Abstract

We report direct experimental observation of interesting pulse synchronization dynamics in a cavity-combined Er and Yb mode-locked fiber lasers by measuring the relative position between the two-color pulses in the shared fiber section. The influence of the 1.03 μm pulse on the 1.56 μm single pulse as well as bound soliton pairs can be clearly identified as an effective phase modulation through the XPM effect with the walk-off effect taken into account. For the 1.56 μm single pulse under synchronization, the dependence of the relative position variation and the center wavelength shift on the cavity mismatch detuning is found analogous to the typical characteristics of FM mode-locked lasers with modulation frequency detuning. Moreover, depending on the cavity mismatch, the passively synchronized 1.56 μm bound soliton pairs are found to exhibit two different dynamical behaviors, i.e., phase-locked (in-phase) as well as non-phase-locked. The physical origins for these two kinds of bound soliton pairs are investigated experimentally by disclosing their locations with respective to the copropagating 1.03 μm pulse.

©2011 Optical Society of America

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References

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  1. C. Fürst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:sapphire laser,” IEEE J. Sel. Top. Quantum Electron. 2(3), 473–479 (1996).
    [Crossref]
  2. G. Andriukaitis, T. Balčiūnas, S. Ališauskas, A. Pugžlys, A. Baltuška, T. Popmintchev, M.-C. Chen, M. M. Murnane, and H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36(15), 2755–2757 (2011).
    [Crossref] [PubMed]
  3. O. Chalus, A. Thai, P. K. Bates, and J. Biegert, “Six-cycle mid-infrared source with 3.8 μJ at 100 kHz,” Opt. Lett. 35(19), 3204–3206 (2010).
    [Crossref] [PubMed]
  4. R. Selm, M. Winterhalder, A. Zumbusch, G. Krauss, T. Hanke, A. Sell, and A. Leitenstorfer, “Ultrabroadband background-free coherent anti-Stokes Raman scattering microscopy based on a compact Er:fiber laser system,” Opt. Lett. 35(19), 3282–3284 (2010).
    [Crossref] [PubMed]
  5. M. Zhi and A. V. Sokolov, “Broadband coherent light generation in a Raman-active crystal driven by two-color femtosecond laser pulses,” Opt. Lett. 32(15), 2251–2253 (2007).
    [Crossref] [PubMed]
  6. R. Weigand, J. T. Mendonça, and H. M. Crespo, “Cascaded nondegenerate four-wave-mixing technique for high-power single-cycle pulse synthesis in the visible and ultraviolet ranges,” Phys. Rev. A 79(6), 063838 (2009).
    [Crossref]
  7. A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. A. Diddams, “Broadband phase-coherent optical frequency synthesis with actively linked Ti:sapphire and Cr:forsterite femtosecond lasers,” Opt. Lett. 29(4), 403–405 (2004).
    [Crossref] [PubMed]
  8. D. Yoshitomi, X. Zhou, Y. Kobayashi, H. Takada, and K. Torizuka, “Long-term stable passive synchronization of 50 µJ femtosecond Yb-doped fiber chirped-pulse amplifier with a mode-locked Ti:sapphire laser,” Opt. Express 18(25), 26027–26036 (2010).
    [Crossref] [PubMed]
  9. Z. Wei, Y. Kaboyashi, and K. Torizuka, “Passive synchronization between femtosecond Ti:sapphire and Cr:forsterite lasers,” Appl. Phys. B 74(9), S171–S176 (2002).
    [Crossref]
  10. M. Rusu, R. Herda, and O. G. Okhotnikov, “Passively synchronized erbium (1550-nm) and ytterbium (1040-nm) mode-locked fiber lasers sharing a cavity,” Opt. Lett. 29(19), 2246–2248 (2004).
    [Crossref] [PubMed]
  11. M. Rusu, R. Herda, and O. Okhotnikov, “Passively synchronized two-color mode-locked fiber system based on master-slave lasers geometry,” Opt. Express 12(20), 4719–4724 (2004).
    [Crossref] [PubMed]
  12. W.-W. Hsiang, C.-H. Chang, C.-P. Cheng, and Y. Lai, “Passive synchronization between a self-similar pulse and a bound-soliton bunch in a two-color mode-locked fiber laser,” Opt. Lett. 34(13), 1967–1969 (2009).
    [Crossref] [PubMed]
  13. W. Chang, N. Akhmediev, and S. Wabnitz, “Effect of external periodic potential on pairs of dissipative solitons,” Phys. Rev. A 80(1), 013815 (2009).
    [Crossref]
  14. W. Chang, N. Akhmediev, S. Wabnitz, and M. Taki, “Influence of external phase and gain-loss modulation on bound solitons in laser systems,” J. Opt. Soc. Am. B 26(11), 2204–2210 (2009).
    [Crossref]
  15. Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett. 34(19), 2976–2978 (2009).
    [Crossref] [PubMed]
  16. H. G. Winful and D. T. Walton, “Passive mode locking through nonlinear coupling in a dual-core fiber laser,” Opt. Lett. 17(23), 1688–1690 (1992).
    [Crossref] [PubMed]
  17. J. Atai and B. A. Malomed, “Bound states of solitary pulses in linearly coupled Ginzburg-Landau equations,” Phys. Lett. A 244(6), 551–556 (1998).
    [Crossref]
  18. H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2B), 036605 (2002).
    [Crossref] [PubMed]
  19. P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, “Induced-frequency shift of copropagating ultrafast optical pulses,” Appl. Phys. Lett. 52(23), 1939–1941 (1988).
    [Crossref]
  20. A. E. Siegman and D. J. Kuizenga, “Modulation frequency detuning effects in the FM Mode-locked laser,” IEEE J. Quantum Electron. 6(12), 803–808 (1970).
    [Crossref]
  21. M. J. Lederer, B. Luther-Davies, H. H. Tan, C. Jagadish, N. N. Akhmediev, and J. M. Soto-Crespo, “Multipulse operation of a Ti:sapphire laser mode locked by an ion-implanted semiconductor saturable-absorber mirror,” J. Opt. Soc. Am. B 16(6), 895–904 (1999).
    [Crossref]
  22. B. Ortaç, A. Zaviyalov, C. K. Nielsen, O. Egorov, R. Iliew, J. Limpert, F. Lederer, and A. Tünnermann, “Observation of soliton molecules with independently evolving phase in a mode-locked fiber laser,” Opt. Lett. 35(10), 1578–1580 (2010).
    [Crossref] [PubMed]

