecumbe, N. Satyan, G. Rakuljic, V. Jayaraman, C. Burgner, and A. Yariv, “1.6 kW Yb fiber amplifier using chirped seed amplification for stimulated Brillouin scattering suppression,” Appl. Opt. 56(3), B116–B122 (2017).
    [Crossref] [PubMed]
  13. A. Vasilyev, E. Petersen, N. Satyan, G. Rakuljic, A. Yariv, and J. O. White, “Coherent power combining of chirped-seed Erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 25(16), 1616–1618 (2013).
    [Crossref]
  14. E. Petersen, Z. Y. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
    [Crossref]
  15. 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]
  16. V. Jayaraman, G. D. Cole, M. Robertson, C. Burgner, D. John, A. Uddin, and A. Cable, “Rapidly swept, ultra-widely-tunable 1060 nm MEMS-VCSELs,” Electron. Lett. 48(21), 1331–1333 (2012).
    [Crossref] [PubMed]
  17. A. V. Harish and J. Nilsson, “Optimization of phase modulation with arbitrary waveform generators for optical spectral control and suppression of stimulated Brillouin scattering,” Opt. Express 23(6), 6988–6999 (2015).
    [Crossref] [PubMed]
  18. B. M. Anderson, R. Hui, A. Flores, and I. Dajani, “SBS suppression and coherence properties of a flat top optical spectrum in a high power fiber amplifier,” Proc. SPIE 10083, 100830V (2017).
    [Crossref]
  19. A. V. Harish and J. Nilsson, “Optimization of phase modulation formats for suppression of stimulated Brillouin scattering in optical fibers,” IEEE J. Sel. Topics in Quantum Elect. 24, 5100110 (2018).
  20. Fringes occur in the raw triangle chirp spectrum due to the interference stemming from the same frequency occurring at two places in the period. For this reason, the raw spectrum has been smoothed on a very fine scale with a moving average over 69 MHz. This is close to the same averaging that will occur physically, by virtue of the 57.1 MHz Brillouin linewidth.
  21. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990).
    [Crossref] [PubMed]
  22. D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band-shape and bandwidth modification,” Phys. Rev. A 26(1), 12–18 (1982).
    [Crossref]
  23. C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
    [Crossref] [PubMed]

2018 (2)

A. V. Harish and J. Nilsson, “Optimization of phase modulation formats for suppression of stimulated Brillouin scattering in optical fibers,” IEEE J. Sel. Topics in Quantum Elect. 24, 5100110 (2018).

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref] [PubMed]

2017 (2)

B. M. Anderson, R. Hui, A. Flores, and I. Dajani, “SBS suppression and coherence properties of a flat top optical spectrum in a high power fiber amplifier,” Proc. SPIE 10083, 100830V (2017).
[Crossref]

J. O. White, M. Harfouche, J. Edgecumbe, N. Satyan, G. Rakuljic, V. Jayaraman, C. Burgner, and A. Yariv, “1.6 kW Yb fiber amplifier using chirped seed amplification for stimulated Brillouin scattering suppression,” Appl. Opt. 56(3), B116–B122 (2017).
[Crossref] [PubMed]

2016 (4)

M. Vorontsov, G. Filimonov, V. Ovchinnikov, E. Polnau, S. Lachinova, T. Weyrauch, and J. Mangano, “Comparative efficiency analysis of fiber-array and conventional beam director systems in volume turbulence,” Appl. Opt. 55(15), 4170–4185 (2016).
[Crossref] [PubMed]

P. I. Ionov and T. S. Rose, “SBS reduction in nanosecond fiber amplifiers by frequency chirping,” Opt. Express 24(13), 13763–13777 (2016).
[Crossref] [PubMed]

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combination of narrow-linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

A. Flores, T. Ehrehreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

2015 (1)

2013 (3)

A. Vasilyev, E. Petersen, N. Satyan, G. Rakuljic, A. Yariv, and J. O. White, “Coherent power combining of chirped-seed Erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 25(16), 1616–1618 (2013).
[Crossref]

E. Petersen, Z. Y. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[Crossref]

V. R. Supradeepa, “Stimulated Brillouin scattering thresholds in optical fibers for lasers linewidth broadened with noise,” Opt. Express 21(4), 4677–4687 (2013).
[Crossref] [PubMed]

2012 (2)

C. Zeringue, I. Dajani, S. Naderi, G. T. Moore, and C. Robin, “A theoretical study of transient stimulated Brillouin scattering in optical fibers seeded with phase-modulated light,” Opt. Express 20(19), 21196–21213 (2012).
[Crossref] [PubMed]

V. Jayaraman, G. D. Cole, M. Robertson, C. Burgner, D. John, A. Uddin, and A. Cable, “Rapidly swept, ultra-widely-tunable 1060 nm MEMS-VCSELs,” Electron. Lett. 48(21), 1331–1333 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (3)

2009 (1)

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]

1982 (1)

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band-shape and bandwidth modification,” Phys. Rev. A 26(1), 12–18 (1982).
[Crossref]

Alic, N.

