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Abstract
We introduce a calcium carbonate birefringent crystal into an Er-fiber laser mode-locked by a saturable absorber, where dual-comb ultrashort pulses with orthogonal polarization have been obtained. The two ultrashort pulse trains from the laser exhibit polarization contrast ratios of 30 dB and 20 dB, indicating that the dual-comb mode-locking is due to the polarization-multiplexing mechanism. The dual-comb ultrashort pulses have central wavelengths of 1564.41 nm and 1564.51 nm, and pulse durations of 825 fs and 805 fs respectively. The optical spectra and pulse durations of the asynchronous ultrashort pulses are nearly identical, so that the output of the laser could be directly used for dual-comb applications. Besides, the repetition-rate difference of the two mode-locked pulses is 673 Hz, while its drift is only 0.093 Hz within 2 hours’ time. The low drift of the repetition-rate difference manifests the single-cavity dual-comb Er-fiber laser has a high stability and high common-mode noise suppression. At last, we have tested the dual-comb fiber laser in a ranging experiment, where clear interferogram signal can be observed. The experimental results prove that this single-cavity dual-comb Er-fiber laser based on the birefringent crystal and saturable absorber can be a potential source for spectroscopy, optical imaging, absolute distance measurement and other dual-comb applications.
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1. Introduction
Optical frequency combs which have series of equally spaced teeth in the frequency domain have greatly improved the accuracy of optical measurements and brought a technological revolution to the current metrology science [1–3]. In recent years, the emerging dual-comb technology which uses two sets of optical frequency combs with slightly different comb spacing, has shown its advantages of ultra-high resolution, high sensitivity, and high sampling rate for precision measurements. It is deemed as a remarkable advancement in the fields of spectroscopy [4,5], optical imaging [6–8], absolute distance measurement [9–11] and ultra-stable optical clock generation [12]. At present, there are several ways to generate dual-comb light sources, such as tight frequency-locking the comb teeth of two independently mode-locked lasers [13,14], electro-optic modulation [15,16], or Kerr-optical frequency comb generation in micro-ring resonator [17,18]. However, the above-mentioned methods may suffer from complex frequency-locking system, small number of comb teeth, difficult manufacturing process, poor stability and etc.
Mode-locked single-cavity dual-comb lasers can produce two asynchronous ultrashort pulses with slightly different repetition rates, high common-mode noise suppression and high relative frequency stability in one oscillator. Besides, they don’t need any active control such as frequency-locking of the laser cavities, which significantly reduces the complexity and cost of the dual-comb laser system. The implementation schemes for single-cavity dual-comb lasers can be mainly divided into three categories: wavelength-multiplexing, bidirectional-multiplexing and polarization-multiplexing. For wavelength-multiplexing, mechanical filters [19] and Lyot filters [20,21] are usually introduced in the oscillator to obtain dual-wavelength mode-locking. Such wavelength-multiplexed single-cavity laser sources have demonstrated their possibility as light sources for dual-comb applications [22]. Whereas, the output spectra of the dual-comb ultrashort pulses from these wavelength-multiplexed lasers are always separated, so it is always needed for the spectra to be nonlinearly broadened and overlapped before the laser being used for dual-comb measurements. To a certain extent, this increases the overall complexity of the system. Bidirectional-multiplexing is another way to generate dual-comb ultrashort pulses by counter-propagating two lasers in one oscillator. In these lasers, two asynchronous ultrashort pulses with nearly the same spectrum can be realized [23,24]. The bidirectional single-cavity lasers have inherently high common-mode noise suppression and coherence characteristics, and they have been successfully applied in gas absorption measurements [25]. However, the repetition-rate difference from such bidirectionally mode-locked lasers is always constrained, which may limit their applications when high sampling rate is required. Polarization-multiplexing makes use of the birefringent effect between polarizations to generate asynchronously mode-locked pulses. For example, by squeezing the single-mode fiber with polarization controllers, a polarization-multiplexed dual-comb Tm-Ho fiber lasers have been obtained [26]. Besides, by introducing a section of polarization maintaining fiber, polarization-multiplexed dual-comb ultrashort pulses have been generated in Er-fiber lasers [27]. Recently, it is reported that dual-comb ultrashort pulses can be generated by simply inserting birefringent crystals into mode-locked laser cavities. The birefringent crystal will split a laser into two orthogonal beams, so these two beams can share the cavity mirrors and travel with different optical paths in the cavity. Based on this method, solid-state dual-comb Nd:YAG and Yb:CaF2 lasers have been demonstrated [28–30]. As the solid-state lasers have comparably long free-space cavities, it is easier to spatially separate the two orthogonal beams by tunning the cavity mirrors to avoid polarization crosstalks. However, it is not the case for fiber lasers. Until now, there are few works that have been reported about dual-comb fiber lasers by this method.