2011 (1)

2010 (4)

2009 (5)

2007 (1)

2004 (3)

2002 (2)

Z. Wei, Y. Kaboyashi, and K. Torizuka, “Passive synchronization between femtosecond Ti:sapphire and Cr:forsterite lasers,” Appl. Phys. B 74(9), S171–S176 (2002).
[Crossref]

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2B), 036605 (2002).
[Crossref] [PubMed]

1999 (1)

1998 (1)

J. Atai and B. A. Malomed, “Bound states of solitary pulses in linearly coupled Ginzburg-Landau equations,” Phys. Lett. A 244(6), 551–556 (1998).
[Crossref]

1996 (1)

C. Fürst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:sapphire laser,” IEEE J. Sel. Top. Quantum Electron. 2(3), 473–479 (1996).
[Crossref]

1992 (1)

1988 (1)

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, “Induced-frequency shift of copropagating ultrafast optical pulses,” Appl. Phys. Lett. 52(23), 1939–1941 (1988).
[Crossref]

1970 (1)

A. E. Siegman and D. J. Kuizenga, “Modulation frequency detuning effects in the FM Mode-locked laser,” IEEE J. Quantum Electron. 6(12), 803–808 (1970).
[Crossref]

Agrawal, G. P.

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, “Induced-frequency shift of copropagating ultrafast optical pulses,” Appl. Phys. Lett. 52(23), 1939–1941 (1988).
[Crossref]

Akhmediev, N.

W. Chang, N. Akhmediev, and S. Wabnitz, “Effect of external periodic potential on pairs of dissipative solitons,” Phys. Rev. A 80(1), 013815 (2009).
[Crossref]

W. Chang, N. Akhmediev, S. Wabnitz, and M. Taki, “Influence of external phase and gain-loss modulation on bound solitons in laser systems,” J. Opt. Soc. Am. B 26(11), 2204–2210 (2009).
[Crossref]

Akhmediev, N. N.

Alfano, R. R.

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, “Induced-frequency shift of copropagating ultrafast optical pulses,” Appl. Phys. Lett. 52(23), 1939–1941 (1988).
[Crossref]

Ališauskas, S.

Andriukaitis, G.

Atai, J.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2B), 036605 (2002).
[Crossref] [PubMed]

J. Atai and B. A. Malomed, “Bound states of solitary pulses in linearly coupled Ginzburg-Landau equations,” Phys. Lett. A 244(6), 551–556 (1998).
[Crossref]

Balciunas, T.