Anderson, B.

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combination of narrow-linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

A. Flores, T. Ehrehreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

Anderson, B. M.

B. M. Anderson, R. Hui, A. Flores, and I. Dajani, “SBS suppression and coherence properties of a flat top optical spectrum in a high power fiber amplifier,” Proc. SPIE 10083, 100830V (2017).
[Crossref]

Andrekson, P. A.

Augst, S. J.

Bertrand, M.

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref] [PubMed]

Boggio, J. M. C.

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]

Bres, C.-S.

Burgner, C.

Cable, A.

V. Jayaraman, G. D. Cole, M. Robertson, C. Burgner, D. John, A. Uddin, and A. Cable, “Rapidly swept, ultra-widely-tunable 1060 nm MEMS-VCSELs,” Electron. Lett. 48(21), 1331–1333 (2012).
[Crossref] [PubMed]

Chandrasekhar, S.

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref] [PubMed]

Chen, X.

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref] [PubMed]

Cole, G. D.

V. Jayaraman, G. D. Cole, M. Robertson, C. Burgner, D. John, A. Uddin, and A. Cable, “Rapidly swept, ultra-widely-tunable 1060 nm MEMS-VCSELs,” Electron. Lett. 48(21), 1331–1333 (2012).
[Crossref] [PubMed]

Coles, . B.

Dajani, I.

B. M. Anderson, R. Hui, A. Flores, and I. Dajani, “SBS suppression and coherence properties of a flat top optical spectrum in a high power fiber amplifier,” Proc. SPIE 10083, 100830V (2017).
[Crossref]

A. Flores, T. Ehrehreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combination of narrow-linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

C. Zeringue, I. Dajani, S. Naderi, G. T. Moore, and C. Robin, “A theoretical study of transient stimulated Brillouin scattering in optical fibers seeded with phase-modulated light,” Opt. Express 20(19), 21196–21213 (2012).
[Crossref] [PubMed]

Edgecumbe, J.

Ehrehreich, T.

A. Flores, T. Ehrehreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

Ehrenreich, T.

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combination of narrow-linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

Elliott, D. S.

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band-shape and bandwidth modification,” Phys. Rev. A 26(1), 12–18 (1982).
[Crossref]

Fan, T. Y.

Filimonov, G.

Flores, A.

B. M. Anderson, R. Hui, A. Flores, and I. Dajani, “SBS suppression and coherence properties of a flat top optical spectrum in a high power fiber amplifier,” Proc. SPIE 10083, 100830V (2017).
[Crossref]

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combination of narrow-linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

A. Flores, T. Ehrehreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

Goldizen, K. C.

Goodno, G. D.

Harfouche, M.

Harish, A. V.

A. V. Harish and J. Nilsson, “Optimization of phase modulation formats for suppression of stimulated Brillouin scattering in optical fibers,” IEEE J. Sel. Topics in Quantum Elect. 24, 5100110 (2018).

A. V. Harish and J. Nilsson, “Optimization of phase modulation with arbitrary waveform generators for optical spectral control and suppression of stimulated Brillouin scattering,” Opt. Express 23(6), 6988–6999 (2015).
[Crossref] [PubMed]

Holten, R.

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combination of narrow-linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

A. Flores, T. Ehrehreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

Hui, R.

B. M. Anderson, R. Hui, A. Flores, and I. Dajani, “SBS suppression and coherence properties of a flat top optical spectrum in a high power fiber amplifier,” Proc. SPIE 10083, 100830V (2017).
[Crossref]

Ionov, P. I.

Jayaraman, V.

John, D.

V. Jayaraman, G. D. Cole, M. Robertson, C. Burgner, D. John, A. Uddin, and A. Cable, “Rapidly swept, ultra-widely-tunable 1060 nm MEMS-VCSELs,” Electron. Lett. 48(21), 1331–1333 (2012).
[Crossref] [PubMed]

Karlsson, M.

Kuo, B. P.-P.

Lachinova, S.

Le Parquier, M.