In this paper, we have for the first time demonstrated a dual-comb Er-fiber laser based on birefringent crystal and saturable absorber mirror. A 1 mm thick calcium carbonate birefringent crystal is used in the laser, so that different optical paths can be introduced for the two orthogonal laser beams. In addition, a focusing collimator is used in the cavity so as to ensure the two beams can be separated effectively in space and interact independently with the saturable absorber. By properly setting the pump power and polarization controller in the cavity, dual-comb ultrashort pulses are generated from the polarization-multiplexed fiber laser. High polarization contrast ratios are observed for both of the two beams, verifying that the dual-comb mode-locking is indeed due to the polarization-multiplexing mechanism. The dual-comb ultrashort pulses have central wavelengths of 1564.41 nm and 1564.51 nm, and pulse durations of 825 fs and 805 fs respectively. The repetition-rate difference of the two asynchronous pulses is 673 Hz, while its drift has a root-mean-square (RMS) value of 0.093 Hz within 2 hours’ time. The low drift of the repetition-rate difference manifests the single-cavity dual-comb Er-fiber laser has a high stability and a high common-mode noise suppression. Finally, we have tested the laser system in a dual-comb ranging experiment, where clear interferogram signal have been obtained.
2. Experimental setup
The experimental setup of the dual-comb mode-locked Er-fiber oscillator based on birefringent crystal and saturable absorber is schematically shown in Fig. 1. The dual-comb fiber laser is comprised of a ring part and a linear part. The ring part has 3.1 m SMF-28e fiber, 1 m Hi1060 fiber and 0.8 m active Er-fiber (nLight, EDF80-4/125). The active Er-fiber is pumped by a 980 nm laser diode through a wavelength-division multiplexer (WDM). To achieve dual-comb mode-locking, an in-line polarization controller is installed to control the polarization evolution in the oscillator. A 20% optical coupler is used to couple out the laser from the cavity. The ring and the linear parts are connected by an optical circulator. The circulator also acts as an isolator to ensure uni-directional running of the laser. The port 2 of the circulator in the linear part is connected with a fiber focusing collimator which is used to focus the laser on a saturable absorber. The beam waist diameter of the focusing collimator is around 33 µm. The absorber used in the experiment is a semiconductor saturable absorber mirror (SESAM) with a relaxation time of 2 ps, a modulation depth of 19% and a non-saturable absorption of 14%. In fact, other kinds of saturable absorbers (such as graphene, carbon nanotube, molybdenum disulfide and so forth) are applicable for the experiment. We choose the SESAM because it is commercial, stable and have been widely used in industrials.
Fig. 1. Schematic setup of the polarization multiplexed dual-comb fiber laser with birefringent crystal and SESAM; WDM: Wavelength-division multiplexer; PC: Polarization controller; OC: Optical coupler; Col: Collimator; EDF: Er-fiber.
To achieve polarization-multiplexed dual-comb mode-locking, a 1 mm thick birefringent crystal is inserted between the focusing collimator and the SESAM. Birefringent materials have different refractive indices (${n_o}\; $and ${n_e}$) for the ordinary axis and extraordinary axis. When laser beams are incident on a birefringent crystal, the ordinary beam (indicated by the vertically polarized beam in Fig. 1) will pass through the crystal in a straight line and the extraordinary beam (indicated by the horizontally polarized beam in Fig. 1) will be deflected under a walk-off angle of ρ. In this way, with the introduction of the birefringent crystal, the two orthogonal beams will travel different optical distances which can be calculated by the crystal’s thickness and walk-off angle of ρ [31]. The theoretical relationship of the beam-path difference with the crystal thickness can be calculated by$\; D = 2{L_0}({{n_o} - {n_e}/\cos (\mathrm{\rho } )} )$ and the transverse separation of the two beams can be expressed by $T = {L_0} \cdot \tan (\mathrm{\rho } )$, where ${L_0}$ is the thickness of the crystal. The focusing collimator has much smaller spot diameter at its beam waist. Then, due to the walk-off effect of the birefringent crystal, the two orthogonal beams can be focused separately onto the saturable absorber. Hence, the polarization crosstalk can be avoided which will deteriorate the dual-comb mode-locking. In addition, the focusing collimator can also make the laser relatively compact, as only 9 mm free space path is introduced in the cavity. The birefringent material we used in this experiment is the calcium carbonate, which has a relatively high refractive index difference (${n_o}$=1.63368 and ${n_e}$=1.47722 at the wavelength of 1550 nm) and an anti-reflective bandwidth from 1500 nm to 1600 nm. The cutting angle with respect to the crystal c-axis is 45° and the corresponding walk off angle (ρ) is 5.73°. When 1 mm thick crystal is used, the optical paths’ difference and transverse separation of the two orthogonal beams are 300 µm and 100 µm respectively, which are suitable for stable dual-comb mode-locking.
