Abstract

SPM is an important limitation in some fiber lasers and amplifier systems. In this paper, the influence of gain saturation on the SPM-induced spectral broadening for coherent and incoherent nanosecond pulses is discussed. The models of SPM-induced spectral broadening for coherent and incoherent nanosecond pulses are generalized to the amplification with gain saturation. Experiments are conducted to validate our theoretical analysis for incoherent nanosecond pulses in a super-luminescent diode seeded cascaded fiber amplifier system where pulses with high peak power and high pulse energy are generated and gain saturation occurs. Excellent agreements between theoretical analysis and experimental results are obtained, and the influence of higher order nonlinear terms on the SPM effect is observed and analyzed .

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Four-wave mixing in nanosecond pulsed fiber amplifiers

Jean-Philippe Fève, Paul E. Schrader, Roger L. Farrow, and Dahv A.V. Kliner
Opt. Express 15(8) 4647-4662 (2007)

Spectral broadening of incoherent nanosecond pulses in a fiber amplifier

Alexey G. Kuznetsov, Evgeniy V. Podivilov, and Sergey A. Babin
J. Opt. Soc. Am. B 29(6) 1231-1236 (2012)

Influence of pulse shape in self-phase-modulation-limited chirped pulse fiber amplifier systems

T. Schreiber, D. Schimpf, D. Müller, F. Röser, J. Limpert, and A. Tünnermann
J. Opt. Soc. Am. B 24(8) 1809-1814 (2007)

References

  • View by:
  • |
  • |
  • |

  1. S. T. Hendow and S. A. Shakir, “Structuring materials with nanosecond laser pulses,” Opt. Express 18(10), 10188–10199 (2010).
    [Crossref] [PubMed]
  2. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27(11), B63–B92 (2010).
    [Crossref]
  3. H. Kang, H. Zhang, and D. S. Wang, “Thermal-induced refractive-index planar waveguide laser,” Appl. Phys. Lett. 95(18), 181102 (2009).
    [Crossref]
  4. J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, “Extended single-mode photonic crystal fiber lasers,” Opt. Express 14(7), 2715–2720 (2006).
    [Crossref] [PubMed]
  5. C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
    [Crossref]
  6. K. K. Chen, J. H. V. Price, S. U. Alam, J. R. Hayes, D. Lin, A. Malinowski, and D. J. Richardson, “Polarisation maintaining 100W Yb-fiber MOPA producing µJ pulses tunable in duration from 1 to 21 ps,” Opt. Express 18(14), 14385–14394 (2010).
    [Crossref] [PubMed]
  7. G. M. Harry, “LIGO Scientific Collaboration. Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Gravity 27(8), 084006 (2010).
    [Crossref]
  8. N. E. Yu, J. W. Choi, H. Kang, D.-K. Ko, S.-H. Fu, J.-W. Liou, A. H. Kung, H. J. Choi, B. J. Kim, M. Cha, and L.-H. Peng, “Speckle noise reduction on a laser projection display via a broadband green light source,” Opt. Express 22(3), 3547–3556 (2014).
    [Crossref] [PubMed]
  9. D. A. V. Kliner, F. Di Teodoro, J. P. Koplow, S. W. Moore, and A. V. Smith, “Efficient second, third, fourth, and fifth harmonic generation of a Yb-doped fiber amplifier,” Opt. Commun. 210(3–6), 393–398 (2002).
    [Crossref]
  10. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
  11. S. C. Pinault and M. J. Potasek, “Frequency broadening by self-phase modulation in optical fibers,” J. Opt. Soc. Am. B 2(8), 1318–1319 (1985).
    [Crossref]
  12. J. T. Manassah, “Self-phase modulation of incoherent light revisited,” Opt. Lett. 16(21), 1638–1640 (1991).
    [Crossref] [PubMed]
  13. J. T. Manassah, “Self-phase modulation of incoherent light,” Opt. Lett. 15(6), 329–331 (1990).
    [Crossref] [PubMed]
  14. A. G. Kuznetsov, E. V. Podivilov, and S. A. Babin, “Spectral broadening of incoherent nanosecond pulses in a fiber amplifier,” J. Opt. Soc. Am. B 29(6), 1231–1236 (2012).
    [Crossref]
  15. A. Fernandez, S. Balac, A. Mugnier, F. Mahé, R. Texier-Picard, T. Chartier, and D. Pureur, “Numerical simulation of incoherent optical wave propagation in nonlinear fibers,” Eur. Phys. J. Appl. Phys. 64(2), 24506 (2013).
    [Crossref]
  16. J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985).
  17. D. N. Schimpf, C. Ruchert, D. Nodop, J. Limpert, A. Tünnermann, and F. Salin, “Compensation of pulse-distortion in saturated laser amplifiers,” Opt. Express 16(22), 17637–17646 (2008).
    [Crossref] [PubMed]
  18. A. E. Siegman, Lasers (University Science Books, 1986).

