Abstract

Multiple dissipative solitons are numerically studied in the normal-cavity-dispersion Yb-doped fiber laser. Soliton pairs and triplets of different types are found in parameter domain where single soliton mode-locking is unstable. Similar scenario is found for soliton pair and triplet: an additional weak soliton supplements already existing solitons, then with increasing gain the solitons start oscillating and at higher gain the soliton complex becomes stable. Spectral profiles of the solitons dynamically change taking either parabolic-like or Π-like or M-like shape similar to those described in the literature for individual dissipative soliton at different pump level.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, "High-power ultrafast fiber laser systems,"IEEE J. Sel. Top. Quantum Electron. 12, 233 - 244 (2006).
    [CrossRef]
  2. D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. L. Quiroga-Teixeiro, "Wave-breaking-free pulses in nonlinear optical fibers," J. Opt. Soc. Am. B 10, 1185-1190 (1993).
    [CrossRef]
  3. F. O. Ilday, J. R. Buckley, W. G. Clark, and F. E. Wise, "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
    [CrossRef] [PubMed]
  4. L. M. Zhao, D. Y. Tang, and J. Wu, "Gain-guided soliton in a positive group-dispersion fiber laser," Opt. Lett. 31, 1788-1790 (2006).
    [CrossRef] [PubMed]
  5. L. M. Zhao, D. Y. Tang, H. Zhang, T. H. Cheng, H. Y. Tam, and C. Lu, "Dynamics of gain-guided solitons in an all-normal-dispersion fiber laser," Opt. Lett. 32, 1806-1808 (2007).
    [CrossRef] [PubMed]
  6. A. Chong, W. H. Renninger, and F. W. Wise, "Properties of Normal-Dispersion Femtosecond Fiber Lasers," J. Opt. Soc. Am B 25(2), 140-148 (2008).
    [CrossRef]
  7. W.H. Renninger, A. Chong, and F. W. Wise, "Dissipative Solitons in Normal-Dispersion Fiber Lasers," Phys. Rev. A 77, 023814 (2008).
    [CrossRef]
  8. K. Kieu, W. H. Renninger, A. Chong, and F. W. Wise, "Sub-100 fs pulses at watt-level powers from a dissipative-soliton fiber laser," Opt. Lett. 34, 593-595 (2009).
    [CrossRef] [PubMed]
  9. A. Komarov, H. Leblond, and F. Sanchez, "Multistability and hysteresis phenomena in passively mode-locked fiber lasers," Phys. Rev. A 71, 053809 (2005).
    [CrossRef]
  10. D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, "Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers," Phys. Rev. A 72, 043816 (2005).
    [CrossRef]
  11. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo "Multisoliton solution of the complex Ginzburg-Landau equation," Phy. Rev. Lett. 79, 4047-4051 (1997).
    [CrossRef]
  12. N. Akhmediev, A. Ankiewicz, and J.M. Soto-Crespo "Stable soliton pairs in optical transmission lines and fiber lasers," J. Opt. Soc. Am B 15, 2, 515-523 (1998).
    [CrossRef]
  13. L. M. Zhao, D. Y. Tang, T. H. Cheng, H. Y. Tam, and C. Lu, "Generation of Multiple Gain-Guided Solitons in a Fiber Laser," Opt. Lett. 32(11), 1581 (2007).
    [CrossRef]
  14. J. M. Soto-Crespo, P. Grelu, N. Akhmediev and N. Devine, "Soliton complexes in dissipative systems: Vibrating, shaking, and mixed soliton pairs," Phys. Rev. E 75, 016613 (2007).
    [CrossRef]
  15. M. A. Abdelalim, Y. Logvin, D. Khalil, and H. Anis, "Properties and stability limits of an optimized Yb-doped femtosecond fiber laser," Opt. Express 17(4), 2264 - 2279 (2009).
    [CrossRef]
  16. V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-Pulse Oscillators: Theory and Experiment," Appl. Phys. B 83, 503 - 510 (2006).
    [CrossRef]
  17. N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu,"Roadmap to ultra-short record high-energy pulses out of laser oscillators," Phy. Lett. A 372, 3124-3128 (2008).
    [CrossRef]
  18. N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu," Dissipative soliton interactions inside a fiber laser cavity," Opt. Fiber Technol. 11, 209-228 (2005).
    [CrossRef]