A. Mussot, M. Le Parquier, and P. Szriftgiser, “Thermal noise for SBS suppression in fiber optical parametric amplifiers,” Opt. Commun. 283(12), 2607–2610 (2010).
[Crossref]

Leyva, V.

Loncar, M.

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref] [PubMed]

Mangano, J.

McComb, T. S.

McNaught, S. J.

Moore, G. T.

Moro, S.

Murphy, D. V.

Mussot, A.

A. Mussot, M. Le Parquier, and P. Szriftgiser, “Thermal noise for SBS suppression in fiber optical parametric amplifiers,” Opt. Commun. 283(12), 2607–2610 (2010).
[Crossref]

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]

Nilsson, J.

A. V. Harish and J. Nilsson, “Optimization of phase modulation formats for suppression of stimulated Brillouin scattering in optical fibers,” IEEE J. Sel. Topics in Quantum Elect. 24, 5100110 (2018).

A. V. Harish and J. Nilsson, “Optimization of phase modulation with arbitrary waveform generators for optical spectral control and suppression of stimulated Brillouin scattering,” Opt. Express 23(6), 6988–6999 (2015).
[Crossref] [PubMed]

Ovchinnikov, V.

Petersen, E.

A. Vasilyev, E. Petersen, N. Satyan, G. Rakuljic, A. Yariv, and J. O. White, “Coherent power combining of chirped-seed Erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 25(16), 1616–1618 (2013).
[Crossref]

E. Petersen, Z. Y. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[Crossref]

Polnau, E.

Pulford, B.

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combination of narrow-linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

Radic, S.

Rakuljic, G.

J. O. White, M. Harfouche, J. Edgecumbe, N. Satyan, G. Rakuljic, V. Jayaraman, C. Burgner, and A. Yariv, “1.6 kW Yb fiber amplifier using chirped seed amplification for stimulated Brillouin scattering suppression,” Appl. Opt. 56(3), B116–B122 (2017).
[Crossref] [PubMed]

A. Vasilyev, E. Petersen, N. Satyan, G. Rakuljic, A. Yariv, and J. O. White, “Coherent power combining of chirped-seed Erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 25(16), 1616–1618 (2013).
[Crossref]

E. Petersen, Z. Y. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[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]

Redmond, S. M.

Robertson, M.

V. Jayaraman, G. D. Cole, M. Robertson, C. Burgner, D. John, A. Uddin, and A. Cable, “Rapidly swept, ultra-widely-tunable 1060 nm MEMS-VCSELs,” Electron. Lett. 48(21), 1331–1333 (2012).
[Crossref] [PubMed]

Robin, C.

Rose, T. S.

Rothenberg, J. E.

Roy, R.

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band-shape and bandwidth modification,” Phys. Rev. A 26(1), 12–18 (1982).
[Crossref]

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]

Sanchez, A.

Satyan, N.

J. O. White, M. Harfouche, J. Edgecumbe, N. Satyan, G. Rakuljic, V. Jayaraman, C. Burgner, and A. Yariv, “1.6 kW Yb fiber amplifier using chirped seed amplification for stimulated Brillouin scattering suppression,” Appl. Opt. 56(3), B116–B122 (2017).
[Crossref] [PubMed]

E. Petersen, Z. Y. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[Crossref]

A. Vasilyev, E. Petersen, N. Satyan, G. Rakuljic, A. Yariv, and J. O. White, “Coherent power combining of chirped-seed Erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 25(16), 1616–1618 (2013).
[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]

Shams-Ansari, A.

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref] [PubMed]

Smith, S. J.

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band-shape and bandwidth modification,” Phys. Rev. A 26(1), 12–18 (1982).
[Crossref]

Supradeepa, V. R.

Szriftgiser, P.

A. Mussot, M. Le Parquier, and P. Szriftgiser, “Thermal noise for SBS suppression in fiber optical parametric amplifiers,” Opt. Commun. 283(12), 2607–2610 (2010).
[Crossref]

Thielen, P. A.

Uddin, A.

V. Jayaraman, G. D. Cole, M. Robertson, C. Burgner, D. John, A. Uddin, and A. Cable, “Rapidly swept, ultra-widely-tunable 1060 nm MEMS-VCSELs,” Electron. Lett. 48(21), 1331–1333 (2012).
[Crossref] [PubMed]

Vasilyev, A.

