1. Introduction

Passively mode-locked fiber lasers have become a practical ultrafast laser source for a wide range of scientific and industrial fields [1–3]. The key properties that make mode-locked fiber lasers attractive are the inherent robust, compact designs and the rich mode-locking states powered by intracavity nonlinear pulse dynamics manipulation. Emphasizing the ultrafast pulse dynamics, a variety of intriguing mode-locking states [4–7] have been obtained, such as similariton and dissipative soliton generation, bound states, vector pulses, chaotic pulse bunches, to name a few. These mode-locking states not only enrich the nonlinear optical cavity dynamics, but also shine light on an extensive range of applications.

In recent years, a dual-wavelength operation mode in passively mode-locked fiber lasers have drawn increased attention [8–11]. In particular, this operation mode provides an offset repetition rate for the two pulse trains by taking advantage of the cavity dispersion. Extremely high mutual coherence between the two pulse trains is maintained given the shared cavity, making these lasers competitive for the emerging dual-comb-based high precision metrological applications [12–14]. Comb-line resolved molecular spectroscopy as well as sub-micrometer precision absolute distance measurement has been demonstrated based on a single free running dual-wavelength passively mode-locked fiber laser [15–18].

A diversity of mechanisms have been proposed for dual-wavelength mode-locking in a passively mode-locked fiber laser [8–11,19–25]. A straightforward method utilizes a combination of fiber Bragg gratings with different transmission wavelengths. Multi-wavelength operations in carbon nanotube or semiconductor saturable absorber (SESAM) mode-locked fiber lasers have been reported [19,20]. Up to triple-wavelength picosecond pulses centered at 1539.5, 1549.5 and 1559.5 nm have been simultaneously obtained in [19]. The full width at half maximum (FWHM) for each optical spectrum is less than 0.5 nm set by the reflective bandwidth of FBG. The repetition rates are 6.87, 6.18 and 5.61 MHz, respectively. Dual-wavelength mode-locking has also been achieved by simple adjustment of the pump strength [21] or cavity loss [10]. To this end, the balance between fiber gain and cavity loss at desired wavelengths plays the key role on dual-wavelength mode-locking. However, the reproducibility of this method is limited by the pump hysteresis phenomena. In [10], the fiber laser simultaneously mode-locked at ~1532 and 1557 nm with ~9 MHz fundamental repetition rate and ~580 Hz repetition rate difference. The summed output power of the dual-wavelength laser was 248 μW. In most cases, an intra-cavity birefringence-induced periodic filtering effect [11,21–25] is implemented to provide mandatory spectral filtering. Besides, the filter manifests the tunability and switchability of the operation wavelength pairs, while the mode-locking can be achieved by a real saturable absorber [22] or additive pulse mode-locking techniques [11,23–25]. The birefringence-induced comb filter can be realized with various implementations, such as Lyot filter [23], Mach-Zehnder interferometer [24] and Sagnac loop filter [11]. In particular, [11] demonstrates dual-wavelength dissipative solitons with central wavelengths of 1572 nm and 1587 nm. The fundamental repetition rates are ~3.3 MHz and the repetition rate difference is 40 Hz. In addition to the diverse dual-wavelength generation approaches, the dual-color-soliton intracavity collision dynamics has also been revealed recently by dispersive Fourier transform technique [26].

The dual-wavelength passively mode-locked fiber lasers mentioned above are based on single-mode-fibers. For practical dual-comb metrological applications, an all polarization maintaining (PM) fiber design is highly desired. A few authors start to search for the route to all PM fiber dual-wavelength dual-comb mode-locking recently [27,28]. Y. Nakajima, et al. [27] utilized polarization-multiplexing between the fast and slow axes of PM fiber for dual-wavelength operation, with each mode-locking wavelength propagating in one axis. To this end, two segments of gain fibers and two SESAMs are used for mode-locking, rendering the laser system complicated. Alternatively, R. Wang, et al. [28] made use of a Lyot filter accompanied with a carbon nanotube saturable absorber for all PM fiber dual-wavelength mode-locking in a ring cavity.