2009 (2)

2008 (3)

A. Chong, W. H. Renninger, and F. W. Wise, "Properties of Normal-Dispersion Femtosecond Fiber Lasers," J. Opt. Soc. Am B 25(2), 140-148 (2008).
[CrossRef]

W.H. Renninger, A. Chong, and F. W. Wise, "Dissipative Solitons in Normal-Dispersion Fiber Lasers," Phys. Rev. A 77, 023814 (2008).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu,"Roadmap to ultra-short record high-energy pulses out of laser oscillators," Phy. Lett. A 372, 3124-3128 (2008).
[CrossRef]

2007 (3)

2006 (3)

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-Pulse Oscillators: Theory and Experiment," Appl. Phys. B 83, 503 - 510 (2006).
[CrossRef]

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, "High-power ultrafast fiber laser systems,"IEEE J. Sel. Top. Quantum Electron. 12, 233 - 244 (2006).
[CrossRef]

L. M. Zhao, D. Y. Tang, and J. Wu, "Gain-guided soliton in a positive group-dispersion fiber laser," Opt. Lett. 31, 1788-1790 (2006).
[CrossRef] [PubMed]

2005 (3)

A. Komarov, H. Leblond, and F. Sanchez, "Multistability and hysteresis phenomena in passively mode-locked fiber lasers," Phys. Rev. A 71, 053809 (2005).
[CrossRef]

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, "Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers," Phys. Rev. A 72, 043816 (2005).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu," Dissipative soliton interactions inside a fiber laser cavity," Opt. Fiber Technol. 11, 209-228 (2005).
[CrossRef]

2004 (1)

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. E. Wise, "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

1998 (1)

N. Akhmediev, A. Ankiewicz, and J.M. Soto-Crespo "Stable soliton pairs in optical transmission lines and fiber lasers," J. Opt. Soc. Am B 15, 2, 515-523 (1998).
[CrossRef]

1997 (1)

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo "Multisoliton solution of the complex Ginzburg-Landau equation," Phy. Rev. Lett. 79, 4047-4051 (1997).
[CrossRef]

1993 (1)

Abdelalim, M. A.

Akhmediev, N.

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu,"Roadmap to ultra-short record high-energy pulses out of laser oscillators," Phy. Lett. A 372, 3124-3128 (2008).
[CrossRef]

J. M. Soto-Crespo, P. Grelu, N. Akhmediev and N. Devine, "Soliton complexes in dissipative systems: Vibrating, shaking, and mixed soliton pairs," Phys. Rev. E 75, 016613 (2007).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu," Dissipative soliton interactions inside a fiber laser cavity," Opt. Fiber Technol. 11, 209-228 (2005).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and J.M. Soto-Crespo "Stable soliton pairs in optical transmission lines and fiber lasers," J. Opt. Soc. Am B 15, 2, 515-523 (1998).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo "Multisoliton solution of the complex Ginzburg-Landau equation," Phy. Rev. Lett. 79, 4047-4051 (1997).
[CrossRef]

Anderson, D.

Anis, H.

Ankiewicz, A.

N. Akhmediev, A. Ankiewicz, and J.M. Soto-Crespo "Stable soliton pairs in optical transmission lines and fiber lasers," J. Opt. Soc. Am B 15, 2, 515-523 (1998).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo "Multisoliton solution of the complex Ginzburg-Landau equation," Phy. Rev. Lett. 79, 4047-4051 (1997).
[CrossRef]

Apolonski, A.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-Pulse Oscillators: Theory and Experiment," Appl. Phys. B 83, 503 - 510 (2006).
[CrossRef]

Buckley, J. R.

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. E. Wise, "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Cheng, T. H.

Chernykh, A.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-Pulse Oscillators: Theory and Experiment," Appl. Phys. B 83, 503 - 510 (2006).
[CrossRef]

Chong, A.