3. Dual-comb laser characterization
To characterize the performance of the dual-comb Er-fiber laser, the output power of the oscillator is measured by a power meter (Thorlabs, PM100D and S144C). The mode-locked pulses are detected by a home-made high-speed InGaAs photodetector and the detected signal is simultaneously monitored by a digital oscilloscope (Keysight, DSOX2024A) with a bandwidth of 500 MHz and a radio frequency (RF) analyzer (R & S, FSV40). When the pump power of the laser is 72 mW and the intra-cavity polarization state is properly set, asynchronously mode-locked pulse trains can be clearly observed on the oscilloscope, which are shown in Fig. 2(a). In this situation, the output power of the oscillator is 0.55 mW. In the meanwhile, two repetition-rate signals can be observed around 32.5 MHz from the RF spectrum, and the corresponding repetition-rate difference is 673 Hz, as shown in Fig. 2(b). Both of the repetition rates have high signal-to-noise-ratios (SNRs) over 70 dB, indicating that the asynchronously mode-locked pulses are stable. For dual-comb applications, it is necessary to further sperate the two pulses. Theoretically, the asynchronously mode-locked pulses are orthogonal with each other, so the output pulses can be separated into two beams by an external polarizing-beam-splitter (PBS) and be characterized independently. In order to get a high SNR for each pulse train, a polarization controller is used before the PBS. After separation, the output power is 0.28 mW for the extraordinary beam, while it is 0.27 mW for the ordinary beam. The corresponding pulse trains for the two beams are shown in Fig. 2(c). From Fig. 2(d), it can be seen that the high repetition-rate RF signal (the extraordinary beam) and low repetition-rate RF signal (the ordinary beam) can obtain SNRs of 30 dB and 20 dB, which are sufficient for dual-comb applications. The high SNRs for the two pulses have also verified that the dual-comb mode-locking is indeed derived from the polarization-multiplexing. On the other hand, when the birefringent crystal is removed from the laser, dual-comb mode-locking cannot be obtained no matter how we change the cavity’s parameters.
Fig. 2. (a) Pulse train of the dual-comb mode-locked laser; (b) The RF spectrum of the dual-comb ultrashort pulses; (c) Pulse trains and (d) RF spectra of the separated pulses.
Furtherly, the optical spectra of the separated mode-locked pulses are measured by an optical spectrum analyzer (Anritsu, MS9740A), which are illustrated in Fig. 3(a) and (b). The central wavelengths of the two mode-locked pulses are 1564.41 nm and 1564.51 nm, and the corresponding full-width-of-half-maximum (FWHM) bandwidths are 3.2 nm and 3.4 nm respectively. The net dispersion of the cavity is amount to -0.0517 ps2. Therefore, small Kelly-sidebands can be observed for both of the two pulses as they are running in the soliton mode-locking region. In the meanwhile, the autocorrelation traces of the separated pulses are measured by a commercial autocorrelator (Femtochrome, FR-103XL). If a sech2 pulse profile is assumed, the corresponding pulse durations are 825 fs and 805 fs respectively, as shown in Fig. 3(c) and (d). The optical spectra and pulse durations of the asynchronous ultrashort pulses are nearly identical so that the output of the laser could be directly used for dual-comb applications.
Fig. 3. Optical spectra of the (a) extraordinary and (b) ordinary beams; Autocorrelation traces of the pulses at central wavelength of (c) 1564.41 nm and (d) 1564.51 nm.
