Abstract

The effect of cavity dispersion on the dynamics of bound soliton states in a fiber laser has been studied both experimentally and numerically. The mode-locking mechanism in a laser was provided by the frequency-shifted feedback to avoid the influence of soliton attraction that could be induced by saturable absorption. It was found that phase-locked bound solitons are stable for dispersion below the “threshold” value of 0.2 ps/nm which depends on the other cavity parameters. For higher dispersion the bound states collapse resulting in the multiple weakly-interacting soliton regime, circulating randomly within the cavity.

© 2014 Optical Society of America

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References

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  1. D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, H. Y. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68(1), 013816 (2003).
    [CrossRef]
  2. B. Ortaç, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16(5), 1274–1276 (2004).
    [CrossRef]
  3. D. Y. Tang, L. M. Zhao, B. Zhao, “Multipulse bound solitons with fixed pulse separations formed by direct soliton interaction,” Appl. Phys. B 80(2), 239–242 (2005).
    [CrossRef]
  4. L. M. Zhao, D. Y. Tang, T. H. Cheng, H. Y. Tam, C. Lu, “Bound states of dispersion-managed solitons in a fiber laser at near zero dispersion,” Appl. Opt. 46(21), 4768–4773 (2007).
    [CrossRef] [PubMed]
  5. R. Gumenyuk, O. G. Okhotnikov, “Polarization control of bound state of vector soliton,” Laser Phys. Lett. 10(5), 055111 (2013).
    [CrossRef]
  6. L. Gui, X. Xiao, C. Yang, “Observation of various bound solitons in a carbon-nanotube-based erbium fiber laser,” J. Opt. Soc. Am. B 30(1), 158–164 (2013).
    [CrossRef]
  7. Y. Gong, P. Shum, T. H. Cheng, Q. Wen, D. Tang, “Bound soliton pulses in passively mode-locked fiber laser,” Opt. Commun. 200(1-6), 389–399 (2001).
    [CrossRef]
  8. P. Grelu, F. Belhache, F. Gutty, J. M. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20(5), 863–870 (2003).
    [CrossRef]
  9. X. Wu, D. Y. Tang, X. N. Luan, Q. Zhang, “Bound states of solitons in a fiber laser mode-locked with carbon nanotubes saturable absorber,” Opt. Commun. 284(14), 3615–3618 (2011).
    [CrossRef]
  10. R. Gumenyuk, O. G. Okhotnikov, “Temporal control of vector soliton bunching by slow/fast saturable absorption,” J. Opt. Soc. Am. B 29(1), 1–7 (2012).
    [CrossRef]
  11. R. Gumenyuk, O. G. Okhotnikov, “Impact of gain medium dispersion on stability of soliton bound states in fiber laser,” IEEE Photon. Technol. Lett. 25(2), 133–135 (2013).
    [CrossRef]
  12. R. Gumenyuk, O. G. Okhotnikov, “Multiple solitons grouping in fiber lasers by dispersion management and nonlinearity control,” J. Opt. Soc. Am. B 30(4), 776–781 (2013).
    [CrossRef]
  13. S. U. Alam, A. B. Grudinin, “Tunable picoseconds frequency-shifted feedback fiber laser at 1550 nm,” IEEE Photon. Technol. Lett. 16(9), 2012–2014 (2004).
    [CrossRef]
  14. J. M. Sousa, O. G. Okhotnikov, “Short pulse generation and control in Er-doped frequency-shifted-feedback fibre lasers,” Opt. Commun. 183(1-4), 227–241 (2000).
    [CrossRef]
  15. Y. Kodama, S. Wabnitz, “Reduction and suppression of soliton interactions by bandpass filter,” Opt. Lett. 18, 1311–1313 (1993).
    [CrossRef] [PubMed]

2013 (4)

R. Gumenyuk, O. G. Okhotnikov, “Polarization control of bound state of vector soliton,” Laser Phys. Lett. 10(5), 055111 (2013).
[CrossRef]

L. Gui, X. Xiao, C. Yang, “Observation of various bound solitons in a carbon-nanotube-based erbium fiber laser,” J. Opt. Soc. Am. B 30(1), 158–164 (2013).
[CrossRef]

R. Gumenyuk, O. G. Okhotnikov, “Impact of gain medium dispersion on stability of soliton bound states in fiber laser,” IEEE Photon. Technol. Lett. 25(2), 133–135 (2013).
[CrossRef]

R. Gumenyuk, O. G. Okhotnikov, “Multiple solitons grouping in fiber lasers by dispersion management and nonlinearity control,” J. Opt. Soc. Am. B 30(4), 776–781 (2013).
[CrossRef]

2012 (1)

2011 (1)