K. Kieu, W. H. Renninger, A. Chong, and F. W. Wise, "Sub-100 fs pulses at watt-level powers from a dissipative-soliton fiber laser," Opt. Lett. 34, 593-595 (2009).
[CrossRef] [PubMed]

A. Chong, W. H. Renninger, and F. W. Wise, "Properties of Normal-Dispersion Femtosecond Fiber Lasers," J. Opt. Soc. Am B 25(2), 140-148 (2008).
[CrossRef]

W.H. Renninger, A. Chong, and F. W. Wise, "Dissipative Solitons in Normal-Dispersion Fiber Lasers," Phys. Rev. A 77, 023814 (2008).
[CrossRef]

Clark, W. G.

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. E. Wise, "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Desaix, M.

Devine, N.

J. M. Soto-Crespo, P. Grelu, N. Akhmediev and N. Devine, "Soliton complexes in dissipative systems: Vibrating, shaking, and mixed soliton pairs," Phys. Rev. E 75, 016613 (2007).
[CrossRef]

Grapinet, M.

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu," Dissipative soliton interactions inside a fiber laser cavity," Opt. Fiber Technol. 11, 209-228 (2005).
[CrossRef]

Grelu, P.

J. M. Soto-Crespo, P. Grelu, N. Akhmediev and N. Devine, "Soliton complexes in dissipative systems: Vibrating, shaking, and mixed soliton pairs," Phys. Rev. E 75, 016613 (2007).
[CrossRef]

Grelu, Ph.

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu,"Roadmap to ultra-short record high-energy pulses out of laser oscillators," Phy. Lett. A 372, 3124-3128 (2008).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu," Dissipative soliton interactions inside a fiber laser cavity," Opt. Fiber Technol. 11, 209-228 (2005).
[CrossRef]

Ilday, F. O.

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. E. Wise, "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Kalashnikov, V. L.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-Pulse Oscillators: Theory and Experiment," Appl. Phys. B 83, 503 - 510 (2006).
[CrossRef]

Karlsson, M.

Khalil, D.

Kieu, K.

Komarov, A.

A. Komarov, H. Leblond, and F. Sanchez, "Multistability and hysteresis phenomena in passively mode-locked fiber lasers," Phys. Rev. A 71, 053809 (2005).
[CrossRef]

Leblond, H.

A. Komarov, H. Leblond, and F. Sanchez, "Multistability and hysteresis phenomena in passively mode-locked fiber lasers," Phys. Rev. A 71, 053809 (2005).
[CrossRef]

Limpert, J.

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, "High-power ultrafast fiber laser systems,"IEEE J. Sel. Top. Quantum Electron. 12, 233 - 244 (2006).
[CrossRef]

Lisak, M.

Liu, A. Q.

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, "Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers," Phys. Rev. A 72, 043816 (2005).
[CrossRef]

Logvin, Y.

Lu, C.

Podivilov, E.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-Pulse Oscillators: Theory and Experiment," Appl. Phys. B 83, 503 - 510 (2006).
[CrossRef]

Quiroga-Teixeiro, M. L.

Renninger, W. H.

K. Kieu, W. H. Renninger, A. Chong, and F. W. Wise, "Sub-100 fs pulses at watt-level powers from a dissipative-soliton fiber laser," Opt. Lett. 34, 593-595 (2009).
[CrossRef] [PubMed]

A. Chong, W. H. Renninger, and F. W. Wise, "Properties of Normal-Dispersion Femtosecond Fiber Lasers," J. Opt. Soc. Am B 25(2), 140-148 (2008).
[CrossRef]

Renninger, W.H.

W.H. Renninger, A. Chong, and F. W. Wise, "Dissipative Solitons in Normal-Dispersion Fiber Lasers," Phys. Rev. A 77, 023814 (2008).
[CrossRef]

Roser, F.

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, "High-power ultrafast fiber laser systems,"IEEE J. Sel. Top. Quantum Electron. 12, 233 - 244 (2006).
[CrossRef]

Sanchez, F.

A. Komarov, H. Leblond, and F. Sanchez, "Multistability and hysteresis phenomena in passively mode-locked fiber lasers," Phys. Rev. A 71, 053809 (2005).
[CrossRef]

Schreiber, T.

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, "High-power ultrafast fiber laser systems,"IEEE J. Sel. Top. Quantum Electron. 12, 233 - 244 (2006).
[CrossRef]

Soto-Crespo, J. M.

