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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 24 — Nov. 21, 2011
  • pp: 24507–24515
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Direct observation of two-color pulse dynamics in passively synchronized Er and Yb mode-locked fiber lasers

Wei-Wei Hsiang, Wei-Chih Chiao, Chia-Yi Wu, and Yinchieh Lai  »View Author Affiliations


Optics Express, Vol. 19, Issue 24, pp. 24507-24515 (2011)
http://dx.doi.org/10.1364/OE.19.024507


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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 OSA

1. Introduction

In this paper, we report direct experimental observation results of two-color pulse dynamics under passive synchronization by measuring their relative pulse position in the shared fiber section of the cavity-combined Er and Yb mode-locked fiber lasers. A collinear sum-frequency generation (SFG) cross-correlator is built to perform the relative position measurement between the 1.56 μm and 1.03 μm pulses. It is found that the 1.56 μm fs pulses pass through a significant portion of the 1.03 μm chirped ps pulse and experience the frequency shifts through the XPM effects to maintain the passive synchronization. By analyzing the dependence of the relative position on the cavity mismatch detuning, the effects of the cross-phase modulation, the pulse walk-off, the group velocity dispersion, and the laser center wavelength restoration on the two-color pulse dynamics under synchronization can be clearly identified. Moreover, depending on the cavity mismatch, the passively synchronized 1.56 μm bound soliton pairs are found to be able to exhibit two different dynamical behaviors. They can be either in-pahse phase-locked or not phase-locked at all. The origins of these two kinds of bound soliton pairs are investigated experimentally by disclosing their locations with respective to the copropagating 1.03 μm pulse.

2. Passively synchronized Er and Yb mode-locked fiber lasers

2.1 Experimental setup

The passive synchronization can be achieved when the pulse repetition rates of the two individual mode-locked fiber lasers are close enough. In our setup the cavity length mismatch between the Er-fiber and Yb-fiber lasers can be tuned by moving one of the fiber collimators in the Yb-fiber laser. Besides, additional fine adjustments of the waveplates in the fiber lasers are also helpful to stabilize the synchronization. After stable passive synchronization is achieved, two stable pulse trains with the repetition rate of ~34.5 MHz are observed in the oscilloscope with the same trigger signal. Figure 1(b) and 1(c) shows the intensity autocorrelation trace of the 1.56 μm pulse and the two-photon absorption (TPA) interferometric autocorrelation trace of the 1.03 μm pulse. The corresponding FWHM pulse widths of the 1.56 μm and 1.03 μm pulses are 0.3 ps and 2.9 ps respectively. It indicates that in the shared fiber section the pulse width of the 1.03 μm pulse is much wider than that of the 1.56 μm pulse. These different pulse widths correspond to the distinct characteristics of stretched-pulse and self-similar mode-locking regimes. The net cavity group delay dispersion (GDD) of mode-locked Er-fiber and Yb-fiber lasers are estimated to be −0.03 ps2 and 0.058 ps2 respectively.

2.2 Relative position and walk-off of the two-color pulses in the shared fiber section

The home-built cross-correlator consists of a Michelson interferometer with the scanning delay, a BBO nonlinear crystal, an optical bandpass filter, and a photomultiplier tube (PMT). The incident light of the two-color pulses from the laser output is firstly split into two beams by the beam splitter (BS). After introducing the scanning delay in one arm of the interferometer, the two separated beams with and without the delay are combined on the beam splitter and then focused into a BBO crystal. The SFG signal after passing through the optical bandpass filter is detected by a photomultiplier tube (PMT) and can be expressed as
XSFG(τ)|E1.03(t)E1.56(t+τ)+E1.03(t+τ)E1.56(t)|2dt,
(1)
where τis the scanning delay, and the electric fields of 1.56 μm and 1.03 μm pulses are represented by E1.56(t)=u1.56(t)exp(iω1.56t), E1.03(t)=u1.03(t)exp(iω1.03t), respectively. Equation (1) t
XSFG(τ)2I1.03(t)I1.56(t)dt+I1.03(t)I1.56(t+τ)dt+I1.03(t+τ)I1.56(t)dt+A(τ)cos(ω1.03τ)+B(τ)cos(ω1.56τ)+C(τ)cos[(ω1.03+ω1.56)τ],+D(τ)cos[(ω1.03ω1.56)τ]
(2)
where I1.56(t)=|u1.56(t)|2, and I1.03(t)=|u1.03(t)|2 are the intensities of 1.56 μm and 1.03 μm pulses. In Eq. (2), the first term represents the background dc SFG signal, the second and third terms are the two intensity cross-correlation traces corresponding to either the 1.56 μm or 1.03 μm pulses with the delay, and the last four terms are the rapidly oscillating ac SFG signals. The intensity cross-correlation traces can be extracted from XSFG(τ) to identify the relative position. In the following, we illustrate how to identify the relative position as well as the pulse walk-off between the 1.56 μm and 1.03 μm pulses.