In this report, we demonstrate a novel scheme of dual-wavelength dual-comb generation in an all-PM mode-locked fiber laser based on Sagnac loop filtering effect. The laser is based on an all-PM nonlinear amplifying loop mirror (NALM) design [29–31]. Similar design has been demonstrated as a robust ultrafast laser source with very low intrinsic noise for optical frequency combs and space-borne applications [32]. Here, we extend this cavity design by adding a segment (~0.5 m) of angle-spliced PM fiber to the tail of the NALM, yielding a birefringence-induced periodic Sagnac loop filter with 5 nm neighboring transmissive peak. To this end, this fiber laser can operate at switchable single-wavelength or dual-wavelength mode-locking states. The pulsed operation shows high environmental stability due to the all PM fiber configuration. A ~1 kHz differential repetition rate between two mode-locking wavelengths is observed and the frequency fluctuation is < 0.1% rms over 90 min.

2. Experimental setup and principle

The structure of the all PM dual-wavelength mode-locked fiber laser is shown in Fig. 1(a). The laser is based on a linear cavity using an NALM as one end-mirror. The NALM contains a wavelength-division multiplexer (WDM), a fiber-pigtailed polarization beam splitter (labeled as PBS1, Thorlabs, PBC1550PM) and a 1-meter-long Erbium-doped fiber (EDF) (nLight Liekki, Er80-4/125-HD-PM) with group velocity dispersion (GVD) of −28.8 ps/nm/km @1580 nm. The gain fiber is pumped by a single mode laser diode operating at 980 nm. The linear arm consists of a fiber collimator (COL), a nonreciprocal phase shifter, a polarization beam splitter cube (labeled as PBS2), a quarter waveplate (labeled as QWP2). A full-reflective mirror (M) serves as the other end mirror. The beams counter-circulating in the NALM are combined by PBS1 and then coupled into free space path through the COL. Note that the PM fiber pigtails that connect PBS1 and COL are spliced with a 16-degree angle. The nonreciprocal phase shifter consists of a Faraday rotator (FR), a half-wave plate (HWP) and a quarter waveplate (labeled as QWP1), as shown in the dashed box of Fig. 1(a). QWP2 is used to finely tune the output coupling ratio and intra-cavity loss. To this end, bidirectional outputs with tunable output power can be obtained at PBS2. Apart from the EDF, the rest fiber is single-mode PM fiber with GVD of ~19.3 ps/nm/km @1580nm and the total length of the PM fiber is 4.08 m. The net cavity dispersion is estimated to be −0.066 ps² and the laser operates at stretched-pulse mode-locking regime.

 

Fig. 1 (a) Experimental setup. COL: collimator; EDF: Erbium-doped fiber; FR: Faraday rotator; HWP: half-wave plate; M: mirror; PBS: polarization beam splitter; QWP: quarter-wave plate; WDM: wavelength division multiplexer. (b) Working principle of the Sagnac loop filter. (c) Intra-cavity wavelength-dependent filter transmission curves with different modulation depths at different phase bias provided by nonreciprocal phase shifter.

Download Full Size | PDF

Bidirectional pulses in the fiber loop interfere at PBS2, introducing an intensity-dependent loss which acts as a saturable absorber. The nonreciprocal phase shifter provides an additional phase bias between the clockwise (CW) and the counter-clockwise (CCW) direction and secures self-started mode-locking [29–31]. Specific intracavity optical filtering function should be established for dual-wavelength operation. In non-PM fiber lasers, this can be obtained by birefringent filtering effect. A periodic spectral transmission function is generated with the neighboring pass-band separation inversely proportional to the intra-cavity birefringence. However, this technique is hard to implement in PM fiber lasers due to the large amount of birefringence between the slow and fast axes. To solve this problem, we insert a short segment of angle-spliced PM fiber into the linear part of the cavity for generating a birefringent filter with controlled pass-band separation while the pulses still propagate along the slow axis in the majority of intracavity PM fibers. The modified PM-NALM functions as a Sagnac loop filter. The sequence of pulse propagation through the optical elements in the Sagnac loop filter is depicted in Fig. 1(b). Note that we connect two ends of the PBS1 to make it a fiber loop. To this end, one PM fiber pigtail is twisted by 90 degree. This process plays the role of an HWP in the fiber loop, as represented in Fig. 1(b). The transmission function of the Sagnac loop filter is derived as