X. Wu, D. Y. Tang, X. N. Luan, Q. Zhang, “Bound states of solitons in a fiber laser mode-locked with carbon nanotubes saturable absorber,” Opt. Commun. 284(14), 3615–3618 (2011).
[CrossRef]

2007 (1)

2005 (1)

D. Y. Tang, L. M. Zhao, B. Zhao, “Multipulse bound solitons with fixed pulse separations formed by direct soliton interaction,” Appl. Phys. B 80(2), 239–242 (2005).
[CrossRef]

2004 (2)

B. Ortaç, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16(5), 1274–1276 (2004).
[CrossRef]

S. U. Alam, A. B. Grudinin, “Tunable picoseconds frequency-shifted feedback fiber laser at 1550 nm,” IEEE Photon. Technol. Lett. 16(9), 2012–2014 (2004).
[CrossRef]

2003 (2)

D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, H. Y. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68(1), 013816 (2003).
[CrossRef]

P. Grelu, F. Belhache, F. Gutty, J. M. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20(5), 863–870 (2003).
[CrossRef]

2001 (1)

Y. Gong, P. Shum, T. H. Cheng, Q. Wen, D. Tang, “Bound soliton pulses in passively mode-locked fiber laser,” Opt. Commun. 200(1-6), 389–399 (2001).
[CrossRef]

2000 (1)

J. M. Sousa, O. G. Okhotnikov, “Short pulse generation and control in Er-doped frequency-shifted-feedback fibre lasers,” Opt. Commun. 183(1-4), 227–241 (2000).
[CrossRef]

1993 (1)

Alam, S. U.

S. U. Alam, A. B. Grudinin, “Tunable picoseconds frequency-shifted feedback fiber laser at 1550 nm,” IEEE Photon. Technol. Lett. 16(9), 2012–2014 (2004).
[CrossRef]

Belhache, F.

Brunel, M.

B. Ortaç, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16(5), 1274–1276 (2004).
[CrossRef]

Chartier, T.

B. Ortaç, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16(5), 1274–1276 (2004).
[CrossRef]

Cheng, T. H.

L. M. Zhao, D. Y. Tang, T. H. Cheng, H. Y. Tam, C. Lu, “Bound states of dispersion-managed solitons in a fiber laser at near zero dispersion,” Appl. Opt. 46(21), 4768–4773 (2007).
[CrossRef] [PubMed]

Y. Gong, P. Shum, T. H. Cheng, Q. Wen, D. Tang, “Bound soliton pulses in passively mode-locked fiber laser,” Opt. Commun. 200(1-6), 389–399 (2001).
[CrossRef]

Gong, Y.

Y. Gong, P. Shum, T. H. Cheng, Q. Wen, D. Tang, “Bound soliton pulses in passively mode-locked fiber laser,” Opt. Commun. 200(1-6), 389–399 (2001).
[CrossRef]

Grelu, P.

B. Ortaç, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16(5), 1274–1276 (2004).
[CrossRef]

P. Grelu, F. Belhache, F. Gutty, J. M. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20(5), 863–870 (2003).
[CrossRef]

Grudinin, A. B.

S. U. Alam, A. B. Grudinin, “Tunable picoseconds frequency-shifted feedback fiber laser at 1550 nm,” IEEE Photon. Technol. Lett. 16(9), 2012–2014 (2004).
[CrossRef]

Gui, L.

Gumenyuk, R.

R. Gumenyuk, O. G. Okhotnikov, “Multiple solitons grouping in fiber lasers by dispersion management and nonlinearity control,” J. Opt. Soc. Am. B 30(4), 776–781 (2013).
[CrossRef]

R. Gumenyuk, O. G. Okhotnikov, “Polarization control of bound state of vector soliton,” Laser Phys. Lett. 10(5), 055111 (2013).
[CrossRef]

R. Gumenyuk, O. G. Okhotnikov, “Impact of gain medium dispersion on stability of soliton bound states in fiber laser,” IEEE Photon. Technol. Lett. 25(2), 133–135 (2013).
[CrossRef]

R. Gumenyuk, O. G. Okhotnikov, “Temporal control of vector soliton bunching by slow/fast saturable absorption,” J. Opt. Soc. Am. B 29(1), 1–7 (2012).
[CrossRef]

Gutty, F.

Hideur, A.

B. Ortaç, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16(5), 1274–1276 (2004).
[CrossRef]

Kodama, Y.

Leblond, H.

B. Ortaç, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16(5), 1274–1276 (2004).
[CrossRef]

Lu, C.

L. M. Zhao, D. Y. Tang, T. H. Cheng, H. Y. Tam, C. Lu, “Bound states of dispersion-managed solitons in a fiber laser at near zero dispersion,” Appl. Opt. 46(21), 4768–4773 (2007).
[CrossRef] [PubMed]

D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, H. Y. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68(1), 013816 (2003).
[CrossRef]

Luan, X. N.