Baldeck, P. L.

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, “Induced-frequency shift of copropagating ultrafast optical pulses,” Appl. Phys. Lett. 52(23), 1939–1941 (1988).
[Crossref]

Baltuška, A.

Bartels, A.

Bates, P. K.

Biegert, J.

Chalus, O.

Chang, C.-H.

Chang, W.

W. Chang, N. Akhmediev, and S. Wabnitz, “Effect of external periodic potential on pairs of dissipative solitons,” Phys. Rev. A 80(1), 013815 (2009).
[Crossref]

W. Chang, N. Akhmediev, S. Wabnitz, and M. Taki, “Influence of external phase and gain-loss modulation on bound solitons in laser systems,” J. Opt. Soc. Am. B 26(11), 2204–2210 (2009).
[Crossref]

Chen, M.-C.

Cheng, C.-P.

Crespo, H. M.

R. Weigand, J. T. Mendonça, and H. M. Crespo, “Cascaded nondegenerate four-wave-mixing technique for high-power single-cycle pulse synthesis in the visible and ultraviolet ranges,” Phys. Rev. A 79(6), 063838 (2009).
[Crossref]

Diddams, S. A.

Efremidis, N.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2B), 036605 (2002).
[Crossref] [PubMed]

Egorov, O.

Frantzeskakis, D. J.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2B), 036605 (2002).
[Crossref] [PubMed]

Fürst, C.

C. Fürst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:sapphire laser,” IEEE J. Sel. Top. Quantum Electron. 2(3), 473–479 (1996).
[Crossref]

Hanke, T.

He, Y. J.

Herda, R.

Hizanidis, K.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2B), 036605 (2002).
[Crossref] [PubMed]

Hollberg, L.

Hsiang, W.-W.

Huang, H. C.

Iliew, R.

Jagadish, C.

Kaboyashi, Y.

Z. Wei, Y. Kaboyashi, and K. Torizuka, “Passive synchronization between femtosecond Ti:sapphire and Cr:forsterite lasers,” Appl. Phys. B 74(9), S171–S176 (2002).
[Crossref]

Kapteyn, H. C.

Kobayashi, Y.

Krauss, G.

Kuizenga, D. J.

A. E. Siegman and D. J. Kuizenga, “Modulation frequency detuning effects in the FM Mode-locked laser,” IEEE J. Quantum Electron. 6(12), 803–808 (1970).
[Crossref]

Lai, Y.

Laubereau, A.

C. Fürst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:sapphire laser,” IEEE J. Sel. Top. Quantum Electron. 2(3), 473–479 (1996).
[Crossref]

Lederer, F.

Lederer, M. J.

Leitenstorfer, A.

R. Selm, M. Winterhalder, A. Zumbusch, G. Krauss, T. Hanke, A. Sell, and A. Leitenstorfer, “Ultrabroadband background-free coherent anti-Stokes Raman scattering microscopy based on a compact Er:fiber laser system,” Opt. Lett. 35(19), 3282–3284 (2010).
[Crossref] [PubMed]

C. Fürst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:sapphire laser,” IEEE J. Sel. Top. Quantum Electron. 2(3), 473–479 (1996).
[Crossref]

Limpert, J.

Liu, B.

Luther-Davies, B.

Malomed, B. A.

Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett. 34(19), 2976–2978 (2009).
[Crossref] [PubMed]

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2B), 036605 (2002).
[Crossref] [PubMed]

J. Atai and B. A. Malomed, “Bound states of solitary pulses in linearly coupled Ginzburg-Landau equations,” Phys. Lett. A 244(6), 551–556 (1998).
[Crossref]

Mendonça, J. T.

R. Weigand, J. T. Mendonça, and H. M. Crespo, “Cascaded nondegenerate four-wave-mixing technique for high-power single-cycle pulse synthesis in the visible and ultraviolet ranges,” Phys. Rev. A 79(6), 063838 (2009).
[Crossref]

Mihalache, D.

Murnane, M. M.

Newbury, N. R.

Nielsen, C. K.

Nistazakis, H. E.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2B), 036605 (2002).
[Crossref] [PubMed]

Okhotnikov, O.

Okhotnikov, O. G.

Ortaç, B.

Popmintchev, T.

Pugžlys, A.

Rusu, M.

Sell, A.

Selm, R.

