Abstract

The theoretical research of supercontinuum (SC) generation in a fiber amplifier system has been seldom reported. For the purpose of further understanding the mechanism of SC generation in fiber amplifiers, we propose a combined numerical model of the laser rate equations and the generalized non-linear Schrödinger equation to simulate the amplification of 1060 nm picosecond pulses and their spectral broadening in an ytterbium-doped fiber amplifier. The calculation results of this model are compared with the experimental results under the same conditions and a good agreement is achieved. We find that the pulse is gain amplified initially, and then dominated by stimulated Raman scattering in the normal dispersion region. In anomalous dispersion region, modulation instability, higher-order soliton fission and soliton self-frequency shift dominates the spectral broadening. It is found numerically and experimentally that the length of the gain fiber and the 976 nm pump power are the most imperative parameters to control the output power, spectral range and flatness of the SC. The pulse width of signal pulse also plays a part in influencing SC generation. The results verify that our model is promising for analyzing the physical processes of pulse evolution and SC generation in a fiber amplifier system.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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2014 (1)

2013 (4)

K. Yin, B. Zhang, W. Yang, H. Chen, and J. Hou, “Over an octave cascaded Raman scattering in short highly germanium-doped silica fiber,” Opt. Express 21(13), 15987–15997 (2013).
[Crossref] [PubMed]

R. Song, J. Hou, T. Liu, W. Q. Yang, and Q. S. Lu, “A hundreds of watt all-fiber near-infrared supercontinuum,” Laser Phys. Lett. 10(6), 065402 (2013).
[Crossref]

R. Song, J. Hou, Z. F. Wang, R. Xiao, and Q. S. Lu, “Effect of initial chirp on near-infrared supercontinuum generation by a nanosecond pulse in a nonlinear fiber amplifier,” Chin. Phys. B 22(8), 084206 (2013).
[Crossref]

J. Lægsgaard and H. Tu, “How long wavelengths can one extract from silica-core fibers?” Opt. Lett. 38(21), 4518–4521 (2013).
[Crossref] [PubMed]

2012 (2)

2010 (1)

S. M. Kobtsev and S. V. Kukarin, “All-fiber Raman supercontinuum generator,” Laser Phys. 20(2), 372–374 (2010).
[Crossref]

2009 (1)

S. M. Kobtsev and S. V. Kukarin, “Spectral broadening of femtosecond pulses in a nonlinear optical fiber amplifier,” Opt. Spectrosc. 107(3), 344–346 (2009).
[Crossref]

2007 (1)

2003 (1)

Ankudinov, I.

Champert, P. A.

Chen, H.

Chen, S.

Couderc, V.

Deng, Y.

Holzlohner, R.

Hou, J.

R. Song, J. Hou, Z. F. Wang, R. Xiao, and Q. S. Lu, “Effect of initial chirp on near-infrared supercontinuum generation by a nanosecond pulse in a nonlinear fiber amplifier,” Chin. Phys. B 22(8), 084206 (2013).
[Crossref]

R. Song, J. Hou, T. Liu, W. Q. Yang, and Q. S. Lu, “A hundreds of watt all-fiber near-infrared supercontinuum,” Laser Phys. Lett. 10(6), 065402 (2013).
[Crossref]

K. Yin, B. Zhang, W. Yang, H. Chen, and J. Hou, “Over an octave cascaded Raman scattering in short highly germanium-doped silica fiber,” Opt. Express 21(13), 15987–15997 (2013).
[Crossref] [PubMed]

R. Song, J. Hou, S. Chen, W. Yang, and Q. Lu, “High power supercontinuum generation in a nonlinear ytterbium-doped fiber amplifier,” Opt. Lett. 37(9), 1529–1531 (2012).
[Crossref] [PubMed]

Huang, Z.

Kobtsev, S.

Kobtsev, S. M.

S. M. Kobtsev and S. V. Kukarin, “All-fiber Raman supercontinuum generator,” Laser Phys. 20(2), 372–374 (2010).
[Crossref]

S. M. Kobtsev and S. V. Kukarin, “Spectral broadening of femtosecond pulses in a nonlinear optical fiber amplifier,” Opt. Spectrosc. 107(3), 344–346 (2009).
[Crossref]

Kukarin, S.

Kukarin, S. V.

S. M. Kobtsev and S. V. Kukarin, “All-fiber Raman supercontinuum generator,” Laser Phys. 20(2), 372–374 (2010).
[Crossref]

S. M. Kobtsev and S. V. Kukarin, “Spectral broadening of femtosecond pulses in a nonlinear optical fiber amplifier,” Opt. Spectrosc. 107(3), 344–346 (2009).
[Crossref]

Lægsgaard, J.

Leproux, P.