First of all, we measure the cross-correlation traces (the Si filter removed in Fig. 2(a)) at the laser outputs C1 and C2 simultaneously and the results are shown in Fig. 2(b) and 2(c) respectively. It can be clearly seen that in this case the sum of the rapidly oscillating ac SFG signals vanishes so that only the two intensity cross-correlation traces with the background dc SHG signal are remained. Therefore the time separation between the two-color pulses is just the absolute value of the delays for the peaks of the SFG signals, i.e., 2.7 ps in Fig. 2(b) and 3.8 ps in Fig. 2(c). Secondly, besides the separation of the two-color pulses, we need to determine which one of the two-color pulses leads the other. This can be simply achieved by inserting a thin Si filter in one arm of the interferometer to block the 1.03 μm pulses, as shown in Fig. 2(a). This results, on the one hand, the original second term I1.03(t)I1.56(t+τ)dt in Eq. (2) to be diminished. On the other hand, the original third term I1.03(t+τ)I1.56(t)dt in Eq. (2) will turn to I1.03(t+τ)I1.56(t+τSi)dt, where τSi is the additional delay introduced by the thin Si filter. The peaks, indicated by the red arrows in Fig. 2(b) and its inset, correspond to the intensity cross-correlation traces of I1.03(t+τ)I1.56(t)dt and I1.03(t+τ)I1.56(t+τSi)dt respectively. Therefore the peak of I1.03(t+τ)I1.56(t)dt located at a negative delay of −2.7 ps in Fig. 2(b) indicates that the 1.56 μm pulse leads the 1.03 μm pulse at the laser output C1. Similarly, Fig. 2(c) and its inset show that the 1.56 μm pulse leads the 1.03 μm pulse by 3.8 ps at the output C2. By comparing the relative position variation between the outputs C1 and C2 one can conclude that the group velocity mismatch (1vg,1.561vg,1.03) between the 1.56 μm and 1.03 μm pulses in the two fiber couplers (65-cm-long HI 1060 fiber) is ~-1.7 ps/m.

In addition, we have also measured the pulse walk-off in the WDM3 and WDM4, which is comprised of the OFS 980 fiber. After an additional section of the OFS 980 fiber is spliced to the output C2, the measurement of the relative position between the two-color pulses is performed again. The experimental results show that the 1.56 μm pulse leads the 1.03 μm pulse by an additional 4.1 ps after propagating the 50-cm-long OFS 980 fiber. Thus the total pulse walk-off accumulated in the 3 fiber sections of the shared cavity (WDM3-C1: 22-cm-long OFS 980 fiber, C1-C2: 112-cm-long HI 1060 fiber, C2-WDM4: 29-cm-long OFS 980 fiber) is estimated to be 6.1 ps, which is larger than the pulse width of the 1.03 μm pulse. This indicates that the 1.56 μm fs pulses pass through a significant portion of the 1.03 μm chirped ps pulse under the passive synchronization process. The measured relative position as well as pulse walk-off is used in the following section to evaluate the influence of the 1.03 μm pulse on the 1.56 μm pulse via the XPM effect.

3. Experimental observation of two-color pulse dynamics

3.1 Dynamics of a single 1.56 μm pulse synchronized to the 1.03 μm pulse

When the pump powers of the two-color mode-locked fiber lasers are kept low, one single 1.56 μm pulse and one single 1.03 μm pulse are generated. For the 1.03 μm pulse, no obvious change in the optical spectrum or autocorrelation trace of the 1.03 μm pulse is observed before and after achieving the passive synchronization. However, for the synchronized 1.56 μm pulse, the variations of the optical spectrum and the location relative to the copropagating 1.03 μm pulse can be clearly observed when the cavity mismatch is detuned. As the cavity length of the mode-locked Yb-fiber laser increases by each step of 2 μm, the center wavelength of the 1.56 μm pulse continuingly shifts towards longer wavelengths, as shown in Fig. 3(a)
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.
. In the meanwhile, the corresponding relative positions between the two-color pulses measured at the output C1 are shown in Fig. 3(b). These cross-correlation traces show that the 1.56 μm pulse moves toward the leading part of the 1.03 μm pulse as the cavity length of the Yb-fiber laser increased.

3.2 Dynamics of the 1.56 μm bound soliton pair synchronized to a 1.03 μm pulse

When the pump power of the Er-fiber laser is increased while the pump power of the Yb-fiber laser is kept unchanged, the 1.56 μm bound soliton pairs are generated and also can be synchronized with a 1.03 μm pulse [12

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]

]. Depending on the cavity mismatch, two different kinds of the 1.56 μm bound soliton pairs, i.e., phase-locked and non-phase-locked, have been both observed. For the synchronized 1.56 μm bound soliton pair with the locked relative phase, the optical spectrum and the corresponding intensity autocorrelation trace are shown in Fig. 5(a)
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.
and 5(b) respectively. In Fig. 5(a), the obvious interferometric visibility and the center peak in the optical spectrum reveal that the relative phase between the bound soliton pair is locked close to zero (in-phase). The period of the modulation on the optical spectrum is 12.5 nm, which is consistent with the close separation of 0.65 ps of the bound soliton pair observed in Fig. 5(b). However, as shown in Fig. 5(d) and 5(e), the bound soliton pair with a wider separation of 2.4 ps does not exhibit any observable modulation, indicating that the relative phase between the bound soliton pair is not locked. In the experiment, the transition between these two different kinds of bound soliton pair is made only by detuning the cavity length mismatch.