3. Results and discussion

3.1 Switchable single wavelength mode-locking

Single wavelength mode-locking operation can be easily achieved when the pump power increases beyond the mode-locking threshold, which is typically ~400 mW. Multi-pulses operation is firstly formed in the cavity. By decreasing the pump power or increasing output coupling ratio by rotating QWP2, mode-locking can transfer to single-pulse operation. The spectrum of the output pulse train is wavelength-switchable among 1570, 1581 and 1593.6 nm. The spectra measured by an optical spectrum analyzer (YOKOGAWA, AQ6370D) are shown in Fig. 2(a). We find that each single wavelength mode-locking state tends to establish at the peaks of the Sagnac loop filter transmission spectrum. Moreover, when the output coupling ratio is increased by tuning QWP2, the mode-locked central wavelength will switch to shorter wavelength. This is because the increase of output coupling ratio leads to an increased cavity loss which can only be balanced at a shorter wavelength where EDF has larger gain.

 

Fig. 2 Output characterization of the single-wavelength mode-locked fiber laser. (a) Normalized optical spectra with switchable wavelengths. (b) RF spectra from output Port 1 at 100 Hz RBW when the laser is mode-locked at 1570 nm (magenta curve), 1581 nm (red curve) and 1594 nm (blue curve).

Download Full Size | PDF

The output parameters of the laser mode-locked at different wavelengths are summarized in Table 1. Table 1 shows that the ratio between the power of output Port 1 and output Port 2 decreases when the output spectrum is switched to longer wavelength. The reason is that longer wavelength refers to lower output coupling ratio and smaller cavity loss, leading to lower output power at Port 2. Meanwhile, the repetition rate of the output pulse train also decreases with the increase of wavelength due to the negative net cavity dispersion. The slight difference in full width at half maximum (FWHM) of optical spectrum may be owing to different pump intensities. Higher pump power corresponds to higher intracavity pulse energy and larger nonlinear effects, which result in wider optical spectrum. The radio frequency (RF) spectra of the fundamental repetition rates are measured by a radio frequency spectrum analyzer (RIGO, DSA815), as shown in Fig. 2(b). The RF spectra clearly resolve single repetition rate at 40.521789 MHz, 40.520529 MHz and 40.519767 MHz with a signal-to-noise ratio > 55 dB at 100 Hz resolution bandwidth (RBW), limited by the low optical power. These three radio frequencies match the cavity round trip time at each mode-locking wavelength. Note that the two sidebands of the RF peaks when the laser operates at 1581 nm suggests a vector soliton state [33–35], where the polarization of pulse before output may periodically evolve with round trips.

Table 1. Output parameters when the laser mode-locked at different wavelengths.