Lin, H.

Liu, T.

R. Song, J. Hou, T. Liu, W. Q. Yang, and Q. S. Lu, “A hundreds of watt all-fiber near-infrared supercontinuum,” Laser Phys. Lett. 10(6), 065402 (2013).
[Crossref]

Lu, Q.

Lu, Q. S.

R. Song, J. Hou, Z. F. Wang, R. Xiao, and Q. S. Lu, “Effect of initial chirp on near-infrared supercontinuum generation by a nanosecond pulse in a nonlinear fiber amplifier,” Chin. Phys. B 22(8), 084206 (2013).
[Crossref]

R. Song, J. Hou, T. Liu, W. Q. Yang, and Q. S. Lu, “A hundreds of watt all-fiber near-infrared supercontinuum,” Laser Phys. Lett. 10(6), 065402 (2013).
[Crossref]

Menyuk, C. R.

Pioger, P. H.

Sinkin, O. V.

Smirnov, S.

Song, R.

R. Song, J. Hou, Z. F. Wang, R. Xiao, and Q. S. Lu, “Effect of initial chirp on near-infrared supercontinuum generation by a nanosecond pulse in a nonlinear fiber amplifier,” Chin. Phys. B 22(8), 084206 (2013).
[Crossref]

R. Song, J. Hou, T. Liu, W. Q. Yang, and Q. S. Lu, “A hundreds of watt all-fiber near-infrared supercontinuum,” Laser Phys. Lett. 10(6), 065402 (2013).
[Crossref]

R. Song, J. Hou, S. Chen, W. Yang, and Q. Lu, “High power supercontinuum generation in a nonlinear ytterbium-doped fiber amplifier,” Opt. Lett. 37(9), 1529–1531 (2012).
[Crossref] [PubMed]

Tu, H.

Wang, J.

Wang, Z. F.

R. Song, J. Hou, Z. F. Wang, R. Xiao, and Q. S. Lu, “Effect of initial chirp on near-infrared supercontinuum generation by a nanosecond pulse in a nonlinear fiber amplifier,” Chin. Phys. B 22(8), 084206 (2013).
[Crossref]

Wei, X.

Xiao, R.

R. Song, J. Hou, Z. F. Wang, R. Xiao, and Q. S. Lu, “Effect of initial chirp on near-infrared supercontinuum generation by a nanosecond pulse in a nonlinear fiber amplifier,” Chin. Phys. B 22(8), 084206 (2013).
[Crossref]

Xu, D.

Yang, W.

Yang, W. Q.

R. Song, J. Hou, T. Liu, W. Q. Yang, and Q. S. Lu, “A hundreds of watt all-fiber near-infrared supercontinuum,” Laser Phys. Lett. 10(6), 065402 (2013).
[Crossref]

Yin, K.

Zhang, B.

Zhang, R.

Zweck, J.

Chin. Phys. B (1)

R. Song, J. Hou, Z. F. Wang, R. Xiao, and Q. S. Lu, “Effect of initial chirp on near-infrared supercontinuum generation by a nanosecond pulse in a nonlinear fiber amplifier,” Chin. Phys. B 22(8), 084206 (2013).
[Crossref]

J. Lightwave Technol. (1)

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

Laser Phys. (1)

S. M. Kobtsev and S. V. Kukarin, “All-fiber Raman supercontinuum generator,” Laser Phys. 20(2), 372–374 (2010).
[Crossref]

Laser Phys. Lett. (1)

R. Song, J. Hou, T. Liu, W. Q. Yang, and Q. S. Lu, “A hundreds of watt all-fiber near-infrared supercontinuum,” Laser Phys. Lett. 10(6), 065402 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Opt. Spectrosc. (1)

S. M. Kobtsev and S. V. Kukarin, “Spectral broadening of femtosecond pulses in a nonlinear optical fiber amplifier,” Opt. Spectrosc. 107(3), 344–346 (2009).
[Crossref]

Other (2)

G. P. Agrawal, Applications of nonlinear fiber optics (Academic, 2010).

G. P. Agrawal, Nonlinear fiber optics (Academic, 2013).

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Figures (15)