Siegman, A. E.

A. E. Siegman and D. J. Kuizenga, “Modulation frequency detuning effects in the FM Mode-locked laser,” IEEE J. Quantum Electron. 6(12), 803–808 (1970).
[Crossref]

Sokolov, A. V.

Soto-Crespo, J. M.

Takada, H.

Taki, M.

Tan, H. H.

Thai, A.

Thomann, I.

Torizuka, K.

Tünnermann, A.

Wabnitz, S.

W. Chang, N. Akhmediev, and S. Wabnitz, “Effect of external periodic potential on pairs of dissipative solitons,” Phys. Rev. A 80(1), 013815 (2009).
[Crossref]

W. Chang, N. Akhmediev, S. Wabnitz, and M. Taki, “Influence of external phase and gain-loss modulation on bound solitons in laser systems,” J. Opt. Soc. Am. B 26(11), 2204–2210 (2009).
[Crossref]

Walton, D. T.

Wang, H. Z.

Wei, Z.

Z. Wei, Y. Kaboyashi, and K. Torizuka, “Passive synchronization between femtosecond Ti:sapphire and Cr:forsterite lasers,” Appl. Phys. B 74(9), S171–S176 (2002).
[Crossref]

Weigand, R.

R. Weigand, J. T. Mendonça, and H. M. Crespo, “Cascaded nondegenerate four-wave-mixing technique for high-power single-cycle pulse synthesis in the visible and ultraviolet ranges,” Phys. Rev. A 79(6), 063838 (2009).
[Crossref]

Winful, H. G.

Winterhalder, M.

Yang, H.

Yoshitomi, D.

Zaviyalov, A.

Zhi, M.

Zhou, X.

Zumbusch, A.

Appl. Phys. B (1)

Z. Wei, Y. Kaboyashi, and K. Torizuka, “Passive synchronization between femtosecond Ti:sapphire and Cr:forsterite lasers,” Appl. Phys. B 74(9), S171–S176 (2002).
[Crossref]

Appl. Phys. Lett. (1)

P. L. Baldeck, R. R. Alfano, and G. P. Agrawal, “Induced-frequency shift of copropagating ultrafast optical pulses,” Appl. Phys. Lett. 52(23), 1939–1941 (1988).
[Crossref]

IEEE J. Quantum Electron. (1)

A. E. Siegman and D. J. Kuizenga, “Modulation frequency detuning effects in the FM Mode-locked laser,” IEEE J. Quantum Electron. 6(12), 803–808 (1970).
[Crossref]

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

C. Fürst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:sapphire laser,” IEEE J. Sel. Top. Quantum Electron. 2(3), 473–479 (1996).
[Crossref]

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

Opt. Express (2)

Opt. Lett. (10)

W.-W. Hsiang, C.-H. Chang, C.-P. Cheng, and Y. Lai, “Passive synchronization between a self-similar pulse and a bound-soliton bunch in a two-color mode-locked fiber laser,” Opt. Lett. 34(13), 1967–1969 (2009).
[Crossref] [PubMed]

A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. A. Diddams, “Broadband phase-coherent optical frequency synthesis with actively linked Ti:sapphire and Cr:forsterite femtosecond lasers,” Opt. Lett. 29(4), 403–405 (2004).
[Crossref] [PubMed]

M. Rusu, R. Herda, and O. G. Okhotnikov, “Passively synchronized erbium (1550-nm) and ytterbium (1040-nm) mode-locked fiber lasers sharing a cavity,” Opt. Lett. 29(19), 2246–2248 (2004).
[Crossref] [PubMed]

G. Andriukaitis, T. Balčiūnas, S. Ališauskas, A. Pugžlys, A. Baltuška, T. Popmintchev, M.-C. Chen, M. M. Murnane, and H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36(15), 2755–2757 (2011).
[Crossref] [PubMed]

O. Chalus, A. Thai, P. K. Bates, and J. Biegert, “Six-cycle mid-infrared source with 3.8 μJ at 100 kHz,” Opt. Lett. 35(19), 3204–3206 (2010).
[Crossref] [PubMed]

R. Selm, M. Winterhalder, A. Zumbusch, G. Krauss, T. Hanke, A. Sell, and A. Leitenstorfer, “Ultrabroadband background-free coherent anti-Stokes Raman scattering microscopy based on a compact Er:fiber laser system,” Opt. Lett. 35(19), 3282–3284 (2010).
[Crossref] [PubMed]