View Table | View all tables in this article

3.2 Switchable dual-wavelength mode-locking

When pump power is increased to ~400 mW and the orientations of the waveplates in nonreciprocal phase shifter and QWP2 are properly set, the laser can achieve dual-wavelength mode-locking at 1570 nm and 1581 nm simultaneously. Under such strong pump power, the laser emits multi-pulse trains mode-locked at two wavelengths accompanied with one or two CW spikes in the spectra. By decreasing the pump power to around 73 mW, the pulse trains at two wavelengths can both operate under single-pulse condition, thus resulting in dual-wavelength mode-locking. The output optical spectrum of the dual-wavelength mode-locking state is shown as black curve in Fig. 3(a). The FWHMs of two Gaussian-shaped spectra are 1.86 nm and 2.49 nm, at center wavelength of 1570 nm and 1581 nm, respectively. The two pulse trains have the same polarization states since the pulses are extracted at PBS2. The output power is 1.3 and 0.5 mW for Port 1 and Port 2, respectively. The corresponding RF spectrum of output Port 1 is also measured, as shown in Fig. 3(b). Two main peaks at 40.52167 and 40.52074 MHz with 930 Hz frequency difference present in the RF spectrum, corresponding to the fundamental repetition rates of the pulse trains at 1570 and 1581 nm, respectively. The RF spectrum of the fundamental repetition rate shows the signal-to-noise ratio of >60 dB at 100 Hz RBW, indicating the stability of the mode-locking state. The two weak sidebands coincide with the single wavelength mode-locking state at 1580 nm. The temporal walk-off between the two pulse trains is recorded in Fig. 4 by a digital oscilloscope (Agilent, Infiniium).

 

Fig. 3 (a) Optical spectra of dual-wavelength mode-locking at 1570 nm and 1581 nm within 90 min. (b) Corresponding RF spectrum at 100 Hz RBW. (c) The repetition rate difference fluctuations within 90 min.

Download Full Size | PDF

 

Fig. 4 The walk-off between the two pulse trains.

Download Full Size | PDF

The repetition rate difference between the two mode-locking pulse trains at different wavelengths originates from the group velocity dispersion of the cavity. The relationship between the wavelength difference and fundamental repetition rate difference can be theoretically calculated as $\Delta f_r=L_{fiber}D\Delta \lambda /t^2$, where $\Delta f_r$ is the difference of two fundamental cavity repetition rates, $\Delta \lambda$ is the spectral separation of the two mode-locking pulse trains, L_fiber is the length of the fiber composing the cavity with an average dispersion parameter D, and t is round-trip time of the pulse train [36]. In current dual-wavelength mode-locking fiber laser, it has$D_{PMF+EDF}=9.8ps/(nm\cdot km)$,$\Delta \lambda =11nm$,$n=1.46$, and$L_{fiber}=L_{PMF}+L_{EDF}=5.08m$. Then $\Delta f_r$is calculated as 896 Hz based on the aforementioned parameters. The slight deviation between experimental observation and calculated value may arise from the inaccuracy of dispersion parameter evaluation.

Note that this dual-wavelength mode-locking state is very stable that can sustain when tapping the fiber components in the cavity. The disturbance on the fiber has negligible influence on the dual-wavelength mode-locking operation. To investigate the long-term stability, the output spectrum is continuously recorded within 90 min. As shown in Fig. 3(a), the center wavelengths and separation of the mode-locked pulse trains maintain within 90 min, showing a superior environmental stability of this dual-wavelength mode-locking state. In addition, we examine the stability of the repetition rate difference during this period. Owing to the low output power, the beat of the output pulse train repetition rates is detected through a low noise InGaAs amplified photodetector (Thorlabs, PDA20CS-EC). After suitable voltage bias and amplifying of the RF signal, the beat frequency between the two repetition rates is recorded with a frequency counter (Agilent, 53220A) within 90 min, as shown in Fig. 3(c). The root-mean-square (rms) of the repetition rate difference fluctuation is 0.047%, which shows good environmental stability and indicates the ability to suppress the common mode environmental disturbance. Note that during the stability test, there is no extra shielding of the laser cavity nor active temperature control.