X. Wu, D. Y. Tang, X. N. Luan, Q. Zhang, “Bound states of solitons in a fiber laser mode-locked with carbon nanotubes saturable absorber,” Opt. Commun. 284(14), 3615–3618 (2011).
[CrossRef]

Man, W. S.

D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, H. Y. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68(1), 013816 (2003).
[CrossRef]

Okhotnikov, O. G.

R. Gumenyuk, O. G. Okhotnikov, “Impact of gain medium dispersion on stability of soliton bound states in fiber laser,” IEEE Photon. Technol. Lett. 25(2), 133–135 (2013).
[CrossRef]

R. Gumenyuk, O. G. Okhotnikov, “Polarization control of bound state of vector soliton,” Laser Phys. Lett. 10(5), 055111 (2013).
[CrossRef]

R. Gumenyuk, O. G. Okhotnikov, “Multiple solitons grouping in fiber lasers by dispersion management and nonlinearity control,” J. Opt. Soc. Am. B 30(4), 776–781 (2013).
[CrossRef]

R. Gumenyuk, O. G. Okhotnikov, “Temporal control of vector soliton bunching by slow/fast saturable absorption,” J. Opt. Soc. Am. B 29(1), 1–7 (2012).
[CrossRef]

J. M. Sousa, O. G. Okhotnikov, “Short pulse generation and control in Er-doped frequency-shifted-feedback fibre lasers,” Opt. Commun. 183(1-4), 227–241 (2000).
[CrossRef]

Ortaç, B.

B. Ortaç, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16(5), 1274–1276 (2004).
[CrossRef]

Sanchez, F.

B. Ortaç, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16(5), 1274–1276 (2004).
[CrossRef]

Shen, D. Y.

D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, H. Y. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68(1), 013816 (2003).
[CrossRef]

Shum, P.

Y. Gong, P. Shum, T. H. Cheng, Q. Wen, D. Tang, “Bound soliton pulses in passively mode-locked fiber laser,” Opt. Commun. 200(1-6), 389–399 (2001).
[CrossRef]

Soto-Crespo, J. M.

Sousa, J. M.

J. M. Sousa, O. G. Okhotnikov, “Short pulse generation and control in Er-doped frequency-shifted-feedback fibre lasers,” Opt. Commun. 183(1-4), 227–241 (2000).
[CrossRef]

Tam, H. Y.

L. M. Zhao, D. Y. Tang, T. H. Cheng, H. Y. Tam, C. Lu, “Bound states of dispersion-managed solitons in a fiber laser at near zero dispersion,” Appl. Opt. 46(21), 4768–4773 (2007).
[CrossRef] [PubMed]

D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, H. Y. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68(1), 013816 (2003).
[CrossRef]

Tang, D.

Y. Gong, P. Shum, T. H. Cheng, Q. Wen, D. Tang, “Bound soliton pulses in passively mode-locked fiber laser,” Opt. Commun. 200(1-6), 389–399 (2001).
[CrossRef]

Tang, D. Y.

X. Wu, D. Y. Tang, X. N. Luan, Q. Zhang, “Bound states of solitons in a fiber laser mode-locked with carbon nanotubes saturable absorber,” Opt. Commun. 284(14), 3615–3618 (2011).
[CrossRef]

L. M. Zhao, D. Y. Tang, T. H. Cheng, H. Y. Tam, C. Lu, “Bound states of dispersion-managed solitons in a fiber laser at near zero dispersion,” Appl. Opt. 46(21), 4768–4773 (2007).
[CrossRef] [PubMed]

D. Y. Tang, L. M. Zhao, B. Zhao, “Multipulse bound solitons with fixed pulse separations formed by direct soliton interaction,” Appl. Phys. B 80(2), 239–242 (2005).
[CrossRef]

D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, H. Y. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68(1), 013816 (2003).
[CrossRef]

Wabnitz, S.

Wen, Q.

Y. Gong, P. Shum, T. H. Cheng, Q. Wen, D. Tang, “Bound soliton pulses in passively mode-locked fiber laser,” Opt. Commun. 200(1-6), 389–399 (2001).
[CrossRef]

Wu, X.

X. Wu, D. Y. Tang, X. N. Luan, Q. Zhang, “Bound states of solitons in a fiber laser mode-locked with carbon nanotubes saturable absorber,” Opt. Commun. 284(14), 3615–3618 (2011).
[CrossRef]

Xiao, X.

Yang, C.

Zhang, Q.

X. Wu, D. Y. Tang, X. N. Luan, Q. Zhang, “Bound states of solitons in a fiber laser mode-locked with carbon nanotubes saturable absorber,” Opt. Commun. 284(14), 3615–3618 (2011).
[CrossRef]

Zhao, B.