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu,"Roadmap to ultra-short record high-energy pulses out of laser oscillators," Phy. Lett. A 372, 3124-3128 (2008).
[CrossRef]

J. M. Soto-Crespo, P. Grelu, N. Akhmediev and N. Devine, "Soliton complexes in dissipative systems: Vibrating, shaking, and mixed soliton pairs," Phys. Rev. E 75, 016613 (2007).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu," Dissipative soliton interactions inside a fiber laser cavity," Opt. Fiber Technol. 11, 209-228 (2005).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo "Multisoliton solution of the complex Ginzburg-Landau equation," Phy. Rev. Lett. 79, 4047-4051 (1997).
[CrossRef]

Soto-Crespo, J.M.

N. Akhmediev, A. Ankiewicz, and J.M. Soto-Crespo "Stable soliton pairs in optical transmission lines and fiber lasers," J. Opt. Soc. Am B 15, 2, 515-523 (1998).
[CrossRef]

Tam, H. Y.

Tang, D. Y.

Tunnermann, A.

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, "High-power ultrafast fiber laser systems,"IEEE J. Sel. Top. Quantum Electron. 12, 233 - 244 (2006).
[CrossRef]

Wise, F. E.

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. E. Wise, "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Wise, F. W.

K. Kieu, W. H. Renninger, A. Chong, and F. W. Wise, "Sub-100 fs pulses at watt-level powers from a dissipative-soliton fiber laser," Opt. Lett. 34, 593-595 (2009).
[CrossRef] [PubMed]

A. Chong, W. H. Renninger, and F. W. Wise, "Properties of Normal-Dispersion Femtosecond Fiber Lasers," J. Opt. Soc. Am B 25(2), 140-148 (2008).
[CrossRef]

W.H. Renninger, A. Chong, and F. W. Wise, "Dissipative Solitons in Normal-Dispersion Fiber Lasers," Phys. Rev. A 77, 023814 (2008).
[CrossRef]

Wu, J.

Zhang, H.

Zhao, B.

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, "Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers," Phys. Rev. A 72, 043816 (2005).
[CrossRef]

Zhao, L. M.

Appl. Phys. B (1)

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-Pulse Oscillators: Theory and Experiment," Appl. Phys. B 83, 503 - 510 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, "High-power ultrafast fiber laser systems,"IEEE J. Sel. Top. Quantum Electron. 12, 233 - 244 (2006).
[CrossRef]

J. Opt. Soc. Am B (2)

A. Chong, W. H. Renninger, and F. W. Wise, "Properties of Normal-Dispersion Femtosecond Fiber Lasers," J. Opt. Soc. Am B 25(2), 140-148 (2008).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and J.M. Soto-Crespo "Stable soliton pairs in optical transmission lines and fiber lasers," J. Opt. Soc. Am B 15, 2, 515-523 (1998).
[CrossRef]

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

Opt. Express (1)

Opt. Fiber Technol. (1)

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu," Dissipative soliton interactions inside a fiber laser cavity," Opt. Fiber Technol. 11, 209-228 (2005).
[CrossRef]

Opt. Lett. (4)

Phy. Lett. A (1)

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu,"Roadmap to ultra-short record high-energy pulses out of laser oscillators," Phy. Lett. A 372, 3124-3128 (2008).
[CrossRef]

Phy. Rev. Lett. (1)

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo "Multisoliton solution of the complex Ginzburg-Landau equation," Phy. Rev. Lett. 79, 4047-4051 (1997).
[CrossRef]

Phys. Rev. A (3)

A. Komarov, H. Leblond, and F. Sanchez, "Multistability and hysteresis phenomena in passively mode-locked fiber lasers," Phys. Rev. A 71, 053809 (2005).
[CrossRef]

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, "Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers," Phys. Rev. A 72, 043816 (2005).
[CrossRef]

W.H. Renninger, A. Chong, and F. W. Wise, "Dissipative Solitons in Normal-Dispersion Fiber Lasers," Phys. Rev. A 77, 023814 (2008).
[CrossRef]

Phys. Rev. E (1)

J. M. Soto-Crespo, P. Grelu, N. Akhmediev and N. Devine, "Soliton complexes in dissipative systems: Vibrating, shaking, and mixed soliton pairs," Phys. Rev. E 75, 016613 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

F. O. Ilday, J. R. Buckley, W. G. Clark, and F. E. Wise, "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

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 (16)

Fig. 1.
Fig. 1.