Still under a pump power of ~400 mW and keep the waveplates in the nonreciprocal phase shifter at the same position with aforementioned condition, mode-locking state can be switched to dual-wavelength operation at 1581 and 1594 nm simultaneously by slightly adjusting QWP2 to decrease the output coupling ratio and the cavity loss. The black curve in Fig. 5(a) shows the normalized optical spectrum of this dual-wavelength mode-locking state when the pump power is reduced to 70.6 mW. The FWHMs of the two Gaussian-shaped spectra are 2.6 and 3.0 nm at center wavelength of 1581 and 1594 nm, respectively. The fundamental repetition rates are 40.519682 and 40.520764 MHz, as shown in Fig. 5(b). The repetition rate difference is increased to 1082 Hz owing to the larger spectrum separation. The mode-locking state shows similar stability with the aforementioned state, which is shown by the stable spectra measured within 90 min. Figure 5(c) shows the fluctuation of repetition rate difference within 90 min, which presents 0.016% rms. In this dual-wavelength mode-locking state, the output power of Port 1 and Port 2 is 1.2 and 0.38 mW, respectively. It is worth noting that the dual-wavelength mode-locking state can be routinely switched between 1581/1594 nm and 1570/1581 nm operation just by rotating QWP2, shows that cavity loss plays an important role in the wavelength switching process.

 

Fig. 5 (a) Optical spectra of dual-wavelength mode-locking at 1581 nm and 1594 nm within 90 min. (b) Corresponding RF spectrum at 100 Hz RBW. The two main peaks correspond to pulse trains mode-locked at 1581 nm and 1594 nm, respectively. (c) The repetition rate difference fluctuations within 90 min.

Download Full Size | PDF

Furthermore, the triple-wavelength mode-locking operation is also observed in the experiment. But this mode-locking state is unstable and can be easily broken due to the strong gain competition effect. Eventually, dual-wavelength mode-locked at 1570/1581nm or 1581/1594nm is achieved.

4. Conclusion

In conclusion, we demonstrated an all-PM dual-wavelength passively mode-locked Er-fiber laser. A 0.5m length PM fiber angle-spliced to a NALM provides a simple route to obtaining a periodic filtering function in an all-PM fiber laser, enabling a robust and controllable dual-wavelength mode-locking. A ~1 kHz offset repetition rate between the two-color pulse trains is observed, resulting in a dual-wavelength dual-comb mode-locked laser. Recently, there have been rapid growth on the dual-comb molecular spectroscopic demonstrations based on a single free running laser [15,16,37,38]. The all-PM dual-wavelength dual-comb Er-fiber laser in this work is expected to pave the way for the practical and versatile dual-comb applications in the near future.

Appendix

The derivation process for Eq. (1).

The transmission function of Sagnac loop filter is derived using Jones matrices, where the optical elements’ Jones matrices are listed in Table 2.

Table 2. Jones matrices of optical elements

View Table | View all tables in this article

The Jones matrix of incident pulses can be expressed by $\overrightarrow{E_1}=\left[\begin{array}{c}0\\ 1\end{array}\right]$ since pulses incident from PBS2 have horizontal polarization state. We use $\overrightarrow{E_{cw}}$ and $\overrightarrow{E_{ccw}}$ to represent the Jones matrices of bidirectional pulses in the fiber loop. Then, $\overrightarrow{E_{cw}}$ and $\overrightarrow{E_{ccw}}$ are expressed through successively multiplying the Jones matrices of each optical element:

(2)$$\begin{array}{c}\overrightarrow{E_{cw}}=\left[\begin{array}{c}\overrightarrow{E_{cwx}}\\ \overrightarrow{E_{cwy}}\end{array}\right]=J_{PS}\left({\theta }_1-{\theta }_2\right)\times J_{PMF1}\left({\phi }_1\right)\times J_{rotate}\left(-\beta \right)\times J_{PMF2}\left({\phi }_2\right)\times J_R\times \left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]\times J_T\times J_{PMF2}\left({\phi }_2\right)\\ \times J_{rotate}\left(\beta \right)\times J_{PMF1}\left({\phi }_1\right)\times J_{PS}\left({\theta }_1+{\theta }_2\right)\times \overrightarrow{E_1}\\ \overrightarrow{E_{ccw}}=\left[\begin{array}{c}\overrightarrow{E_{ccwx}}\\ \overrightarrow{E_{ccwy}}\end{array}\right]=J_{PS}\left({\theta }_1-{\theta }_2\right)\times J_{PMF1}\left({\phi }_1\right)\times J_{rotate}\left(-\beta \right)\times J_{PMF2}\left({\phi }_2\right)\times J_T\times \left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]\times J_R\times J_{PMF2}\left({\phi }_2\right)\\ \times J_{rotate}\left(\beta \right)\times J_{PMF\text{1}}\left({\phi }_1\right)\times J_{PS}\left({\theta }_1+{\theta }_2\right)\times \overrightarrow{E_1}\end{array}$$