2014 (1)

2013 (2)

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

A. Fernandez, S. Balac, A. Mugnier, F. Mahé, R. Texier-Picard, T. Chartier, and D. Pureur, “Numerical simulation of incoherent optical wave propagation in nonlinear fibers,” Eur. Phys. J. Appl. Phys. 64(2), 24506 (2013).
[Crossref]

2012 (1)

2010 (4)

2009 (1)

H. Kang, H. Zhang, and D. S. Wang, “Thermal-induced refractive-index planar waveguide laser,” Appl. Phys. Lett. 95(18), 181102 (2009).
[Crossref]

2008 (1)

2006 (1)

2002 (1)

D. A. V. Kliner, F. Di Teodoro, J. P. Koplow, S. W. Moore, and A. V. Smith, “Efficient second, third, fourth, and fifth harmonic generation of a Yb-doped fiber amplifier,” Opt. Commun. 210(3–6), 393–398 (2002).
[Crossref]

1991 (1)

1990 (1)

1985 (1)

Alam, S. U.

Babin, S. A.

Balac, S.

A. Fernandez, S. Balac, A. Mugnier, F. Mahé, R. Texier-Picard, T. Chartier, and D. Pureur, “Numerical simulation of incoherent optical wave propagation in nonlinear fibers,” Eur. Phys. J. Appl. Phys. 64(2), 24506 (2013).
[Crossref]

Cha, M.

Chartier, T.

A. Fernandez, S. Balac, A. Mugnier, F. Mahé, R. Texier-Picard, T. Chartier, and D. Pureur, “Numerical simulation of incoherent optical wave propagation in nonlinear fibers,” Eur. Phys. J. Appl. Phys. 64(2), 24506 (2013).
[Crossref]

Chen, K. K.

Choi, H. J.

Choi, J. W.

Clarkson, W. A.

Di Teodoro, F.

D. A. V. Kliner, F. Di Teodoro, J. P. Koplow, S. W. Moore, and A. V. Smith, “Efficient second, third, fourth, and fifth harmonic generation of a Yb-doped fiber amplifier,” Opt. Commun. 210(3–6), 393–398 (2002).
[Crossref]

Ermeneux, S.

Fernandez, A.

A. Fernandez, S. Balac, A. Mugnier, F. Mahé, R. Texier-Picard, T. Chartier, and D. Pureur, “Numerical simulation of incoherent optical wave propagation in nonlinear fibers,” Eur. Phys. J. Appl. Phys. 64(2), 24506 (2013).
[Crossref]

Fu, S.-H.

Harry, G. M.

G. M. Harry, “LIGO Scientific Collaboration. Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Gravity 27(8), 084006 (2010).
[Crossref]

Hayes, J. R.

Hendow, S. T.

Jauregui, C.

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

Kang, H.

Kim, B. J.

Kliner, D. A. V.

D. A. V. Kliner, F. Di Teodoro, J. P. Koplow, S. W. Moore, and A. V. Smith, “Efficient second, third, fourth, and fifth harmonic generation of a Yb-doped fiber amplifier,” Opt. Commun. 210(3–6), 393–398 (2002).
[Crossref]

Ko, D.-K.

Koplow, J. P.

D. A. V. Kliner, F. Di Teodoro, J. P. Koplow, S. W. Moore, and A. V. Smith, “Efficient second, third, fourth, and fifth harmonic generation of a Yb-doped fiber amplifier,” Opt. Commun. 210(3–6), 393–398 (2002).
[Crossref]

Kung, A. H.

Kuznetsov, A. G.

Limpert, J.

Lin, D.

Liou, J.-W.

Mahé, F.

A. Fernandez, S. Balac, A. Mugnier, F. Mahé, R. Texier-Picard, T. Chartier, and D. Pureur, “Numerical simulation of incoherent optical wave propagation in nonlinear fibers,” Eur. Phys. J. Appl. Phys. 64(2), 24506 (2013).
[Crossref]

Malinowski, A.

Manassah, J. T.

Moore, S. W.

D. A. V. Kliner, F. Di Teodoro, J. P. Koplow, S. W. Moore, and A. V. Smith, “Efficient second, third, fourth, and fifth harmonic generation of a Yb-doped fiber amplifier,” Opt. Commun. 210(3–6), 393–398 (2002).
[Crossref]

Mugnier, A.

A. Fernandez, S. Balac, A. Mugnier, F. Mahé, R. Texier-Picard, T. Chartier, and D. Pureur, “Numerical simulation of incoherent optical wave propagation in nonlinear fibers,” Eur. Phys. J. Appl. Phys. 64(2), 24506 (2013).
[Crossref]

Nilsson, J.

Nodop, D.

Peng, L.-H.

Pinault, S. C.

Podivilov, E. V.

Potasek, M. J.

Price, J. H. V.

Pureur, D.

A. Fernandez, S. Balac, A. Mugnier, F. Mahé, R. Texier-Picard, T. Chartier, and D. Pureur, “Numerical simulation of incoherent optical wave propagation in nonlinear fibers,” Eur. Phys. J. Appl. Phys. 64(2), 24506 (2013).
[Crossref]

Richardson, D. J.