Schematic view of the laser cavity: WDM – wavelength division multiplexer coupler, PBS – polarization beam splitter, WP – wave plate, SMF – single mode fiber.

Fig. 2.
Fig. 2.

The light intensity profiles of the OSP for go=47 dB/m in linear (a) and logarithmic (b) scales at three moments of time corresponding to different roundtrips (RT) number: blue at RT=9840, green at RT=9930, and red at RT=10010.

Fig. 3.
Fig. 3.

The normalized pulse profiles of the OSP for go=47 dB/m at different parts of the cavity within the same roundtrip: (a) RT=9840, and (b) RT=10010. Blue represents SMF output, green represents Yb output, and red represents SA output.

Fig. 4.
Fig. 4.

Oscillating soliton pair (OSP) spectrum at go=47 dB/m: (a) spectra of the separated pulses where the blue curve represents the M-like spectrum at maximum pulse energy (L or R) while the green one is the parabolic-type spectrum at minimum energy (L or R), (b) the spectrum of the OSP when one pulse is at maximum (L or R) and the other is at minimum (R or L).

Fig. 5.
Fig. 5.

The stable soliton pair (SSP) at go=50 dB/m in linear (a) and logarithmic (b) scales.

Fig. 6.
Fig. 6.

Stable soliton pair (SSP) spectra at go=50 dB/m: (a) individual pulse spectrum and (b) spectrum of the SSP.

Fig. 7.
Fig. 7.

Evolution of the total normalized light energy ‘Q’ in the cavity for different values of the gain parameter go: energy oscillations for the case of the OSP from go=45 dB/m to go=48 dB/m and steady-state final value of Q for SSP from go=49 dB/m to go=54 dB/m.

Fig.8.
Fig.8.

Eemporal intensity profiles of the OST in linear (a) and logarithmic scale (b) at go=60 dB/m. Two curves correspond to the moments of time separated by 75 roundtrips when either the single soliton on the left L or the other two nearly identical solitons, C and R have maximum power.

Fig. 9.
Fig. 9.

Oscillating soliton triplet (OTS) spectrum at go=60 dB/m at RT=14000: (a) spectra of the individual pulses where blue curve is the spectrum of the L pulse at minimum energy while the green (red) curve is the spectrum of the C (R) pulse at maximum, (b) the spectrum of the whole OTS.

Fig. 10.
Fig. 10.

Oscillating soliton triplet (OTS) spectrum at go=60 dB/m at RT=14075: (a) spectra of the individual pulses where blue curve is the spectrum of the L pulse at maximum energy while the green (red) curve is the spectrum of the C (R) pulse at minimum, (b) the spectrum of the whole OTS.

Fig. 11.
Fig. 11.

Temporal intensity profiles of the stable soliton triplet (SST) in linear (a) and logarithmic scale (b) at go=61 dB/m..

Fig.12.
Fig.12.

Stationary soliton triplet (SST) spectrum at go=61dB/m: (a) spectrum of the individual pulse and (b) spectrum of whole SST.

Fig. 13.
Fig. 13.

Total normalized energy ‘Q’ versus roundtrip number for different values of the gain parameter go : from go=56 dB/m to go=60 dB/m the final state is the oscillating soliton triplet while at go=61 dB/m – the stable soliton triplet.

Fig.14.
Fig.14.

The total normalized energy ‘Q’ for the soliton pair and triplet border states.

Fig. 15.
Fig. 15.

Stable asymmetric soliton pair at go=44 dB/m : (a) intensity profile and (b) the corresponding spectrum.

Fig.16.
Fig.16.

Stable asymmetric soliton triplet at go=55 dB/m: (a) intensity profile and (b) the corresponding spectrum.

Equations (1)

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

Az=α2Ajβ222At2+jγA2A+(g01+EpulseEsat.)(1+1Ωg22t2)A,

Metrics