In order to clarify the origin that causes the synchronized 1.56 μm bound soliton pair to exhibit the different characteristics, the locations of these bound soliton pairs relative to the copropagating 1.03 μm pulse in the shared fiber section is also measured experimentally. Figure 5(c) and its inset show the cross-correlation traces measured at the outputs C1 and C2 respectively. The change between the relative positions at the output C1 and C2 shows that the group velocity of the 1.56 bound soliton pair is the same as that of a 1.56 μm single pulse, owing to the same center wavelength of these pulses. The center of the phase-locked bound soliton pair measured at the output C1 is at ~-1.6 ps with respect to the center of the 1.03 μm pulse, which corresponds to the location where the XPM-induced phase modulation (the inset of Fig. 4) is approximately linear. Therefore for the phase-locked bound soliton pair with a very small time separation, the influence of the 1.03 μm pulse can be reasonably approximated by a linear phase modulation. The bound states of soliton in the CGLE with a linear potential has been studied in the theoretical work [15

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]

]. The results in Ref [15

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]

] show a stable solution of the phase-locked bound soliton pair moving along with the linear potential, which is similar to the observations in our experiment. However, the observed relative phase in our case is close to zero, instead of π/2. This may be resulted from the fact that the zero phase difference can provides a stronger repulsive force from the effect of larger quintic loss in the CGLE model to avoid the closely bound soliton pair to merge.

When the non-phase-locked bound soliton pair occurs under the passive synchronization, the cross-correlation traces measured at the output C1 without and with suing the Si filter are shown in Fig. 5(f) and its inset respectively. By subtracting the delay of ~5.5 ps introduced by the thin Si filter from the delay time corresponding to the center (i.e., ~6 ps) of the intensity cross-correlation trace in the inset of Fig. 5(f), the center of non-phase-locked bound soliton pair is estimated to be located at ~0.5 ps relative to the center of the 1.03 μm pulse. This indicates the two individual pulses are located at −0.7 ps and 1.7 ps respectively. Therefore the 1.56 μm bound soliton pair experiences an asymmetry influence from the 1.03 μm pulse to cause the phase unlocked. To our knowledge, the experimental observation of the stable two-pulse bound state with entire loss of observable interference pattern in the optical spectrum was only reported in the Ti-sapphire laser mode-locked by a semiconductor saturable-absorber mirror [21

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]

]. One of the possible scenarios underlying the non-phase-locked bound soliton pairs is that the phase difference is dynamically rotating or independently evolving [21

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

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]

]. However, more experimentally dynamical observations of the bound soliton pair’s relative phase as well as theoretically numerical investigations based on the CGLE may be needed to further clarify these phenomena.

4. Conclusion

We have carefully measured the relative positions and the walk-off between the two-color pulses along the shared fiber section in passively synchronized mode-locked Er-fiber and Yb-fiber lasers. The influence of a 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 from the XPM effect with the walk-off effect taken into account. For the 1.56 μm single pulse under the synchronization, the dependence of the relative position variation and the center wavelength shift on the cavity mismatch detuning is analogous to the typical characteristics of FM mode-locked lasers with the modulation frequency detuning effects. For the 1.56 μm bound soliton pairs under synchronization, two new dynamical behaviors subject to different kinds of relative cross-phase modulation have been observed experimentally. One is the phase-locked soliton pair moving along with the effective linear phase modulation, which are bound very closely and in-phase. The other one, in which two individual pulses are located asymmetrically with respective to the effective phase modulation, exhibits the different dynamical behavior with possibly rotating or independently evolving phase difference.

Acknowledgments

This work is supported by the National Science Council of the R.O.C. under the contracts NSC 99-2112-M-030-002-MY3 and NSC 99-2221-E-009-045-MY3. The authors also gratefully acknowledge the funding from the FJU Physics alumni.

References and links

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]

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(140.3510) Lasers and laser optics : Lasers, fiber
(140.4050) Lasers and laser optics : Mode-locked lasers
(320.7100) Ultrafast optics : Ultrafast measurements

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: September 12, 2011
Revised Manuscript: November 2, 2011
Manuscript Accepted: November 3, 2011
Published: November 15, 2011

Citation
Wei-Wei Hsiang, Wei-Chih Chiao, Chia-Yi Wu, and Yinchieh Lai, "Direct observation of two-color pulse dynamics in passively synchronized Er and Yb mode-locked fiber lasers," Opt. Express 19, 24507-24515 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24507


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References

  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. A79(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. Express18(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. B74(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. Express12(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. A80(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. B26(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. A244(6), 551–556 (1998). [CrossRef]
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