Röser, F.

Rothhardt, J.

Ruchert, C.

Salin, F.

Schimpf, D. N.

Schmidt, O.

Schreiber, T.

Shakir, S. A.

Smith, A. V.

D. A. V. Kliner, F. Di Teodoro, J. P. Koplow, S. W. Moore, and A. V. Smith, “Efficient second, third, fourth, and fifth harmonic generation of a Yb-doped fiber amplifier,” Opt. Commun. 210(3–6), 393–398 (2002).
[Crossref]

Texier-Picard, R.

A. Fernandez, S. Balac, A. Mugnier, F. Mahé, R. Texier-Picard, T. Chartier, and D. Pureur, “Numerical simulation of incoherent optical wave propagation in nonlinear fibers,” Eur. Phys. J. Appl. Phys. 64(2), 24506 (2013).
[Crossref]

Tünnermann, A.

Wang, D. S.

H. Kang, H. Zhang, and D. S. Wang, “Thermal-induced refractive-index planar waveguide laser,” Appl. Phys. Lett. 95(18), 181102 (2009).
[Crossref]

Yu, N. E.

Yvernault, P.

Zhang, H.

H. Kang, H. Zhang, and D. S. Wang, “Thermal-induced refractive-index planar waveguide laser,” Appl. Phys. Lett. 95(18), 181102 (2009).
[Crossref]

Appl. Phys. Lett. (1)

H. Kang, H. Zhang, and D. S. Wang, “Thermal-induced refractive-index planar waveguide laser,” Appl. Phys. Lett. 95(18), 181102 (2009).
[Crossref]

Class. Quantum Gravity (1)

G. M. Harry, “LIGO Scientific Collaboration. Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Gravity 27(8), 084006 (2010).
[Crossref]

Eur. Phys. J. Appl. Phys. (1)

A. Fernandez, S. Balac, A. Mugnier, F. Mahé, R. Texier-Picard, T. Chartier, and D. Pureur, “Numerical simulation of incoherent optical wave propagation in nonlinear fibers,” Eur. Phys. J. Appl. Phys. 64(2), 24506 (2013).
[Crossref]

J. Opt. Soc. Am. B (3)

Nat. Photonics (1)

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

Opt. Commun. (1)

D. A. V. Kliner, F. Di Teodoro, J. P. Koplow, S. W. Moore, and A. V. Smith, “Efficient second, third, fourth, and fifth harmonic generation of a Yb-doped fiber amplifier,” Opt. Commun. 210(3–6), 393–398 (2002).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

A. E. Siegman, Lasers (University Science Books, 1986).

J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1 Experimental setup
Fig. 2
Fig. 2 (a) The power gain evolution along the fiber calculated with gain saturation (solid) and with small-signal (dashed) model for leading edge and trailing edge of the pulse respectively; the inset is input (blue dashed) and output pulse shape (red solid) of the 15/130 μm fiber amplifier stage, and the predicted output pulse shape (red dot-dashed) with Eq. (7); (b) the effective length as a function of T with (red dot-dashed) and without gain saturation (blue dashed) in consideration, and the difference between two models (black solid); (c) the measured and calculated output spectrum with small-signal model and gain saturation model together with the measured input spectrum; (d) the measured spectral broadening factors as a function of peak power, compared with the calculated results from our extended model and small-signal model.
Fig. 3
Fig. 3 (a)At pulse energy of 0.324 mJ, the RMS bandwidth of the output spectrum as a function of γ' ; the inset is experimental results (red star) compared with the predicted results of our original model (black dot); (b) the measured output spectrum at peak power of 25 kW, compared with the predicted spectrum calculated by gain saturation model and the small-signal model with γ' ; (c) the measured output spectrum at peak power of 50 kW, compared with the predicted spectrum calculated by gain saturation model and the small-signal model with γ' ; (d) the measured and calculated broadening factors as a function of peak power, and compared with the calculated results in small-signal model.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

i A(z,T) z =i g(z,T) 2 A(z,T)γ | A(z,T) | 2 A(z,T)
A(z,T)= G(z,T) A(0,T)exp[iγP(0,T) L eff (z,T)]
G(z,T)= P(z,T) P(0,T) =exp( 0 z g(z',T)dz ')
L eff (z,T)= 0 z G(z',T)dz'
I(z,ω)= | FT[A(z,T)] | 2 ,
I(z,ω)= 1 2π + dTG(z,T)P(0,T) + dτ κ(0,τ) e iω'τ [1+ (γP(0,T) L eff (z,T)) 2 (1 | κ(0,τ) | 2 )] 2
P(z,T)= P(0,T) 1[1exp( g 0 z)]exp( E sat 1 T P(0,t) dt)
G(z,T)= P(z,T) P(0,T) = 1 1[1exp( g 0 z)]exp( E sat 1 T P(0,t) dt)
L eff (z,T)= 0 z 1 1[1exp( g 0 z')]exp( E sat 1 T P(0,t) dt) dz'

Metrics