Fig. 1
Fig. 1 Schematic steps of numerical simulation of propagation of pulses in YDFA
Fig. 2
Fig. 2 (a) The dispersion curve and (b) the loss curve of the YDF
Fig. 3
Fig. 3 The simulation results of SC generation from an YDFA (5 m gain fiber) (a) the output power for different pulses (b) the output spectrum for the 68th pulse
Fig. 4
Fig. 4 The experimental setup: Isolator (ISO), bandpass filter (BPF), laser diode (LD, 976 nm), and wavelength division multiplexer (WDM)
Fig. 5
Fig. 5 The comparison between the simulated and experimental result
Fig. 6
Fig. 6 The calculation results in pulse iterative calculation process (8 m gain fiber) (a) the output power (b) the residual pump power (c) the peak intensity in time domain at the end of the gain fiber (d) the gain factor along the fiber length
Fig. 7
Fig. 7 The evolution of the spectrum and the time domain along the fiber length (the 68th pulse - the last calculation pulse)
Fig. 8
Fig. 8 The calculation results for different gain fiber lengths (a) the evolution of the spectrum along the 5 m fiber length (b) the evolution of the spectrum along the 8 m fiber length (c) the final output spectrum comparison between two fiber lengths
Fig. 9
Fig. 9 Experimental results for different gain fiber lengths (a) the output power of the SC source versus the incident pump power under different fiber lengths (b) The output spectra of the SC source with maximum output power (The legend is the maximum average output power when the 976 nm pump power is 25 W)
Fig. 10
Fig. 10 (a) The calculated spectra of the SC source when the length of the gain fiber is 5 m (b) (c) The experimental output spectra of the SC source when the length of the gain fiber is 15 m (Legend: output power (pump power))
Fig. 11
Fig. 11 Output powers for different pulse number with (a) 30 ps, (b) 10ps and (c) 1ps pulse width.
Fig. 12
Fig. 12 The (a)-(c) time domain (a) and (d)-(f) frequency domain of the last calculated pulse at the end of fiber length.
Fig. 13
Fig. 13 The experimental setup: Isolator (ISO), bandpass filter (BPF), laser diode (LD, 976 nm), wavelength division multiplexer (WDM) and mode field adapter (MFA).
Fig. 14
Fig. 14 The temporal (a)-(c) and spectral (d)-(f) properties of seed A, B and C
Fig. 15
Fig. 15 Experimental results of different signals: (a) the spectrum and output power of three seed signals after two preamplifiers (b) the output power of three signals versus pump power from the last-stage amplifier (c) (d) output spectra from the last-stage amplifier pumped by seed-A with corresponding output powers (e) the comparison of the final spectra with maximum output power pumped by seed A, B and C.

Tables (2)

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Table 1 Parameters Used in the Simulation

Tables Icon

Table 2 Parameters of Three Pulses

Equations (15)

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A z + α 2 Ai k1 i k β k k! k A t k =iγ( 1+ i ω 0 t )[ A( z,t ) R( t ' )| A( z,t t ' ) | 2 d t ' ]
d N 2 (z,t) dt = Γ p λ p hcA [ σ a ( λ p ) N 1 (z,t) σ e ( λ p ) N 2 (z,t) ] P p (z,t) + 1 hcA k=1 K Γ k λ k [ σ a ( λ k ) N 1 (z,t) σ e ( λ k ) N 2 (z,t) ] P(z,t, λ k ) N 2 (z,t) τ
N= N 1 + N 2
P p (z,t) z + 1 v p P p (z,t) t = Γ p [ σ e ( λ p ) N 2 (z,t) σ a ( λ p ) N 1 (z,t) ]P(z,t, λ k ) α( λ p )P(z,t, λ p )
P(z,t) z + 1 v k P(z,t, λ k ) t = Γ k [ σ e ( λ k ) N 2 (z,t) σ a ( λ k ) N 1 (z,t) ]P(z,t, λ k ) α( λ k )P(z,t, λ k )+2 σ e ( λ k ) N 2 (z,t) h c 2 λ k 3 Δλ
P(z,t) z + 1 v k P(z,t, λ k ) t = Γ k [ σ e ( λ k ) N 2 (z,t) σ a ( λ k ) N 1 (z,t) ]P(z,t, λ k ) α( λ k )P(z,t, λ k )
P(z,t, λ k ) z ={ Γ k [ σ e ( λ k ) N 2 (z,t) σ a ( λ k ) N 1 (z,t) ]α( λ k ) }P(z,t, λ k )
T=t z λ k
G(z,t, λ k )= Γ k [ σ e ( λ k ) N 2 (z,t) σ a ( λ k ) N 1 (z,t) ]α( λ k )
P(z,t, λ k ) z =G(z,t, λ k ) P(z,t, λ k ) z P(z+dz,t, λ k ) e G(z,t, λ k )dz P(z,t, λ k )
G 0 = Γ k [ σ e ( λ k ) N 2 (z,t) σ a ( λ k ) N 1 (z,t) ]exp( 1 E s t | A(z,t) | 2 dt )α( λ k )
A ˜ (z+dz,t, λ k ) e G 0 (z,t, λ k )dz/2 A ˜ (z,t, λ k )
E= T T P(t)dt
P ave =E f rep
α(dB/m)= k 0 N Γ p σ a

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