Here, we ignore PM fiber in the fiber loop where the pulse trains propagate along the slow axis. Therefore, the birefringence of the PM fiber has no contribution. $\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$ in Eq. (2) is caused by the polarization rotation introduced by PBS1. Finally, the transmitted field $\overrightarrow{E_1^{\text{'}}}$ and reflected field $\overrightarrow{E_2^{\text{'}}}$are obtained by the interference between $\overrightarrow{E_{cw}}$ and $\overrightarrow{E_{ccw}}$:

(3)$$\overrightarrow{E_1^{\text{'}}}=J_T\times \left(\overrightarrow{E_{cw}}+\overrightarrow{E_{ccw}}\right),\overrightarrow{E_2^{\text{'}}}=J_R\times \left(\overrightarrow{E_{cw}}+\overrightarrow{E_{ccw}}\right)$$

Then, the transmission and reflection function of the Sagnac loop filter are derived as

(4)$$\begin{array}{c}T={\left|\overrightarrow{E_1^{\text{'}}}\right|}^2/{\left|\overrightarrow{E_1}\right|}^2={\left(\sin 2{\theta }_2\sin 2\beta \cos 2{\phi }_1-\cos 2{\theta }_2\cos 2\beta \right)}^2+{\left(\sin 2{\theta }_1\sin 2\beta \sin 2{\phi }_1\right)}^2\\ R={\left|\overrightarrow{E_2^{\text{'}}}\right|}^2/{\left|\overrightarrow{E_1}\right|}^2=1-T,{\phi }_1=\pi B{L}_1/\lambda \end{array}$$

From Eq. (4), we can see that the spliced angle between PBS1 and COL is critical for the wavelength-dependent response and we take 16 degree in the aforementioned laser. The transmission function is only related to nonreciprocal phase shifter, spliced angle and length of PMF1, while PMF2 has nothing to do with the Sagnac loop filter.

Funding

National Natural Science Foundation of China (NSFC) (11527808, 61675150, 61535009); Tianjin Natural Science Foundation (18JCYBJC16900); Tianjin Research Program of Application Foundation and Advanced Technology (17JCJQJC43500).

References

1. M. E. Fermann and I. Hartl, “Ultrafast fibre lasers,” Nat. Photonics 7(11), 868–874 (2013). [CrossRef]  

2. J. Kim and Y. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8(3), 465–540 (2016). [CrossRef]  

3. W. Fu, L. G. Wright, P. Sidorenko, S. Backus, and F. W. Wise, “Several new directions for ultrafast fiber lasers [Invited],” Opt. Express 26(8), 9432–9463 (2018). [CrossRef]   [PubMed]  

4. P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012). [CrossRef]  

5. F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902 (2004). [CrossRef]   [PubMed]  

6. Y. Lan, Y. Song, M. Hu, B. Liu, L. Chai, and C. Wang, “Enhanced spectral breathing for sub-25 fs pulse generation in a Yb-fiber laser,” Opt. Lett. 38(8), 1292–1294 (2013). [CrossRef]   [PubMed]  

7. Z. Liu, S. Zhang, and F. W. Wise, “Rogue waves in a normal-dispersion fiber laser,” Opt. Lett. 40(7), 1366–1369 (2015). [CrossRef]   [PubMed]  

8. M. Margalit, M. Orenstein, and G. Eisenstein, “Synchronized two-color operation of a passively mode-locked erbium-doped fiber laser by dual injection locking,” Opt. Lett. 21(19), 1585–1587 (1996). [CrossRef]   [PubMed]  

