Abstract

We theoretically demonstrate and experimentally confirm the major influence of gain dynamics on soliton molecules that self-assemble in mode-locked lasers. Both slow gain recovery and depletion play a pivotal role in the formation of chirped soliton molecules characterized by an increasing separation from leading to trailing pulses. These chirped molecules actually consist of many pulses and may be termed macromolecules. They are experimentally observed in a fiber laser and numerically modeled by an approach that properly includes the slow gain dynamics. Furthermore, it is shown that these processes stabilize soliton trains in fiber lasers by inhibiting internal oscillations.

© 2012 Optical Society of America

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References

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  1. Ph. Grelu and J. M. Soto-Crespo, Lect. Notes Phys. 751, 137 (2008).
    [CrossRef]
  2. Ph. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, J. Opt. Soc. Am. B 20, 863 (2003).
    [CrossRef]
  3. A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 79, 053841 (2009).
    [CrossRef]
  4. M. Grapinet and Ph. Grelu, Opt. Lett. 31, 2115 (2006).
    [CrossRef]
  5. B. Ortaç, A. Zaviyalov, C. Nielsen, O. Egorov, R. Iliew, J. Limpert, F. Lederer, and A. Tünnermann, Opt. Lett. 35, 1578(2010).
    [CrossRef]
  6. A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 80, 043829 (2009).
    [CrossRef]
  7. A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Opt. Lett. 34, 3827 (2009).
    [CrossRef]
  8. A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, Opt. Lett. 33, 524 (2008).
    [CrossRef]
  9. S. Chouli and Ph. Grelu, Phys. Rev. A 81, 063829 (2010).
    [CrossRef]
  10. A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, J. Opt. Soc. Am. B 27, 2313 (2010).
    [CrossRef]
  11. G. Agrawal, Phys. Rev. A 44, 7493 (1991).
    [CrossRef]
  12. B. A. Malomed, Phys. Rev. A 44, 6954 (1991).
    [CrossRef]

2010 (3)

2009 (3)

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Opt. Lett. 34, 3827 (2009).
[CrossRef]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 79, 053841 (2009).
[CrossRef]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 80, 043829 (2009).
[CrossRef]

2008 (2)

2006 (1)

2003 (1)

1991 (2)

G. Agrawal, Phys. Rev. A 44, 7493 (1991).
[CrossRef]

B. A. Malomed, Phys. Rev. A 44, 6954 (1991).
[CrossRef]

Agrawal, G.

G. Agrawal, Phys. Rev. A 44, 7493 (1991).
[CrossRef]

Belhache, F.

Chouli, S.

S. Chouli and Ph. Grelu, Phys. Rev. A 81, 063829 (2010).
[CrossRef]

Egorov, O.

Grapinet, M.

Grelu, Ph.

S. Chouli and Ph. Grelu, Phys. Rev. A 81, 063829 (2010).
[CrossRef]

Ph. Grelu and J. M. Soto-Crespo, Lect. Notes Phys. 751, 137 (2008).
[CrossRef]

M. Grapinet and Ph. Grelu, Opt. Lett. 31, 2115 (2006).
[CrossRef]

Ph. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, J. Opt. Soc. Am. B 20, 863 (2003).
[CrossRef]

Gutty, F.

Haboucha, A.

Iliew, R.

Komarov, A.

Leblond, H.

Lederer, F.

Limpert, J.

Malomed, B. A.

B. A. Malomed, Phys. Rev. A 44, 6954 (1991).
[CrossRef]

Nielsen, C.

Ortaç, B.

Salhi, M.

Sanchez, F.

Soto-Crespo, J. M.

Tünnermann, A.

Zaviyalov, A.

Zavyalov, A.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, J. Opt. Soc. Am. B 27, 2313 (2010).
[CrossRef]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Opt. Lett. 34, 3827 (2009).
[CrossRef]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 79, 053841 (2009).
[CrossRef]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 80, 043829 (2009).
[CrossRef]

J. Opt. Soc. Am. B (2)

Lect. Notes Phys. (1)

Ph. Grelu and J. M. Soto-Crespo, Lect. Notes Phys. 751, 137 (2008).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (5)

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 79, 053841 (2009).
[CrossRef]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 80, 043829 (2009).
[CrossRef]

S. Chouli and Ph. Grelu, Phys. Rev. A 81, 063829 (2010).
[CrossRef]

G. Agrawal, Phys. Rev. A 44, 7493 (1991).
[CrossRef]

B. A. Malomed, Phys. Rev. A 44, 6954 (1991).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Direct experimental observation of chirped soliton macromolecules from a mode-locked fiber laser. In (a), the pulse-to-pulse separation inside the 14-soliton macromolecule stretches from 52 to 77 ps with a relative measurement accuracy estimated to be better than 5 ps. The pumping power is 140 mW. In the 31-soliton macromolecule displayed in (b) obtained with a pumping power of 290 mW, the separation stretches from 45 to 76 ps.

Fig. 2.
Fig. 2.

Schematics of the gain dynamics at a fixed point over an entire cavity period TRT.

Fig. 3.
Fig. 3.

Numerical results obtained in the commonly used model were the average value of the gain is used, g0=1.1m1. (a) Separation distance between leading and central pulses (line 1, black) and between central and trailing pulses (line 2, blue) in the soliton molecule as function of the round-trip number. (b) Intensity profile of a soliton molecule (black) and the corresponding gain profile (red).

Fig. 4.
Fig. 4.

Numerical results obtained in the model where slow temporal gain dynamics is implemented. Separation distance between leading and central pulses (line 1, black) and between central and trailing pulses (line 2, blue) in the soliton molecule as function of the round-trip number for (a) g0=1.1m1 and (b) g0=0.95m1. The intensity profile of a soliton molecule (black) and the corresponding gain profile (red) for (c) g0=1.1m1 and (d) g0=0.95m1.

Equations (6)

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[z+g(z,t)T22t+i2(β2+ig(z,t)T22)2t2]U(z,t)=g(z,t)U(z,t)/2+iγ|U(z,t)|2U(z,t),
g(z,t)t=g(z,t)|U(z,t)|2Esat,fort[t1;t2],
g(z,t)t=g0g(z,t)Trelax,fort[0;t1][t2;TRT],
g(z,t1)=g01exp[TRT/Trelax]1exp[TRT/TrelaxQ(z)/Esat],
g(z,t2)=g(z,t1)exp[Q(z)/Esat],
g(z,t)gaver(z)=[g(z,t1)+g(z,t2)]/2.

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