With respect to a dual-comb fiber laser system, the long-term stability is another important issue when it is running in a single-cavity configuration. In order to characterize this, we monitor the two repetition rates of the asynchronously mode-locked ultrashort pulses and their difference in 2 hours. In fact, the laser can maintain dual-comb mode-locking for several days without intense perturbations. Usually, the repetition rates of the two pulses can be recorded by two digital counters referenced to a stable clock source. Whereas in this experiment, we manually record each of the repetition rate by the RF analyzer and then subtract them to obtain their difference. The resolution bandwidth and frequency measurement accuracy of the RF analyzer are 1 Hz according to the equipment’s specification. As illustrated in Fig. 4, although the individual repetition rate (frep1, frep2) of the dual-comb ultrashort pulses has a large drift of 173 Hz within the recorded period, the drift of the repetition-rate difference (Δfrep) remains comparably stable with a RMS value of 0.093 Hz (Allan deviation value is 0.006 Hz with an averaging time of 1 s). It is observed that there are some random bursts in the curve of the Δfrep. It is thought that they are caused by the environmental vibrations and temperature changes, which can be improved by covering the whole laser system with isolated materials. As these bursts happen rarely and have relatively low amplitude, they should have little impact on dual-comb measurements. It is worth noting that the Δfrep of the dual-comb mode-locked ultrashort pulses can also be adjusted within the range from 520 Hz to 740 Hz by finely tuning the polarization controller in the cavity, which provides a small degree of freedom for dual-comb measurements. The tuning possibility is because the repetition-rate difference value is associated not only with the beam-path difference introduced by the crystal but also in some extent with the fiber birefringence in the cavity [26,27]. This is also the reason why the experimental value of the repetition-rate difference is different from the theoretical value $\Delta {f_{rep}} = c\cdot \frac{D}{{4{n^2}{L^2}}}\; $(1 kHz) calculated only through the beam-path difference. In this formula, D is the beam-path difference and L is the length of the fiber in the cavity.
4. Dual-comb ranging with the laser
In order to verify the coherence of the asynchronously mode-locked ultrashort pulses, a proof-of-principle ranging experiment is carried out by using the single-cavity dual-comb fiber laser. The schematic setup of the dual-comb ranging experiment is shown in Fig. 5, which is similar to Ref. [32,33]. The output from the dual-comb fiber laser is coupled to the ranging setup by a fiber collimator. At first, the two asynchronous pulses are separated after passing through PBS1. One beam is used as the signal for ranging, which will be then divided by PBS2 into the reference pulse train and target pulse train. On the other hand, the other beam is used as the local pulse train. The reference and target signal trains will reflect back and combine with the local pulse train by a beam splitter (BS). Subsequently, the reference pulse train will interfere with the local pulse train and the interference signal is detected by one channel of a balanced photodetector (Thorlabs, PDB450C). On the other hand, the interference signal between the target train and local pulse train is detected by the other channel of the balanced photodetector. Normally, a band-pass filter needs to be involved in dual-comb ranging experiments. However, there is no need to introduce such one in our setup, because the spectra of signal and local pulse trains are almost the same and their bandwidths have satisfied the Nyquist sampling bandwidth requirement [34]. The typical output heterodyne interferogram (IGM) recorded by the digital oscilloscope is shown in Fig. 6(a), where Ir is the interference signal between the reference and local pulses and It is the interference signal between target and local pulses. The laser can maintain dual-comb mode-locking for several days, during which the dual-comb IGMs can be clearly observed as well. It is observed that there are several bursts in the IGM, which is mainly due to the noise of the photodetector. As the amplitudes of the bursts are comparably smaller than the main interference signal, they can be easily ignored in the data processing procedure when an appropriate sampling threshold is set. A zoomed-in signal of Ir is illustrated in Fig. 6(b), where clear interferometric fringes can be observed. The period of the interference signal (Ir or It) is 1.48 ms, which matches well with the repetition-rate difference of the dual-comb ultrashort pulses. The time delay between Ir and It is 0.47 ms, which also matches with the target distance of 1.46 m. This ranging experimental result has testified that this single-cavity dual-comb fiber laser based on birefringent crystal and saturable absorber can be a potential light source for other dual-comb applications.
Fig. 5. Setup of dual-comb ranging experiment. DCL: Dual-comb laser; PBS1-3: Polarization-beam-splitters; BS: Beam splitter; HWP: Half-wave plate; QWP: Quarter-wave plate; M1-3: Gold mirrors; Mtar: Target mirror; Mref: Reference mirror; BPD: Balanced photodetector.