9. H. Zhang, D. Y. Tang, X. Wu, and L. M. Zhao, “Multi-wavelength dissipative soliton operation of an erbium-doped fiber laser,” Opt. Express 17(15), 12692–12697 (2009). [CrossRef]   [PubMed]  

10. X. Zhao, Z. Zheng, L. Liu, Y. Liu, Y. Jiang, X. Yang, and J. Zhu, “Switchable, dual-wavelength passively mode-locked ultrafast fiber laser based on a single-wall carbon nanotube modelocker and intracavity loss tuning,” Opt. Express 19(2), 1168–1173 (2011). [CrossRef]   [PubMed]  

11. L. Yun, X. Liu, and D. Mao, “Observation of dual-wavelength dissipative solitons in a figure-eight erbium-doped fiber laser,” Opt. Express 20(19), 20992–20997 (2012). [CrossRef]   [PubMed]  

12. S. Schiller, “Spectrometry with frequency combs,” Opt. Lett. 27(9), 766–768 (2002). [CrossRef]   [PubMed]  

13. I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414–426 (2016). [CrossRef]  

14. I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009). [CrossRef]  

15. X. Zhao, G. Hu, B. Zhao, C. Li, Y. Pan, Y. Liu, T. Yasui, and Z. Zheng, “Picometer-resolution dual-comb spectroscopy with a free-running fiber laser,” Opt. Express 24(19), 21833–21845 (2016). [CrossRef]   [PubMed]  

16. R. Liao, Y. Song, W. Liu, H. Shi, L. Chai, and M. Hu, “Dual-comb spectroscopy with a single free-running thulium-doped fiber laser,” Opt. Express 26(8), 11046–11054 (2018). [CrossRef]   [PubMed]  

17. H. Shi, Y. Song, T. Li, C. Wang, X. Zhao, Z. Zheng, and M. Hu, “Timing jitter of the dual-comb mode-locked laser: a quantum origin and the ultimate effect on high speed time- and frequency- domain metrology,” IEEE J. Sel. Top. Quantum Electron. 24(5), 1102610 (2018). [CrossRef]  

18. B. Lin, X. Zhao, M. He, Y. Pan, J. Chen, S. Cao, Y. Lin, Q. Wang, Z. Zheng, and Z. Fang, “Dual-comb absolute distance measurement based on a dual-wavelength passively mode-locked laser,” IEEE Photonics J. 9(6), 7106508 (2017). [CrossRef]  

19. X. Liu, D. Han, Z. Sun, C. Zeng, H. Lu, D. Mao, Y. Cui, and F. Wang, “Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes,” Sci. Rep. 3(1), 2718 (2013). [CrossRef]   [PubMed]  

20. A. P. Luo, Z. C. Luo, and W. C. Xu, “Switchable dual-wavelength passively mode-locked fiber ring laser using SESAM and cascaded fiber Bragg gratings,” Laser Phys. 21(2), 395–398 (2011). [CrossRef]  

21. L. Yun and D. Han, “Evolution of dual-wavelength fiber laser from continuous wave to soliton pulses,” Opt. Commun. 285(24), 5406–5409 (2012). [CrossRef]  

22. G. Hu, Y. Pan, X. Zhao, S. Yin, M. Zhang, and Z. Zheng, “Asynchronous and synchronous dual-wavelength pulse generation in a passively mode-locked fiber laser with a mode-locker,” Opt. Lett. 42(23), 4942–4945 (2017). [CrossRef]   [PubMed]  

23. Z. Luo, A. Luo, W. Xu, H. Yin, J. Liu, Q. Ye, and Z. Fang, “Tunable multiwavelength passively mode-Locked fiber ring laser using intracavity birefringence-induced comb filter,” IEEE Photonics J. 2(4), 571–577 (2010). [CrossRef]  