M. Zhi and A. V. Sokolov, “Broadband coherent light generation in a Raman-active crystal driven by two-color femtosecond laser pulses,” Opt. Lett. 32(15), 2251–2253 (2007).
[Crossref] [PubMed]

Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett. 34(19), 2976–2978 (2009).
[Crossref] [PubMed]

H. G. Winful and D. T. Walton, “Passive mode locking through nonlinear coupling in a dual-core fiber laser,” Opt. Lett. 17(23), 1688–1690 (1992).
[Crossref] [PubMed]

B. Ortaç, A. Zaviyalov, C. K. Nielsen, O. Egorov, R. Iliew, J. Limpert, F. Lederer, and A. Tünnermann, “Observation of soliton molecules with independently evolving phase in a mode-locked fiber laser,” Opt. Lett. 35(10), 1578–1580 (2010).
[Crossref] [PubMed]

Phys. Lett. A (1)

J. Atai and B. A. Malomed, “Bound states of solitary pulses in linearly coupled Ginzburg-Landau equations,” Phys. Lett. A 244(6), 551–556 (1998).
[Crossref]

Phys. Rev. A (2)

R. Weigand, J. T. Mendonça, and H. M. Crespo, “Cascaded nondegenerate four-wave-mixing technique for high-power single-cycle pulse synthesis in the visible and ultraviolet ranges,” Phys. Rev. A 79(6), 063838 (2009).
[Crossref]

W. Chang, N. Akhmediev, and S. Wabnitz, “Effect of external periodic potential on pairs of dissipative solitons,” Phys. Rev. A 80(1), 013815 (2009).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(33 Pt 2B), 036605 (2002).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) The schematic of the passively synchronized Er and Yb mode-locked fiber lasers. (b) and (c) The intensity and two-photon-absorption autocorrelation traces of the 1.56 μm and 1.03 μm respectively. WDM, wavelength division multiplexer (WDM1, 1030/976 nm; WDM2, 1560/976 nm; WDM3 and WDM4, 1560/1030 nm); LD, laser diode; PI-ISO, polarization-independent isolator; PBS, polarization beam splitter; FC, fiber collimator; GP, grating pair; QWP, quarter-wave plate; HWP, half-wave plate; C1 and C2, fiber couplers; M, mirror.

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Fig. 2
Fig. 2

(a) The setup of the cross-correlator. (b) and (c) The cross-correlation traces measured at the outputs C1 and C2 respectively (the thin Si filter removed). The insets show the measurement results when the thin Si filter is inserted. The red arrows indicate the intensity autocorrelation traces related to the third term in Eq. (2). PMT, photomultiplier tube; BPF, optical bandpass filter; BS, beam splitter; Si, thin Si filter; L, lens; M, mirror.

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Fig. 3
Fig. 3

The optical spectrum of the 1.56 μm pulse (a) and the corresponding relative positions (b) as the the cavity length of the Yb-fiber laser increased. The insets in Fig. 3(b) are the results measured when the Si filter is inserted in the cross-correlator.

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Fig. 4
Fig. 4

XPM-induced phase shift and frequency shift (the inset).

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Fig. 5
Fig. 5

The optical spectra, autocorrelation traces, and cross-correlation traces of the phase-locked (a)-(c) and non-phase-locked (d)-(f) bound soliton pairs. All the cross-correlation traces are measured at the output C1, except the inset of Fig. 5(c). Only the cross-correlation trace in the inset of Fig. 5(f) is measured using a Si filter inserted in the cross-correlator.

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Equations (3)

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

X SFG (τ)∝ ∫ −∞ ∞ | E 1.03 (t) E 1.56 (t+τ)+ E 1.03 (t+τ) E 1.56 (t) | 2 dt,
X SFG (τ)∝2 ∫ −∞ ∞ I 1.03 (t) I 1.56 (t)dt+ ∫ −∞ ∞ I 1.03 (t) I 1.56 (t+τ)dt+ ∫ −∞ ∞ I 1.03 (t+τ) I 1.56 (t)dt +A(τ)cos( ω 1.03 τ)+B(τ)cos( ω 1.56 τ)+C(τ)cos[( ω 1.03 + ω 1.56 )τ] , +D(τ)cos[( ω 1.03 − ω 1.56 )τ]
ϕ XPM = ∑ i=1 3 ∫ 0 L i 2γ I 0 e − ( t i − Δ i z T FWHM /2 ln2 ) 2 dz,

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