A. Vasilyev, E. Petersen, N. Satyan, G. Rakuljic, A. Yariv, and J. O. White, “Coherent power combining of chirped-seed Erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 25(16), 1616–1618 (2013).
[Crossref]

E. Petersen, Z. Y. Yang, N. Satyan, A. Vasilyev, G. Rakuljic, A. Yariv, and J. O. White, “Stimulated Brillouin scattering suppression with a chirped laser seed: comparison of dynamical model to experimental data,” IEEE J. Quantum Electron. 49(12), 1040–1044 (2013).
[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]

Vorontsov, M.

Wang, C.

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref] [PubMed]

Weber, M. E.

Weyrauch, T.

White, J. O.

J. O. White, M. Harfouche, J. Edgecumbe, N. Satyan, G. Rakuljic, V. Jayaraman, C. Burgner, and A. Yariv, “1.6 kW Yb fiber amplifier using chirped seed amplification for stimulated Brillouin scattering suppression,” Appl. Opt. 56(3), B116–B122 (2017).
[Crossref] [PubMed]

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Fringes occur in the raw triangle chirp spectrum due to the interference stemming from the same frequency occurring at two places in the period. For this reason, the raw spectrum has been smoothed on a very fine scale with a moving average over 69 MHz. This is close to the same averaging that will occur physically, by virtue of the 57.1 MHz Brillouin linewidth.

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Figures (11)

Fig. 1
Fig. 1 Phase (above) as a function of time, and frequency (below) as a function of time for the sawtooth (solid line) and triangle (dashed line) frequency chirp.
Fig. 2
Fig. 2 Frequency spectra associated with (1st row) a random phase walk (Lorentzian), (2nd row) a 0-π generic PRBS waveform (sinc2), (3rd row) random frequency modulation (Gaussian), (4th row) one period of a triangle chirp, and (5th row) one period of a sawtooth chirp. Plots in the left (right) column have a linear (log) vertical axis. The log scales all show three orders of magnitude variation. All spectra are normalized to have a total power of one and the same 85% width. The 90% (blue) and 95% (red) widths are also shown. The 90% width is omitted from the last rows.
Fig. 3
Fig. 3 Relationship between the fraction of total power contained within a spectral region and the characteristic width of the spectrum. Results are shown for the following spectra: Lorentzian, Gaussian, sinc2, and rectangular, produced by the phase modulation waveforms: random phase walk, random phase, PRBS, and piecewise parabolic. The characteristic widths are the Lorentzian FWHM, Gaussian FW1/e, PRBS modulation frequency, and the chirp times the period for the sawtooth. For example, 80% of the power in a Lorentzian is included in a region equal to ~3 × the FWHM.
Fig. 4
Fig. 4 (a) Threshold vs. the number of transits with 16 samples per period. (b) Threshold vs. the number of samples per period, for an average over 10 transits.
Fig. 5
Fig. 5 (a) Spectrum of 34 periods of a 23 ns sawtooth frequency chirp. (b) Spectrum of the resulting Stokes wave at threshold. (c) Time trace of the resulting Stokes power at threshold.
Fig. 6
Fig. 6 Backward Stokes power vs. incident laser power for waveforms with 85% bandwidths of 1.5 GHz (left to right): random walk phase, random phase, PRBS 5, PRBS 7, triangle chirp, sawtooth chirp. The latter two have a period of 23 ns.
Fig. 7
Fig. 7 Normalized threshold vs. the period, for the following waveforms: sawtooth frequency chirp, triangle frequency, PRBS 5, PRBS 7, random walk in phase, and random phase. All have an 85% bandwidth of 1.5 GHz. (Right axis) Maximum phase shift required for the chirped waveforms. Also indicated are 2π times the phonon lifetime, fiber transit time (43 ns), and round trip time.
Fig. 8
Fig. 8 Normalized threshold vs. the period for the same waveforms, with a 90% bandwidth of 1.5 GHz. (Right axis) Maximum phase shift required for the chirped waveforms.
Fig. 9
Fig. 9 Normalized threshold vs. the period for the same waveforms with a 95% bandwidth of 1.5 GHz. (Right axis) Maximum phase shift required for the chirped waveforms.
Fig. 10
Fig. 10 Normalized threshold as a function of cutoff frequency for a low-pass filter applied to the phase waveform, for six modulation formats, all with an 85% bandwidth of 1.5 GHz. The data for no filtering is depicted at 10 GHz.
Fig. 11
Fig. 11 The real part of the temporal coherence vs time delay, for six modulation formats in the same conditions as Fig. 10.

Tables (2)

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Table 1 Conversion factors used in comparing various spectra

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Table 2 Parameters used in model

Equations (1)

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g( τ )= E*( t )E( t+τ ) / E*( t )E( t ) .

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