D. Y. Tang, L. M. Zhao, B. Zhao, “Multipulse bound solitons with fixed pulse separations formed by direct soliton interaction,” Appl. Phys. B 80(2), 239–242 (2005).
[CrossRef]

D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, H. Y. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68(1), 013816 (2003).
[CrossRef]

Zhao, L. M.

L. M. Zhao, D. Y. Tang, T. H. Cheng, H. Y. Tam, C. Lu, “Bound states of dispersion-managed solitons in a fiber laser at near zero dispersion,” Appl. Opt. 46(21), 4768–4773 (2007).
[CrossRef] [PubMed]

D. Y. Tang, L. M. Zhao, B. Zhao, “Multipulse bound solitons with fixed pulse separations formed by direct soliton interaction,” Appl. Phys. B 80(2), 239–242 (2005).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

D. Y. Tang, L. M. Zhao, B. Zhao, “Multipulse bound solitons with fixed pulse separations formed by direct soliton interaction,” Appl. Phys. B 80(2), 239–242 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

R. Gumenyuk, O. G. Okhotnikov, “Impact of gain medium dispersion on stability of soliton bound states in fiber laser,” IEEE Photon. Technol. Lett. 25(2), 133–135 (2013).
[CrossRef]

S. U. Alam, A. B. Grudinin, “Tunable picoseconds frequency-shifted feedback fiber laser at 1550 nm,” IEEE Photon. Technol. Lett. 16(9), 2012–2014 (2004).
[CrossRef]

B. Ortaç, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16(5), 1274–1276 (2004).
[CrossRef]

J. Opt. Soc. Am. B (4)

Laser Phys. Lett. (1)

R. Gumenyuk, O. G. Okhotnikov, “Polarization control of bound state of vector soliton,” Laser Phys. Lett. 10(5), 055111 (2013).
[CrossRef]

Opt. Commun. (3)

X. Wu, D. Y. Tang, X. N. Luan, Q. Zhang, “Bound states of solitons in a fiber laser mode-locked with carbon nanotubes saturable absorber,” Opt. Commun. 284(14), 3615–3618 (2011).
[CrossRef]

Y. Gong, P. Shum, T. H. Cheng, Q. Wen, D. Tang, “Bound soliton pulses in passively mode-locked fiber laser,” Opt. Commun. 200(1-6), 389–399 (2001).
[CrossRef]

J. M. Sousa, O. G. Okhotnikov, “Short pulse generation and control in Er-doped frequency-shifted-feedback fibre lasers,” Opt. Commun. 183(1-4), 227–241 (2000).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, H. Y. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68(1), 013816 (2003).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Yb-doped fiber laser setup.

Fig. 2
Fig. 2

Laser output characteristics depending on the net cavity dispersion. a – autocorrelations, b – optical spectra, c – oscilloscope pictures of the pulse train.

Fig. 3
Fig. 3

Two-soliton bound state formation in the cavity with dispersion β = −0.08 ps2 or DΣ = 0.15 ps/nm. (a) Pulse evolution on the phase plane. (b) The frequency of the first (red) and second (blue) solitons when the bound state development. (c) Formation of a bound state, n - number of passes through the cavity.

Fig. 4
Fig. 4

Unstable state dynamics in a cavity with dispersion β = −0.105 ps2 or DΣ = 0.2 ps/nm. (a) Evolution on the phase plane. (b) The frequency disparity of the first (red) and the second weak (blue) pulses. (c) Unstable two-pulse state, n - number of passages through the laser cavity.

Fig. 5
Fig. 5

Single soliton pulse with cavity dispersion β = −0.2 ps2 or DΣ = 0.39 ps/nm . (a) The evolution of single soliton frequency (red) in comparison with frequency of soliton in bound state shown in Fig. 3(b) (blue). (b) Transients in the generation of the individual soliton, n – the number of passes through the laser cavity.

Fig. 6
Fig. 6

The autocorrelation traces of the bound states obtained from experiments (a) and numerical simulation (b) for dispersion values DΣ = 0.11, 0.15, 0.19 ps/nm.

Fig. 7
Fig. 7

The phase and instantaneous frequency distribution of soliton bound states within laser cavity with dispersion of (a) β = −0.102 ps2 or DΣ = 0.19 ps/nm and (b) β = −0.08 ps2 or DΣ = 0.15 ps/nm. (c) Intensity shapes of the bound state for β = −0.102 ps2 or DΣ = 0.19 ps/nm (red) and β = −0.08 ps2 or DΣ = 0.15 ps/nm (blue).

Tables (1)

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Table 1 Laser parameters are used in simulations

Equations (3)

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A z +i β 2 2 2 A t 2 iγ | A | 2 A=( gl )A β 2f 2 2 A t 2 ,
g(z,t)=g(z)= g 0 1+ 0 T R | A(z,t) | 2 dt / E sat
A out =J× A in

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