Fig. 6. (a) Typical interferogram of a dual-comb ranging signal. (b) Zoomed-in figure of the interference signal Ir.
5. Conclusion
In conclusion, we have demonstrated a polarization-multiplexed, single-cavity dual-comb Er-fiber laser based on birefringent crystal and saturable absorber. A 1 mm thick calcium carbonate birefringent crystal is used in the laser, which introduces different optical paths for the two orthogonal beams. In the meanwhile, the two beams can interact independently with the saturable absorber, which is beneficial for dual-comb mode-locking. The repetition rate of the dual-comb mode-locked pulses from the fiber laser is at 32.5 MHz with a difference of 673 Hz. As very compact polarization multiplexing scheme (free-space length of 9 mm) is used in the setup, the repetition rate of the fiber laser is possible to be scaled up to hundreds of MHz in the future. Although each repetition rate of the dual-comb ultrashort pulses exhibits a relatively high fluctuation, their difference has maintained a low drift RMS value of 0.093 Hz within 2 hours, indicating the single-cavity dual-comb fiber laser has a high stability and high common-mode-noise suppression. Besides, it is found that the asynchronous ultrashort pulses from the laser have a high polarization contrast ratio, verifying that polarization-multiplexing is the main mechanism for dual-comb mode-locking. On the other hand, the spectra and pulse durations of the asynchronous ultrashort pulses from the laser are nearly identical, so that the output of the laser can be directly used for dual-comb applications. To verify this, a dual-comb ranging experiment has been carried out by using the laser system, where clear interferogram signal has been obtained. It is proved that this single-cavity dual-comb Er-fiber laser based on the birefringent crystal and the saturable absorber can be a potential light source for spectroscopy, optical imaging, and other dual-comb applications.
Funding
National Natural Science Foundation of China (61805116, 62175016); Natural Science Foundation of Jiangsu Province (BK20192006); Fundamental Research Funds for the Central Universities (021014380109).
Disclosures
The authors declare that there are no conflicts of interest to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. S. W. Kim, “Combs rule,” Nat. Photonics 3(6), 313–314 (2009). [CrossRef]
2. T. Fortier and E. Baumann, “20 years of developments in optical frequency comb technology and applications,” Commun. Phys. 2(1), 153 (2019). [CrossRef]
3. A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012). [CrossRef]
4. I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414 (2016). [CrossRef]
5. F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29(13), 1542–1544 (2004). [CrossRef]
6. E. Hase, T. Minamikawa, T. Mizuno, S. Miyamoto, R. Ichikawa, Y. Hsieh, K. Shibuya, K. Sato, Y. Nakajima, A. Asahara, K. Minoshima, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Scan-less confocal phase imaging based on dual-comb microscopy,” Optica 5(5), 634–643 (2018). [CrossRef]
7. C. Wang, Z. Deng, C. Gu, Y. Liu, D. Luo, Z. Zhu, W. Li, and H. Zeng, “Line-scan spectrum-encoded imaging by dual-comb interferometry,” Opt. Lett. 43(7), 1606–1609 (2018). [CrossRef]
8. T. Mizuno, Y. Nakajima, Y. Hata, T. Tsuda, A. Asahara, T. Kato, T. Minamikawa, T. Yasui, and K. Minoshima, “Computationally image-corrected dual-comb microscopy with a free-running single-cavity dual-comb fiber laser,” Opt. Express 29(4), 5018–5032 (2021). [CrossRef]
9. J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, and Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013). [CrossRef]
10. Z. Zhu, G. Xu, K. Ni, Q. Zhou, and G. Wu, “Synthetic-wavelength-based dual-comb interferometry for fast and precise absolute distance measurement,” Opt. Express 26(5), 5747–5757 (2018). [CrossRef]
11. T.-A. Liu, N. R. Newbury, and I. Coddington, “Sub-micron absolute distance measurements in sub-millisecond times with dual free-running femtosecond Er fiber-lasers,” Opt. Express 19(19), 18501–18509 (2011). [CrossRef]