24. A. A. Latiff, N. A. Kadir, E. I. Ismail, H. Shamsuddin, H. Ahmad, and S. W. Harun, “All-fiber dual-wavelength Q-switched and mode-locked EDFL by SMF-THDF-SMF structure as a saturable absorber,” Opt. Commun. 389, 29–34 (2017). [CrossRef]  

25. Z. Yan, X. Li, Y. Tang, P. P. Shum, X. Yu, Y. Zhang, and Q. J. Wang, “Tunable and switchable dual-wavelength Tm-doped mode-locked fiber laser by nonlinear polarization evolution,” Opt. Express 23(4), 4369–4376 (2015). [CrossRef]   [PubMed]  

26. Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, “Ultrafast spectral dynamics of dual-color-soliton intracavity collision in a mode-locked fiber laser,” Appl. Phys. Lett. 112(8), 081104 (2018). [CrossRef]  

27. Y. Nakajima, Y. Hata, and K. Minoshima, “All-polarization-maintaining dual-comb fiber laser with nonlinear amplifying loop mirror,” in CLEO 2018, OSA Technical Digest (Optical Society of America, 2018), paper STu4K.4.

28. R. Wang, X. Zhao, W. Bai, J. Chen, Y. Pan, and Z. Zheng, “Polarization-maintaining, dual-wavelength, dual-comb mode-locked fiber laser,” in CLEO 2018, OSA Technical Digest (Optical Society of America, 2018), paper JTh2A.139.

29. W. Hänsel, H. Hoogland, M. Giunta, S. Schmid, T. Steinmetz, R. Doubek, P. Mayer, S. Dobner, C. Cleff, M. Fischer, and R. Holzwarth, “All polarization-maintaining fiber laser architecture for robust femtosecond pulse generation,” Appl. Phys. B 123(1), 41 (2017). [CrossRef]  

30. T. Jiang, Y. Cui, P. Lu, C. Li, A. Wang, and Z. Zhang, “All PM fiber laser mode locked with a compact phase biased amplifier loop mirror,” IEEE Photonics Technol. Lett. 28(16), 1786–1789 (2016). [CrossRef]  

31. N. Kuse, J. Jiang, C. C. Lee, T. R. Schibli, and M. E. Fermann, “All polarization-maintaining Er fiber-based optical frequency combs with nonlinear amplifying loop mirror,” Opt. Express 24(3), 3095–3102 (2016). [CrossRef]   [PubMed]  

32. M. Lezius, T. Wilken, C. Deutsch, M. Giunta, O. Mandel, A. Thaller, V. Schkolnik, M. Schiemangk, A. Dinkelaker, A. Kohfeldt, A. Wicht, M. Krutzik, A. Peters, O. Hellmig, H. Duncker, K. Sengstock, P. Windpassinger, K. Lampmann, T. Hülsing, T. W. Hänsch, and R. Holzwarth, “Space-borne frequency comb metrology,” Optica 3(12), 1381–1387 (2016). [CrossRef]  

33. D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett. 101(15), 153904 (2008). [CrossRef]   [PubMed]  

34. A. E. Akosman and M. Y. Sander, “Dual comb generation from a mode-locked fiber laser with orthogonally polarized interlaced pulses,” Opt. Express 25(16), 18592–18602 (2017). [CrossRef]   [PubMed]  

35. A. E. Akosman, J. Zeng, P. D. Samolis, and M. Y. Sander, “Polarization rotation dynamics in harmonically mode-locked vector soliton fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1101107 (2017).

36. X. Yao, “Generation of bidirectional stretched pulses in a nanotube-mode-locked fiber laser,” Appl. Opt. 53(1), 27–31 (2014). [CrossRef]   [PubMed]  

37. T. Ideguchi, T. Nakamura, Y. Kobayashi, and K. Goda, “Kerr-lens mode-locked bidirectional dual-comb ring laser for broadband dual-comb spectroscopy,” Optica 3(7), 748–753 (2016). [CrossRef]  

38. S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164–1168 (2017). [CrossRef]   [PubMed]