12. M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017). [CrossRef]
13. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100(1), 013902 (2008). [CrossRef]
14. A. V. Muraviev, V. O. Smolski, Z. E. Loparo, and K. L. Vodopyanov, “Massively parallel sensing of trace molecules and their isotopologues with broadband subharmonic mid-infrared frequency combs,” Nat. Photonics 12(4), 209–214 (2018). [CrossRef]
15. G. Millot, S. Pitois, M. Yan, T. Hovhannisyan, A. Bendahmane, T. W. Hänsch, and N. Picqué, “Frequency-agile dual-comb spectroscopy,” Nat. Photonics 10(1), 27–30 (2016). [CrossRef]
16. L. Deniel, E. Weckenmann, D. Galacho, C. A-Ramos, F. Boeuf, L. Vivien, and D. M-Morini, “Frequency-tuning dual-comb spectroscopy using silicon Mach-Zehnder modulators,” Opt. Express 28(8), 10888–10898 (2020). [CrossRef]
17. M.-G. Suh, Q. F-Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016). [CrossRef]
18. E. Lucas, G. Lihachev, R. Bouchand, N. G. Pavlov, A. S. Raja, M. Karpov, M. L. Gorodetsky, and T. J. Kippenberg, “Spatial multiplexing of soliton microcombs,” Nat. Photonics 12(11), 699–705 (2018). [CrossRef]
19. J. Fellinger, G. Winkler, A. S. Mayer, L. R. Steidle, and O. H. Heckl, “Tunable dual-color operation of Yb:fiber laser via mechanical spectral subdivision,” Opt. Express 27(4), 5478–5486 (2019). [CrossRef]
20. X. Gu, H. Chen, Y. Li, X. Cao, C. Wang, and Y. Liu, “Ultrashort pulse duration and broadband dual-comb laser system based on a free-running passively mode-locked Er-fiber oscillator,” Laser Phys. Lett. 18(12), 125101 (2021). [CrossRef]
21. X. Luo, T. H. Tuan, T. S. Saini, H. P. T. Nguyen, T. Suzuki, and Y. Ohishi, “Tunable and switchable all-fiber dual-wavelength mode locked laser based on Lyot filtering effect,” Opt. Express 27(10), 14635–14647 (2019). [CrossRef]
22. 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]
23. K. Kieu and M. Mansuripur, “All-fiber bidirectional passively mode-locked ring laser,” Opt. Lett. 33(1), 64–66 (2008). [CrossRef]
24. Y. Nakjima, Y. Hata, and K. Minoshima, “High-coherence ultra-broadband bidirectional dual-comb fiber laser,” Opt. Express 27(5), 5931–5944 (2019). [CrossRef]
25. S. Mehravar, R. A. Norwood, N. Peyghambarian, and K. Kieu, “Real-time dual-comb spectroscopy with a free-running bidirectionally mode-locked fiber laser,” Appl. Phys. Lett. 108(23), 231104 (2016). [CrossRef]
26. 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]
27. X. Zhao, T. Li, Y. Liu, Q. Li, and Z. Zheng, “Polarization-multiplexed, dual-comb all-fiber mode-locked laser,” Photonics Res. 6(9), 853–857 (2018). [CrossRef]
28. S. M. Link, A. Klenner, and U. Keller, “Dual-comb modelocked lasers: semiconductor saturable absorber mirror decouples noise stabilization,” Opt. Express 24(3), 1889–1902 (2016). [CrossRef]
29. B. Willenberg, J. Pupeikis, L. M. Krüger, F. Koch, C. R. Phillips, and U. Keller, “Femtosecond dual-comb Yb: CaF2 laser from a single free-running polarization-multiplexed cavity for optical sampling applications,” Opt. Express 28(20), 30275–30288 (2020). [CrossRef]
30. J. Pupeikis, B. Willenberg, F. Bruno, M. Hettich, A. N-Lapping, M. Golling, C. P. Bauer, S. L. Camenzind, A. Benayad, P. Camy, B. Audoin, C. R. Phillips, and U. Keller, “Picosecond ultrasonics with a free-running dual-comb laser,” Opt. Express 29(22), 35735–35754 (2021). [CrossRef]
31. S. M. Link, A. Klenner, M. Mangold, C. A. Zaugg, M. Golling, B. W. Tilma, and U. Keller, “Dual-comb modelocked laser,” Opt. Express 23(5), 5521–5531 (2015). [CrossRef]
32. G. Wu, S. Xiong, K. Ni, Z. Zhu, and Q. Zhou, “Parameter optimization of a dual-comb ranging system by using a numerical simulation method,” Opt. Express 23(25), 32044–32053 (2015). [CrossRef]
33. R. Jiang, S. Zhou, and G. Wu, “Aliasing-free dual-comb ranging system based on free-running fiber lasers,” Opt. Express 29(21), 33527–33535 (2021). [CrossRef]
34. 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]
